Publications

2018

An Improved Method to Compute the Inverse Mellin Transform of Holonomic Sequences

J. Ablinger

In: Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018, J. Blümlein and P. Marquard (ed.), PoS(LL2018) , pp. 1-10. 2018. ISSN 1824-8039. [url]
[bib]
@inproceedings{RISC5789,
author = {J. Ablinger},
title = {{An Improved Method to Compute the Inverse Mellin Transform of Holonomic Sequences}},
booktitle = {{Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018}},
language = {english},
series = {PoS(LL2018)},
pages = {1--10},
isbn_issn = {ISSN 1824-8039},
year = {2018},
editor = {J. Blümlein and P. Marquard},
refereed = {yes},
length = {10},
url = {https://pos.sissa.it/303/063/pdf}
}

Anti-Unification and Natural Language Processing

N. Amiridze, T. Kutsia

In: Fifth Workshop on Natural Language and Computer Science, NLCS’18, A. Asudeh, V. de Paiva, L. Moss (ed.), EasyChair preprints 203, pp. 1-12. 2018. [url] [pdf]
[bib]
@inproceedings{RISC5707,
author = {N. Amiridze and T. Kutsia},
title = {{Anti-Unification and Natural Language Processing}},
booktitle = {{Fifth Workshop on Natural Language and Computer Science, NLCS’18}},
language = {english},
series = {EasyChair preprints},
number = {203},
pages = {1--12},
isbn_issn = { },
year = {2018},
editor = {A. Asudeh and V. de Paiva and L. Moss},
refereed = {yes},
length = {12},
url = {https://doi.org/10.29007/fkrh}
}

Varieties of apolar subschemes of toric surfaces

Gallet Matteo, Ranestad Kristian, Villamizar Nelly

Ark. Mat. 56(1), pp. 73-99. 2018. ISSN 0004-2080. [url]
[bib]
@article{RISC5796,
author = {Gallet Matteo and Ranestad Kristian and Villamizar Nelly},
title = {{Varieties of apolar subschemes of toric surfaces}},
language = {english},
journal = {Ark. Mat.},
volume = {56},
number = {1},
pages = {73--99},
isbn_issn = { ISSN 0004-2080},
year = {2018},
refereed = {yes},
length = {27},
url = {https://doi.org/10.4310/ARKIV.2018.v56.n1.a6}
}

Term-Graph Anti-Unification

Alexander Baumgartner, Temur Kutsia, Jordi Levy, Mateu Villaret

Technical report no. 18-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2018. [pdf]
[bib]
@techreport{RISC5549,
author = {Alexander Baumgartner and Temur Kutsia and Jordi Levy and Mateu Villaret},
title = {{Term-Graph Anti-Unification}},
language = {english},
number = {18-02},
year = {2018},
length = {19},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

Term-Graph Anti-Unification

Alexander Baumgartner, Temur Kutsia, Jordi Levy, Mateu Villaret

In: 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018), Helene Kirchner (ed.), Leibniz International Proceedings in Informatics (LIPIcs) 108, pp. 9:1-9:17. 2018. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, ISBN 978-3-95977-077-4 ISSN 1868-8969. [url]
[bib]
@inproceedings{RISC5764,
author = {Alexander Baumgartner and Temur Kutsia and Jordi Levy and Mateu Villaret},
title = {{Term-Graph Anti-Unification}},
booktitle = {{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)}},
language = {english},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {108},
pages = {9:1--9:17},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
isbn_issn = {ISBN 978-3-95977-077-4 ISSN 1868-8969},
year = {2018},
editor = {Helene Kirchner},
refereed = {yes},
length = {17},
url = {http://drops.dagstuhl.de/opus/volltexte/2018/9179}
}

On some polynomials and series of Bloch-Polya Type

Berkovich A., Uncu A. K.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 146(7), pp. 2827-2838. July 2018. 1088-6826. [url]
[bib]
@article{RISC5557,
author = {Berkovich A. and Uncu A.~K.},
title = {{On some polynomials and series of Bloch-Polya Type}},
language = {english},
journal = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY},
volume = {146},
number = {7},
pages = {2827--2838},
isbn_issn = {1088-6826},
year = {2018},
month = {July},
refereed = {yes},
keywords = {Mathematics - Number Theory, Mathematics - Combinatorics, 05A17, 05A19, 11B65, 11P81},
length = {12},
url = {http://www.ams.org/journals/proc/2018-146-07/S0002-9939-2018-13982-9/}
}

Some Elementary Partition Inequalities and Their Implications

Berkovich A., Uncu A. K.

