# Realizations of Rigid Graphs

### Project Description

1.1.2019-31.10.2021 hosted by RICAM.

### Project Lead

### Project Duration

01/11/2021 - 31/12/2022## Partners

### The Austrian Science Fund (FWF)

## Publications

### 2024

[AUTHOR]

### Proximity-based matching with arbitrary T-norms

#### Maximilian Donnermair

RISC, Johannes Kepler University Linz. Bachelor Thesis. 2024. [pdf]@

author = {Maximilian Donnermair},

title = {{Proximity-based matching with arbitrary T-norms}},

language = {english},

year = {2024},

translation = {0},

institution = {RISC, Johannes Kepler University Linz},

length = {38}

}

**misc**{RISC7061,author = {Maximilian Donnermair},

title = {{Proximity-based matching with arbitrary T-norms}},

language = {english},

year = {2024},

translation = {0},

institution = {RISC, Johannes Kepler University Linz},

length = {38}

}

[Cerna]

### Equational Anti-unification over Absorption Theories

#### Mauricio Ayala-Rincón, David M. Cerna, Andres Felipe Gonzalez Barragan, Temur Kutsia

In: Automated Reasoning - 12th International Joint Conference, IJCAR 2024, Nancy, France, July 3-6, 2024, Proceedings, Christoph Benzmüller, Marijn J. H. Heule, Renate A. Schmidt (ed.), Lecture Notes in Artificial Intelligence 14740, pp. 317-337. 2024. Springer, ISBN 978-3-031-63500-7. [doi]@

author = {Mauricio Ayala-Rincón and David M. Cerna and Andres Felipe Gonzalez Barragan and Temur Kutsia},

title = {{Equational Anti-unification over Absorption Theories}},

booktitle = {{Automated Reasoning - 12th International Joint Conference, IJCAR 2024, Nancy, France, July 3-6, 2024, Proceedings}},

language = {english},

series = {Lecture Notes in Artificial Intelligence},

volume = {14740},

pages = {317--337},

publisher = {Springer},

isbn_issn = {ISBN 978-3-031-63500-7},

year = {2024},

editor = {Christoph Benzmüller and Marijn J. H. Heule and Renate A. Schmidt},

refereed = {yes},

length = {21},

url = {https://doi.org/10.1007/978-3-031-63501-4_17}

}

**inproceedings**{RISC7064,author = {Mauricio Ayala-Rincón and David M. Cerna and Andres Felipe Gonzalez Barragan and Temur Kutsia},

title = {{Equational Anti-unification over Absorption Theories}},

booktitle = {{Automated Reasoning - 12th International Joint Conference, IJCAR 2024, Nancy, France, July 3-6, 2024, Proceedings}},

language = {english},

series = {Lecture Notes in Artificial Intelligence},

volume = {14740},

pages = {317--337},

publisher = {Springer},

isbn_issn = {ISBN 978-3-031-63500-7},

year = {2024},

editor = {Christoph Benzmüller and Marijn J. H. Heule and Renate A. Schmidt},

refereed = {yes},

length = {21},

url = {https://doi.org/10.1007/978-3-031-63501-4_17}

}

[de Freitas]

### The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$

#### J. Ablinger, A. Behring, J. Bluemlein, A. De Freitas, A. von Manteuffel, C. Schneider, K. Schoenwald

Nuclear Physics B 999(116427), pp. 1-42. 2024. ISSN 0550-3213. arXiv:2311.00644 [hep-ph]. [doi]@

author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},

title = {{The first--order factorizable contributions to the three--loop massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$}},

language = {english},

abstract = {The unpolarized and polarized massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$contain first--order factorizable and non--first--order factorizable contributions in the determining difference or differential equations of their master integrals. We compute their first--order factorizable contributions in the single heavy mass case for all contributing Feynman diagrams. Moreover, we present the complete color--$zeta$ factors for the cases in which also non--first--order factorizable contributions emerge in the master integrals, but cancel in the final result as found by using the method of arbitrary high Mellin moments. Individual contributions depend also on generalized harmonic sums and on nested finite binomial and inverse binomial sums in Mellin $N$--space, and correspondingly, on Kummer--Poincar'e and square--root valued alphabets in Bjorken--$x$ space. We present a complete discussion of the possibilities of solving the present problem in $N$--space analytically and we also discuss the limitations in the present case to analytically continue the given $N$--space expressions to $N in mathbb{C}$ by strict methods. The representation through generating functions allows a well synchronized representation of the first--order factorizable results over a 17--letter alphabet. We finally obtain representations in terms of iterated integrals over the corresponding alphabet in $x$--space, also containing up to weight {sf w = 5} special constants, which can be rationalized to Kummer--Poincar'e iterated integrals at special arguments. The analytic $x$--space representation requires separate analyses for the intervals $x in [0,1/4], [1/4,1/2], [1/2,1]$ and $x > 1$. We also derive the small and large $x$ limits of the first--order factorizable contributions. Furthermore, we perform comparisons to a number of known Mellin moments, calculated by a different method for the corresponding subset of Feynman diagrams, and an independent high--precision numerical solution of the problems.},

journal = {Nuclear Physics B},

volume = {999},

number = {116427},

pages = {1--42},

isbn_issn = {ISSN 0550-3213},

year = {2024},

note = {arXiv:2311.00644 [hep-ph]},

refereed = {yes},

keywords = {Feynman diagram, massive operator matrix elements, computer algebra, differential equations, difference equations, coupled systems, nested integrals, nested sums},

length = {42},

url = {https://doi.org/10.1016/j.nuclphysb.2023.116427}

}

**article**{RISC6755,author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},

title = {{The first--order factorizable contributions to the three--loop massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$}},

language = {english},

abstract = {The unpolarized and polarized massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$contain first--order factorizable and non--first--order factorizable contributions in the determining difference or differential equations of their master integrals. We compute their first--order factorizable contributions in the single heavy mass case for all contributing Feynman diagrams. Moreover, we present the complete color--$zeta$ factors for the cases in which also non--first--order factorizable contributions emerge in the master integrals, but cancel in the final result as found by using the method of arbitrary high Mellin moments. Individual contributions depend also on generalized harmonic sums and on nested finite binomial and inverse binomial sums in Mellin $N$--space, and correspondingly, on Kummer--Poincar'e and square--root valued alphabets in Bjorken--$x$ space. We present a complete discussion of the possibilities of solving the present problem in $N$--space analytically and we also discuss the limitations in the present case to analytically continue the given $N$--space expressions to $N in mathbb{C}$ by strict methods. The representation through generating functions allows a well synchronized representation of the first--order factorizable results over a 17--letter alphabet. We finally obtain representations in terms of iterated integrals over the corresponding alphabet in $x$--space, also containing up to weight {sf w = 5} special constants, which can be rationalized to Kummer--Poincar'e iterated integrals at special arguments. The analytic $x$--space representation requires separate analyses for the intervals $x in [0,1/4], [1/4,1/2], [1/2,1]$ and $x > 1$. We also derive the small and large $x$ limits of the first--order factorizable contributions. Furthermore, we perform comparisons to a number of known Mellin moments, calculated by a different method for the corresponding subset of Feynman diagrams, and an independent high--precision numerical solution of the problems.},

journal = {Nuclear Physics B},

volume = {999},

number = {116427},

pages = {1--42},

isbn_issn = {ISSN 0550-3213},

year = {2024},

note = {arXiv:2311.00644 [hep-ph]},

refereed = {yes},

keywords = {Feynman diagram, massive operator matrix elements, computer algebra, differential equations, difference equations, coupled systems, nested integrals, nested sums},

length = {42},

url = {https://doi.org/10.1016/j.nuclphysb.2023.116427}

}

[de Freitas]

### The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$

#### J. Ablinger, A. Behring, J. Bluemlein, A. De Freitas, A. von Manteuffel, C. Schneider, K. Schoenwald

Physics Letter B 854(138713), pp. 1-8. 2024. ISSN 0370-2693. arXiv:2403.00513 [[hep-ph]. [doi]@

author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},

title = {{The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$}},

language = {english},

abstract = {The non-first-order-factorizable contributions to the unpolarized and polarized massive operator matrix elements to three-loop order, $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$, are calculated in the single-mass case. For the $_2F_1$-related master integrals of the problem, we use a semi-analytic method basedon series expansions and utilize the first-order differential equations for the master integrals whichdoes not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to $O(ep^5)$ in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable $x in ]0,infty[$ using highly precise series expansions to obtain the imaginary part of the physical amplitude for $x in ]0,1]$ at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-$x$ region. We also derive expansions in the region of small and large values of $x$. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.},

journal = {Physics Letter B},

volume = {854},

number = {138713},

pages = {1--8},

isbn_issn = {ISSN 0370-2693},

year = {2024},

note = {arXiv:2403.00513 [[hep-ph]},

refereed = {yes},

keywords = {Feynman diagram, massive operator matrix elements, computer algebra, differential equations, difference equations, coupled systems, numerics},

length = {8},

url = {https://doi.org/10.1016/j.physletb.2024.138713}

}

**article**{RISC7058,author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},

title = {{The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$}},

language = {english},

abstract = {The non-first-order-factorizable contributions to the unpolarized and polarized massive operator matrix elements to three-loop order, $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$, are calculated in the single-mass case. For the $_2F_1$-related master integrals of the problem, we use a semi-analytic method basedon series expansions and utilize the first-order differential equations for the master integrals whichdoes not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to $O(ep^5)$ in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable $x in ]0,infty[$ using highly precise series expansions to obtain the imaginary part of the physical amplitude for $x in ]0,1]$ at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-$x$ region. We also derive expansions in the region of small and large values of $x$. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.},

journal = {Physics Letter B},

volume = {854},

number = {138713},

pages = {1--8},

isbn_issn = {ISSN 0370-2693},

year = {2024},

note = {arXiv:2403.00513 [[hep-ph]},

refereed = {yes},

keywords = {Feynman diagram, massive operator matrix elements, computer algebra, differential equations, difference equations, coupled systems, numerics},

length = {8},

url = {https://doi.org/10.1016/j.physletb.2024.138713}

}

[de Freitas]