ArXiv e-prints (to appear in Annals of Cobinatorics), pp. -. 2018. Preprint. [url]
[bib]
@article{RISC5558,
author = {Berkovich A. and Uncu A.~K.},
title = {{Some Elementary Partition Inequalities and Their Implications}},
language = {english},
journal = {ArXiv e-prints (to appear in Annals of Cobinatorics)},
pages = {--},
isbn_issn = {Preprint},
year = {2018},
refereed = {yes},
keywords = {Mathematics - Combinatorics, Mathematics - Number Theory, 05A15, 05A17, 05A19, 05A20, 11B65, 11P81, 11P84, 33D15},
length = {12},
url = {https://arxiv.org/abs/1708.01957}
}

Polynomial Identities Implying Capparelli's Partition Theorems

Ali Kemal Uncu, Alexander Berkovich

ArXiv e-prints (submitted), pp. -. 2018. N/A. [url]
[bib]
@article{RISC5790,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Polynomial Identities Implying Capparelli's Partition Theorems }},
language = {english},
journal = {ArXiv e-prints (submitted)},
pages = {--},
isbn_issn = {N/A},
year = {2018},
refereed = {yes},
length = {21},
url = {https://arxiv.org/pdf/1807.10974.pdf}
}

Elementary Polynomial Identities Involving q-Trinomial Coefficients

Ali Kemal Uncu, Alexander Berkovich

ArXiv e-prints , pp. -. 2018. N/A. [url]
[bib]
@article{RISC5791,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Elementary Polynomial Identities Involving q-Trinomial Coefficients }},
language = {english},
journal = {ArXiv e-prints },
pages = {--},
isbn_issn = {N/A},
year = {2018},
refereed = {yes},
length = {0},
url = {https://arxiv.org/abs/1810.06497}
}

Generalizing some Results in Field Theory for Rings

Jose Capco

Communications in Algebra, pp. 0-12. 2018. 0092-7872. Preprint. [pdf]
[bib]
@article{RISC5375,
author = {Jose Capco},
title = {{Generalizing some Results in Field Theory for Rings}},
language = {english},
journal = {Communications in Algebra},
pages = {0--12},
isbn_issn = {0092-7872},
year = {2018},
note = {Preprint},
refereed = {no},
length = {13}
}

Primitive Recursive Proof Systems for Arithmetic

David M. Cerna and Anela Lolic

RISC. Technical report, January 2018. In revision. [pdf]
[bib]
@techreport{RISC5528,
author = {David M. Cerna and Anela Lolic},
title = {{Primitive Recursive Proof Systems for Arithmetic}},
language = {english},
abstract = {Peano arithmetic, as formalized by Gentzen, can be presented as an axiom extensionof the LK-calculus with equality and an additional inference rule formalizing induction.While this formalism was enough (with the addition of some meta-theoretic argumentation)to show the consistency of arithmetic, alternative formulations of induction such asthe infinitary ω-rule and cyclic reasoning provide insight into the structure of arithmeticproofs obfuscated by the inference rule formulation of induction. For example, questionsconcerning the elimination of cut, consistency, and proof shape are given more clarity. Thesame could be said for functional interpretations of arithmetic such as system T whichenumerates the recursive functions provably total by arithmetic. A key feature of thesevariations on the formalization of arithmetic is that they get somewhat closer to formalizingthe concept of induction directly using the inferences of the LK-calculus, albeit byadding extra machinery at the meta-level. In this work we present a recursive sequentcalculus for arithmetic which can be syntactically translated into Gentzen formalism ofarithmetic and allows proof normalization to the LK-calculus with equality.},
year = {2018},
month = {January },
note = {In revision},
institution = {RISC},
length = {16}
}