### Challenges for analytic calculations of the massive three-loop form factors

#### J Bluemlein, A. De Freitas, P. Marquard, C. Schneider

In: Proceedings of Loops and Legs in Quantum Field Theory, P. Marquard, M. Steinhauser (ed.)PoS(LL2024)03124-05, pp. 1-18. 2024. ISSN 1824-8039. arXiv:2408.07046 [hep-ph]. [doi]@

author = {J Bluemlein and A. De Freitas and P. Marquard and C. Schneider},

title = {{Challenges for analytic calculations of the massive three-loop form factors}},

booktitle = {{Proceedings of Loops and Legs in Quantum Field Theory}},

language = {english},

abstract = {The calculation of massive three-loop QCD form factors using in particular the large moments method has been successfully applied to quarkonic contributions in [1]. We give a brief review of the different steps of the calculation and report on improvements of our methods that enabled us to push forward the calculations of the gluonic contributions to the form factors.},

volume = {PoS(LL2024)031},

number = {24-05},

pages = {1--18},

isbn_issn = {ISSN 1824-8039},

year = {2024},

note = { arXiv:2408.07046 [hep-ph]},

editor = {P. Marquard and M. Steinhauser},

refereed = {no},

keywords = {Form factor; computer algebra, coupled systems, differential equations, recurrences, analytic continuation, holonomic functions},

length = {18},

url = {https://doi.org/10.22323/1.467.0031 }

}

**inproceedings**{RISC7066,author = {J Bluemlein and A. De Freitas and P. Marquard and C. Schneider},

title = {{Challenges for analytic calculations of the massive three-loop form factors}},

booktitle = {{Proceedings of Loops and Legs in Quantum Field Theory}},

language = {english},

abstract = {The calculation of massive three-loop QCD form factors using in particular the large moments method has been successfully applied to quarkonic contributions in [1]. We give a brief review of the different steps of the calculation and report on improvements of our methods that enabled us to push forward the calculations of the gluonic contributions to the form factors.},

volume = {PoS(LL2024)031},

number = {24-05},

pages = {1--18},

isbn_issn = {ISSN 1824-8039},

year = {2024},

note = { arXiv:2408.07046 [hep-ph]},

editor = {P. Marquard and M. Steinhauser},

refereed = {no},

keywords = {Form factor; computer algebra, coupled systems, differential equations, recurrences, analytic continuation, holonomic functions},

length = {18},

url = {https://doi.org/10.22323/1.467.0031 }

}

[de Freitas]

### The three-loop single-mass heavy flavor corrections to deep-inelastic scattering

#### J. Ablinger, A. Behring, J. Bluemlein, A. De Freitas, A. von Manteuffel, C. Schneider, K. Schoenwald

In: Proceedings of Loops and Legs in Quantum Field Theory, P. Marquard, M. Steinhauser (ed.)PoS(LL2024)047 , pp. 1-12. 2024. SSN 1824-8039. arXiv:2407.02006 [hep-ph]. [doi]@

author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},

title = {{The three-loop single-mass heavy flavor corrections to deep-inelastic scattering}},

booktitle = {{Proceedings of Loops and Legs in Quantum Field Theory}},

language = {english},

abstract = {We report on the status of the calculation of the massive Wilson coefficients and operator matrix elements for deep-inelastic scatterung to three-loop order. We discuss both the unpolarized and the polarized case, for which all the single-mass and nearly all two-mass contributions have been calculated. Numerical results on the structure function $F_2(x,Q^2)$ are presented. In the polarized case, we work in the Larinscheme and refer to parton distribution functions in this scheme. Furthermore, results on the three-loop variable flavor number scheme are presented.},

volume = {PoS(LL2024)047 },

pages = {1--12},

isbn_issn = {SSN 1824-8039},

year = {2024},

note = {arXiv:2407.02006 [hep-ph]},

editor = {P. Marquard and M. Steinhauser},

refereed = {no},

keywords = {Feynman integrals, deep-inelastic scattering, numerical results},

length = {12},

url = {https://doi.org/10.22323/1.467.0047 }

}

**inproceedings**{RISC7067,author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},

title = {{The three-loop single-mass heavy flavor corrections to deep-inelastic scattering}},

booktitle = {{Proceedings of Loops and Legs in Quantum Field Theory}},

language = {english},

abstract = {We report on the status of the calculation of the massive Wilson coefficients and operator matrix elements for deep-inelastic scatterung to three-loop order. We discuss both the unpolarized and the polarized case, for which all the single-mass and nearly all two-mass contributions have been calculated. Numerical results on the structure function $F_2(x,Q^2)$ are presented. In the polarized case, we work in the Larinscheme and refer to parton distribution functions in this scheme. Furthermore, results on the three-loop variable flavor number scheme are presented.},

volume = {PoS(LL2024)047 },

pages = {1--12},

isbn_issn = {SSN 1824-8039},

year = {2024},

note = {arXiv:2407.02006 [hep-ph]},

editor = {P. Marquard and M. Steinhauser},

refereed = {no},

keywords = {Feynman integrals, deep-inelastic scattering, numerical results},

length = {12},

url = {https://doi.org/10.22323/1.467.0047 }

}

[Ehling]

### Solving Quantitative Equations

#### G. Ehling, T. Kutsia

Technical report no. 24-03 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). April 2024. Licensed under CC BY 4.0 International. [doi] [pdf]@

author = {G. Ehling and T. Kutsia},

title = {{Solving Quantitative Equations}},

language = {english},

abstract = {Quantitative equational reasoning provides a framework that extends equality to an abstract notion of proximity by endowing equations with an element of a quantale. In this paper, we discuss the unification problem for a special class of shallow subterm-collapse-free quantitative equational theories. We outline rule-based algorithms for solving such equational unification problems over generic as well as idempotent Lawvereian quantales and study their properties.},

number = {24-03},

year = {2024},

month = {April},

keywords = {quantitative equational reasoning, Lawvereian quantales, equational unification},

length = {23},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

**techreport**{RISC7056,author = {G. Ehling and T. Kutsia},

title = {{Solving Quantitative Equations}},

language = {english},

abstract = {Quantitative equational reasoning provides a framework that extends equality to an abstract notion of proximity by endowing equations with an element of a quantale. In this paper, we discuss the unification problem for a special class of shallow subterm-collapse-free quantitative equational theories. We outline rule-based algorithms for solving such equational unification problems over generic as well as idempotent Lawvereian quantales and study their properties.},

number = {24-03},

year = {2024},

month = {April},

keywords = {quantitative equational reasoning, Lawvereian quantales, equational unification},

length = {23},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

[Ehling]

### Solving Quantitative Equations

#### Georg Ehling, Temur Kutsia

In: Automated Reasoning - 12th International Joint Conference, IJCAR 2024, Nancy, France, July 3-6, 2024, Proceedings, Christoph Benzmüller, Marijn J. H. Heule, Renate A. Schmidt (ed.), Lecture Notes in Artificial Intelligence 14740, pp. 381-400. 2024. Springer, ISBN 978-3-031-63500-7. [doi]@

author = {Georg Ehling and Temur Kutsia},

title = {{Solving Quantitative Equations}},

booktitle = {{Automated Reasoning - 12th International Joint Conference, IJCAR 2024, Nancy, France, July 3-6, 2024, Proceedings}},

language = {english},

series = {Lecture Notes in Artificial Intelligence},

volume = {14740},

pages = {381--400},

publisher = {Springer},

isbn_issn = {ISBN 978-3-031-63500-7},

year = {2024},

editor = {Christoph Benzmüller and Marijn J. H. Heule and Renate A. Schmidt},

refereed = {yes},

length = {20},

url = {https://doi.org/10.1007/978-3-031-63501-4_20}

}

**inproceedings**{RISC7065,author = {Georg Ehling and Temur Kutsia},

title = {{Solving Quantitative Equations}},

booktitle = {{Automated Reasoning - 12th International Joint Conference, IJCAR 2024, Nancy, France, July 3-6, 2024, Proceedings}},

language = {english},

series = {Lecture Notes in Artificial Intelligence},

volume = {14740},

pages = {381--400},

publisher = {Springer},

isbn_issn = {ISBN 978-3-031-63500-7},

year = {2024},

editor = {Christoph Benzmüller and Marijn J. H. Heule and Renate A. Schmidt},

refereed = {yes},

length = {20},

url = {https://doi.org/10.1007/978-3-031-63501-4_20}

}

[Obrovsky]

### Maximum-order Complexity and 2-Adic Complexity

#### Z. Chen, Z. Chen, J. Obrovsky, A. Winterhof

IEEE Transactions on Information Theory 70(8), pp. 6060-6067. 2024. ISSN: 0018-9448. [doi]@

author = {Z. Chen and Z. Chen and J. Obrovsky and A. Winterhof},

title = {{Maximum-order Complexity and 2-Adic Complexity}},

language = {english},

abstract = {The 2-adic complexity has been well-analyzed in the periodic case. However, we are not aware of any theoretical results in the aperiodic case. In particular, the Nth 2-adic complexity has not been studied for any promising candidate of a pseudorandom sequence of finite length N. Also nothing seems be known for a part of the period of length N of any cryptographically interesting periodic sequence. Here we introduce the first method for this aperiodic case. More precisely, we study the relation between Nth maximum-order complexity and Nth 2-adic complexity of binary sequences and prove a lower bound on the Nth 2-adic complexity in terms of the Nth maximum-order complexity. Then any known lower bound on the Nth maximum-order complexity implies a lower bound on the Nth 2-adic complexity of the same order of magnitude. In the periodic case, one can prove a slightly better result. The latter bound is sharp, which is illustrated by the maximum-order complexity of ell -sequences. The idea of the proof helps us to characterize the maximum-order complexity of periodic sequences in terms of the unique rational number defined by the sequence. We also show that a periodic sequence of maximal maximum-order complexity must be also of maximal 2-adic complexity.},

journal = {IEEE Transactions on Information Theory},

volume = {70},

number = {8},

pages = { 6060--6067},

isbn_issn = {ISSN: 0018-9448},

year = {2024},

refereed = {yes},

keywords = {Complexity theory;Polynomials;Random sequences;Cryptography;Surveys;Shift registers;Mathematics;Pseudorandom sequences;maximum-order complexity;2-adic complexity;ℓ-sequences},

length = {8},

url = {https://doi.org/10.1109/TIT.2024.3405946}

}

**article**{RISC7060,author = {Z. Chen and Z. Chen and J. Obrovsky and A. Winterhof},

title = {{Maximum-order Complexity and 2-Adic Complexity}},

language = {english},

abstract = {The 2-adic complexity has been well-analyzed in the periodic case. However, we are not aware of any theoretical results in the aperiodic case. In particular, the Nth 2-adic complexity has not been studied for any promising candidate of a pseudorandom sequence of finite length N. Also nothing seems be known for a part of the period of length N of any cryptographically interesting periodic sequence. Here we introduce the first method for this aperiodic case. More precisely, we study the relation between Nth maximum-order complexity and Nth 2-adic complexity of binary sequences and prove a lower bound on the Nth 2-adic complexity in terms of the Nth maximum-order complexity. Then any known lower bound on the Nth maximum-order complexity implies a lower bound on the Nth 2-adic complexity of the same order of magnitude. In the periodic case, one can prove a slightly better result. The latter bound is sharp, which is illustrated by the maximum-order complexity of ell -sequences. The idea of the proof helps us to characterize the maximum-order complexity of periodic sequences in terms of the unique rational number defined by the sequence. We also show that a periodic sequence of maximal maximum-order complexity must be also of maximal 2-adic complexity.},

journal = {IEEE Transactions on Information Theory},

volume = {70},

number = {8},

pages = { 6060--6067},

isbn_issn = {ISSN: 0018-9448},

year = {2024},

refereed = {yes},

keywords = {Complexity theory;Polynomials;Random sequences;Cryptography;Surveys;Shift registers;Mathematics;Pseudorandom sequences;maximum-order complexity;2-adic complexity;ℓ-sequences},

length = {8},

url = {https://doi.org/10.1109/TIT.2024.3405946}

}

[Qi]

### A tree-based algorithm for the integration of monomials in the Chow ring of the moduli space of stable marked curves of genus zero

#### Jiayue Qi

Journal of Symbolic Computation 122(102253), pp. -. 2024. ISSN: 0747-7171. [doi]@

author = {Jiayue Qi},

title = {{A tree-based algorithm for the integration of monomials in the Chow ring of the moduli space of stable marked curves of genus zero}},

language = {english},

journal = {Journal of Symbolic Computation},

volume = {122},

number = {102253},

pages = {--},

isbn_issn = {ISSN: 0747-7171},

year = {2024},

refereed = {yes},

length = {52},

url = {https://doi.org/10.1016/j.jsc.2023.102253}

}

**article**{RISC6774,author = {Jiayue Qi},

title = {{A tree-based algorithm for the integration of monomials in the Chow ring of the moduli space of stable marked curves of genus zero}},

language = {english},

journal = {Journal of Symbolic Computation},

volume = {122},

number = {102253},

pages = {--},

isbn_issn = {ISSN: 0747-7171},

year = {2024},

refereed = {yes},

length = {52},

url = {https://doi.org/10.1016/j.jsc.2023.102253}

}

[Schneider]

### Representation of hypergeometric products of higher nesting depths in difference rings

#### E.D. Ocansey, C. Schneider

J. Symb. Comput. 120, pp. 1-50. 2024. ISSN: 0747-7171. arXiv:2011.08775 [cs.SC]. [doi]@

author = {E.D. Ocansey and C. Schneider},

title = {{Representation of hypergeometric products of higher nesting depths in difference rings}},

language = {english},

journal = {J. Symb. Comput.},

volume = {120},

pages = {1--50},

isbn_issn = {ISSN: 0747-7171},

year = {2024},

note = {arXiv:2011.08775 [cs.SC]},

refereed = {yes},

length = {50},

url = {https://doi.org/10.1016/j.jsc.2023.03.002}

}

**article**{RISC6688,author = {E.D. Ocansey and C. Schneider},

title = {{Representation of hypergeometric products of higher nesting depths in difference rings}},

language = {english},

journal = {J. Symb. Comput.},

volume = {120},

pages = {1--50},

isbn_issn = {ISSN: 0747-7171},

year = {2024},

note = {arXiv:2011.08775 [cs.SC]},

refereed = {yes},

length = {50},

url = {https://doi.org/10.1016/j.jsc.2023.03.002}

}

[Schneider]

### Creative Telescoping for Hypergeometric Double Sums

#### P. Paule, C. Schneider

Technical report no. 24-01 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). January 2024. arXiv:2401.16314 [cs.SC]. Licensed under CC BY 4.0 International. [doi] [pdf]@

author = {P. Paule and C. Schneider},

title = {{Creative Telescoping for Hypergeometric Double Sums}},

language = {english},

abstract = {We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which guarantees the applicability of our method for many input sums. In addition, we elaborate new techniques to optimize the underlying key task of our method to compute rational solutions of parameterized linear recurrences.},

number = {24-01},

year = {2024},

month = {January},

note = {arXiv:2401.16314 [cs.SC]},

keywords = {creative telescoping; symbolic summation, hypergeometric multi-sums, contiguous relations, parameterized recurrences, rational solutions},

length = {26},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

**techreport**{RISC6894,author = {P. Paule and C. Schneider},

title = {{Creative Telescoping for Hypergeometric Double Sums}},

language = {english},

abstract = {We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which guarantees the applicability of our method for many input sums. In addition, we elaborate new techniques to optimize the underlying key task of our method to compute rational solutions of parameterized linear recurrences.},

number = {24-01},

year = {2024},

month = {January},

note = {arXiv:2401.16314 [cs.SC]},

keywords = {creative telescoping; symbolic summation, hypergeometric multi-sums, contiguous relations, parameterized recurrences, rational solutions},

length = {26},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

[Schreiner]

### Semantics-Based Rapid Prototyping of a Machine Controller Language

#### Wolfgang Schreiner, William Steingartner

In: 2024 IEEE 17th International Scientific Conference on Informatics, Poprad, Slovakia, November 13-15, Valerie Novitzká (ed.), pp. -. 2024. IEEE, ISBN XXXX.@

author = {Wolfgang Schreiner and William Steingartner},

title = {{Semantics-Based Rapid Prototyping of a Machine Controller Language}},

booktitle = {{2024 IEEE 17th International Scientific Conference on Informatics, Poprad, Slovakia, November 13--15}},

language = {english},

abstract = {We present the use of the semantics-based language generator SLANG to implement a machine controller language EFSM which is based on the principle of extended finite state machines. SLANG allows to rapidly prototype EFSM by a formal definition of the language's abstract syntax, concrete syntax, type system, and denotational semantics; from this, SLANG generates a parser, a printer, a type checker, and an interpreter for EFSM. Subsequently we implement in EFSM a controller for an (idealized) robot vacuum cleaner and validate its operation by simulation and visualization. Our presentation may thus also serve as a template for the semantics-based rapid prototyping of other domain-specific languages.},

pages = {--},

publisher = {IEEE},

isbn_issn = {ISBN XXXX},

year = {2024},

editor = {Valerie Novitzká},

refereed = {yes},

keywords = {rapid prototyping, semantics of programming languages, interpreters, automata, embedded systems},

sponsor = {Aktion Österreich-Slowakei grants 2023-03-15-001 and 2024-05-15-001, KEGA project 030TUKE-4/2023},

length = {6}

}

**inproceedings**{RISC7063,author = {Wolfgang Schreiner and William Steingartner},

title = {{Semantics-Based Rapid Prototyping of a Machine Controller Language}},

booktitle = {{2024 IEEE 17th International Scientific Conference on Informatics, Poprad, Slovakia, November 13--15}},

language = {english},

abstract = {We present the use of the semantics-based language generator SLANG to implement a machine controller language EFSM which is based on the principle of extended finite state machines. SLANG allows to rapidly prototype EFSM by a formal definition of the language's abstract syntax, concrete syntax, type system, and denotational semantics; from this, SLANG generates a parser, a printer, a type checker, and an interpreter for EFSM. Subsequently we implement in EFSM a controller for an (idealized) robot vacuum cleaner and validate its operation by simulation and visualization. Our presentation may thus also serve as a template for the semantics-based rapid prototyping of other domain-specific languages.},

pages = {--},

publisher = {IEEE},

isbn_issn = {ISBN XXXX},

year = {2024},

editor = {Valerie Novitzká},

refereed = {yes},

keywords = {rapid prototyping, semantics of programming languages, interpreters, automata, embedded systems},

sponsor = {Aktion Österreich-Slowakei grants 2023-03-15-001 and 2024-05-15-001, KEGA project 030TUKE-4/2023},

length = {6}

}

### 2023

[Banerjee]

### Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach

#### Koustav Banerjee

Enumerative Combinatorics and Applications 3, pp. 1-4. 2023. ISSN 2710-2335. [doi]@

author = {Koustav Banerjee},

title = {{Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach}},

language = {english},

journal = {Enumerative Combinatorics and Applications},

volume = {3},

pages = {1--4},

isbn_issn = {ISSN 2710-2335},

year = {2023},

refereed = {yes},

length = {5},

url = {https://doi.org/10.54550/ECA2023V3S2R12}

}

**article**{RISC6701,author = {Koustav Banerjee},

title = {{Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach}},

language = {english},

journal = {Enumerative Combinatorics and Applications},

volume = {3},

pages = {1--4},

isbn_issn = {ISSN 2710-2335},

year = {2023},

refereed = {yes},

length = {5},

url = {https://doi.org/10.54550/ECA2023V3S2R12}

}

[Banerjee]

### Inequalities for the modified Bessel function of first kind of non-negative order

#### K. Banerjee

Journal of Mathematical Analysis and Applications 524, pp. 1-28. 2023. Elsevier, ISSN 1096-0813. [doi]@

author = {K. Banerjee},

title = {{Inequalities for the modified Bessel function of first kind of non-negative order}},

language = {english},

journal = {Journal of Mathematical Analysis and Applications},

volume = {524},

pages = {1--28},

publisher = {Elsevier},

isbn_issn = {ISSN 1096-0813},

year = {2023},

refereed = {yes},

length = {28},

url = {https://doi.org/10.1016/j.jmaa.2023.127082}

}

**article**{RISC6700,author = {K. Banerjee},

title = {{Inequalities for the modified Bessel function of first kind of non-negative order}},

language = {english},

journal = {Journal of Mathematical Analysis and Applications},

volume = {524},

pages = {1--28},

publisher = {Elsevier},

isbn_issn = {ISSN 1096-0813},

year = {2023},

refereed = {yes},

length = {28},

url = {https://doi.org/10.1016/j.jmaa.2023.127082}

}

[Banerjee]

### 2-Elongated Plane Partitions and Powers of 7: The Localization Method Applied to a Genus 1 Congruence Family

#### K. Banerjee, N.A. Smoot

Technical report no. 23-10 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). August 2023. Licensed under CC BY 4.0 International. [doi] [pdf]@

author = {K. Banerjee and N.A. Smoot},

title = {{2-Elongated Plane Partitions and Powers of 7: The Localization Method Applied to a Genus 1 Congruence Family}},

language = {english},

abstract = {Over the last century, a large variety of infinite congruence families have been discovered and studied, exhibiting a great variety with respect to their difficulty. Major complicating factors arise from the topology of the associated modular curve: classical techniques are sufficient when the associated curve has cusp count 2 and genus 0. Recent work has led to new techniques that have proven useful when the associated curve has cusp count greater than 2 and genus 0. We show here that these techniques may be adapted in the case of positive genus. In particular, we examine a congruence family over the 2-elongated plane partition diamond counting function $d_2(n)$ by powers of 7, for which the associated modular curve has cusp count 4 and genus 1. We compare our method with other techniques for proving genus 1 congruence families, and present a second congruence family by powers of 7 which we conjecture, and which may be amenable to similar techniques.},

number = {23-10},

year = {2023},

month = {August},

keywords = {Partition congruences, infinite congruence family, modular functions, plane partitions, partition analysis, modular curve, Riemann surface},

length = {35},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

**techreport**{RISC6713,author = {K. Banerjee and N.A. Smoot},

title = {{2-Elongated Plane Partitions and Powers of 7: The Localization Method Applied to a Genus 1 Congruence Family}},

language = {english},

abstract = {Over the last century, a large variety of infinite congruence families have been discovered and studied, exhibiting a great variety with respect to their difficulty. Major complicating factors arise from the topology of the associated modular curve: classical techniques are sufficient when the associated curve has cusp count 2 and genus 0. Recent work has led to new techniques that have proven useful when the associated curve has cusp count greater than 2 and genus 0. We show here that these techniques may be adapted in the case of positive genus. In particular, we examine a congruence family over the 2-elongated plane partition diamond counting function $d_2(n)$ by powers of 7, for which the associated modular curve has cusp count 4 and genus 1. We compare our method with other techniques for proving genus 1 congruence families, and present a second congruence family by powers of 7 which we conjecture, and which may be amenable to similar techniques.},

number = {23-10},

year = {2023},

month = {August},

keywords = {Partition congruences, infinite congruence family, modular functions, plane partitions, partition analysis, modular curve, Riemann surface},

length = {35},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

[Buchberger]

### Is ChatGPT Smarter Than Master’s Applicants?

#### Bruno Buchberger

Technical report no. 23-04 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). January 2023. Licensed under CC BY 4.0 International. [doi] [pdf]@

author = {Bruno Buchberger},

title = {{Is ChatGPT Smarter Than Master’s Applicants?}},

language = {English},

abstract = {During the selection procedure for a particular informatics fellowship program sponsored by Upper Austrian companies, I ask the applicants a couple of simple technical questions about programming, etc., in a Zoom meeting. I put the same questions to the dialogue system ChatGPT, [ChatGPT]. The result surprised me: Nearly all answers of ChatGPT were totally correct and nicely explained. Also, in the dialogues to clarify some critical points in the answers, the explanations by ChatGPT were amazingly clear and goal-oriented.In comparison: I tried out the same questions in the personal Zoom interviews with approximately 30 applicants from five countries. Only the top three candidates (with a GPA of 1.0, i.e., the highest possible GPA in their bachelor’s study) performed approximately equally well in the interview. All the others performed (far) worse than ChatGPT. And, of course, all answers from ChatGPT came within 1 to 10 seconds, whereas most of the human applicants' answers needed lengthy and arduous dialogues.I am particularly impressed by the ability of ChatGPT to extract meaningful and well-structured programs from problem specifications in natural language. In this experiment, I also added some questions that ask for proofs for simple statements in natural language, which I do not ask in the student's interviews. The performance of ChatGPT was quite impressive as far as formalization and propositional logic are concerned. In examples where predicate logic reasoning is necessary, the ChatGPT answers are not (yet?) perfect. I am pleased to see that ChatGPT tries to present the proofs in a “natural style” This is something that I had as one of my main goals when I initiated the Theorema project in 1995. I think we already achieved this in the early stage of Theorema, and we performed this slightly better and more systematically than ChatGPT does.I also tried to develop a natural language input facility for Theorema in 2017, i.e., a tool to formalize natural language statements in predicate logic. However, I could not continue this research for a couple of reasons. Now I see that ChatGPT achieved this goal. Thus, I think that the following combination of methods could result in a significant leap forward:- the “natural style” proving methods that we developed within Theorema (for the automated generation of programs from specifications, the automated verification of programs in the frame of knowledge, and the automated proof of theorems in theories), in particular, my “Lazy Thinking Method” for algorithm synthesis from specifications- and the natural language formalization techniques of ChatGPT.I propose this as a research project topic and invite colleagues and students to contact me and join me in this effort: Buchberger.bruno@gmail.com.},

number = {23-04},

year = {2023},

month = {January},

keywords = {ChatGPT, automated programming, program synthesis, automated proving, formalization of natural language, master's screening},

length = {30},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

**techreport**{RISC6684,author = {Bruno Buchberger},

title = {{Is ChatGPT Smarter Than Master’s Applicants?}},

language = {English},

abstract = {During the selection procedure for a particular informatics fellowship program sponsored by Upper Austrian companies, I ask the applicants a couple of simple technical questions about programming, etc., in a Zoom meeting. I put the same questions to the dialogue system ChatGPT, [ChatGPT]. The result surprised me: Nearly all answers of ChatGPT were totally correct and nicely explained. Also, in the dialogues to clarify some critical points in the answers, the explanations by ChatGPT were amazingly clear and goal-oriented.In comparison: I tried out the same questions in the personal Zoom interviews with approximately 30 applicants from five countries. Only the top three candidates (with a GPA of 1.0, i.e., the highest possible GPA in their bachelor’s study) performed approximately equally well in the interview. All the others performed (far) worse than ChatGPT. And, of course, all answers from ChatGPT came within 1 to 10 seconds, whereas most of the human applicants' answers needed lengthy and arduous dialogues.I am particularly impressed by the ability of ChatGPT to extract meaningful and well-structured programs from problem specifications in natural language. In this experiment, I also added some questions that ask for proofs for simple statements in natural language, which I do not ask in the student's interviews. The performance of ChatGPT was quite impressive as far as formalization and propositional logic are concerned. In examples where predicate logic reasoning is necessary, the ChatGPT answers are not (yet?) perfect. I am pleased to see that ChatGPT tries to present the proofs in a “natural style” This is something that I had as one of my main goals when I initiated the Theorema project in 1995. I think we already achieved this in the early stage of Theorema, and we performed this slightly better and more systematically than ChatGPT does.I also tried to develop a natural language input facility for Theorema in 2017, i.e., a tool to formalize natural language statements in predicate logic. However, I could not continue this research for a couple of reasons. Now I see that ChatGPT achieved this goal. Thus, I think that the following combination of methods could result in a significant leap forward:- the “natural style” proving methods that we developed within Theorema (for the automated generation of programs from specifications, the automated verification of programs in the frame of knowledge, and the automated proof of theorems in theories), in particular, my “Lazy Thinking Method” for algorithm synthesis from specifications- and the natural language formalization techniques of ChatGPT.I propose this as a research project topic and invite colleagues and students to contact me and join me in this effort: Buchberger.bruno@gmail.com.},

number = {23-04},

year = {2023},

month = {January},

keywords = {ChatGPT, automated programming, program synthesis, automated proving, formalization of natural language, master's screening},

length = {30},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

[Buchberger]

### Automated Programming, Symbolic computation, Machine Learning: My Personal View

#### Bruno Buchberger

Ann. Math. Artif. Intell. 91(5), pp. 569-589. 2023. 1012-2443.@

author = {Bruno Buchberger},

title = {{Automated Programming, Symbolic computation, Machine Learning: My Personal View}},

language = {english},

journal = {Ann. Math. Artif. Intell.},

volume = {91},

number = {5},

pages = {569--589},

isbn_issn = {1012-2443},

year = {2023},

refereed = {yes},

length = {21}

}

**article**{RISC6895,author = {Bruno Buchberger},

title = {{Automated Programming, Symbolic computation, Machine Learning: My Personal View}},

language = {english},

journal = {Ann. Math. Artif. Intell.},

volume = {91},

number = {5},

pages = {569--589},

isbn_issn = {1012-2443},

year = {2023},

refereed = {yes},

length = {21}

}

[Buchberger]

### International Young Talents Hotspot Austria

#### Bruno Buchberger

In: Ideen, die gehen!, W. Schüssel, G. Kneifel (ed.), pp. 37-39. 2023. Edition Kleine Zeitung, 20234.@

author = {Bruno Buchberger},

title = {{International Young Talents Hotspot Austria}},

booktitle = {{Ideen, die gehen!}},

language = {english},

pages = {37--39},

publisher = {Edition Kleine Zeitung},

isbn_issn = {20234},

year = {2023},

editor = {W. Schüssel and G. Kneifel},

refereed = {no},

length = {3}

}

**incollection**{RISC6896,author = {Bruno Buchberger},

title = {{International Young Talents Hotspot Austria}},

booktitle = {{Ideen, die gehen!}},

language = {english},

pages = {37--39},

publisher = {Edition Kleine Zeitung},

isbn_issn = {20234},

year = {2023},

editor = {W. Schüssel and G. Kneifel},

refereed = {no},

length = {3}

}

[Buchberger]

### Wissenschaft und Meditation: Auf dem Weg zur bewussten Naturgesellschaft

#### Bruno Buchberger

1st edition, December 2023. Amazon, 979-8868299117.@

author = {Bruno Buchberger},

title = {{Wissenschaft und Meditation: Auf dem Weg zur bewussten Naturgesellschaft}},

language = {german},

publisher = {Amazon},

isbn_issn = {979-8868299117},

year = {2023},

month = {December},

edition = {1st},

translation = {0},

length = {184}

}

**book**{RISC6898,author = {Bruno Buchberger},

title = {{Wissenschaft und Meditation: Auf dem Weg zur bewussten Naturgesellschaft}},

language = {german},

publisher = {Amazon},

isbn_issn = {979-8868299117},

year = {2023},

month = {December},

edition = {1st},

translation = {0},

length = {184}

}