Idempotent Anti-unification

David M. Cerna Temur Kutsia

RISC. Technical report, Feb. 2018. Submitted for review. [pdf]
[bib]
@techreport{RISC5530,
author = {David M. Cerna Temur Kutsia},
title = {{Idempotent Anti-unification }},
language = {english},
abstract = {In this paper we address two problems related to idempotent anti-unification. First, we show thatthere exists an anti-unification problem with a single idempotent symbol which has an infiniteminimal complete set of generalizations. It means that anti-unification with a single idempotentsymbol has infinitary or nullary generalization type, similar to anti-unification with two idem-potent symbols, shown earlier by Loı̈c Pottier. Next, we develop an algorithm, which takes anarbitrary idempotent anti-unification problem and computes a representation of its solution set inthe form of a regular tree grammar. The algorithm does not depend on the number of idempotentfunction symbols in the input terms. The language generated by the grammar is the minimalcomplete set of generalizations of the given anti-unification problem, which implies that idem-potent anti-unification is infinitary.},
year = {2018},
month = {Feb.},
note = {Submitted for review},
institution = {RISC},
length = {27}
}

A General Recursive Construction for Schematic Resolution Derivations

David M. Cerna

2018. submitted for review. Preprint. [pdf]
[bib]
@techreport{RISC5594,
author = {David M. Cerna},
title = {{A General Recursive Construction for Schematic Resolution Derivations}},
language = {english},
abstract = {Proof schemata provide an alternative formalism for handling inductive argumentation, while non-trivially extending {\em Herbrand's theorem} to a fragment of arithmetic and thus allowing the construction of {\em Herbrand sequents} and {\em expansion trees}. Existing proof analysis methods for proof schemata extract an unsatisfiable characteristic formula representing the cut structure of the proof and from its refutation construct a Herbrand sequent. Unfortunately, constructing the refutation is a task which is highly non-trivial. An automated method for constructing such refutations exists, but it only works for a very weak fragment of arithmetic and is hard to use interactively. More expressive yet interactive methods for the formalization of recursive resolution refutation are complex, hard to work with, and still limited to an undesirably weak class of recursion. In this work we note a particular problem with previous methods, namely they mix the recursive structure with the calculus of refutation. Also we present a modular recursive structure independent of the resolution formalism and proof construction. We illustrate the expressive power of the so called {\em finite saturated tree} formalism by formalizing the Non-injectivity Assertion's schematic refutation (a variant of the infinitary Pigeonhole principle). None of the previously developed formalism are able to formalize this refutation.},
year = {2018},
note = {submitted for review},
length = {42},
type = {Preprint},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

Higher-Order Equational Pattern Anti-Unification

David M. Cerna, Temur Kutsia

In: 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018), Helene Kirchner (ed.), Leibniz International Proceedings in Informatics (LIPIcs) 108, pp. 12:1-12:17. 2018. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, ISBN 978-3-95977-077-4 ISSN 1868-8969. [url]
[bib]
@inproceedings{RISC5765,
author = {David M. Cerna and Temur Kutsia},
title = {{Higher-Order Equational Pattern Anti-Unification}},
booktitle = {{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)}},
language = {english},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {108},
pages = {12:1--12:17},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
isbn_issn = {ISBN 978-3-95977-077-4 ISSN 1868-8969},
year = {2018},
editor = {Helene Kirchner},
refereed = {yes},
length = {17},
url = {http://drops.dagstuhl.de/opus/volltexte/2018/9182}
}

Mechanical Synthesis of Sorting Algorithms for Binary Trees by Logic and Combinatorial Techniques

Isabela Dramnesc, Tudor Jebelean, Sorin Stratulat

Journal of Symbolic Computation 90, pp. 3-41. 2018. Elsevier, 07477171. [url]
[bib]
@article{RISC5715,
author = {Isabela Dramnesc and Tudor Jebelean and Sorin Stratulat},
title = {{Mechanical Synthesis of Sorting Algorithms for Binary Trees by Logic and Combinatorial Techniques}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {90},
pages = {3--41},
publisher = {Elsevier},
isbn_issn = {07477171},
year = {2018},
refereed = {yes},
keywords = {algorithm synthesis ; automated reasoning ; natural--style proving},
length = {39},
url = {https://doi.org/10.1016/j.jsc.2018.04.002}
}

Pattern-based calculi with finitary matching

Sandra Alves, Besik Dundua, Mário Florido, Temur Kutsia

Logic Journal of the IGPL 26(2), pp. 203-243. 2018. ISSN 1367-0751. [url]
[bib]
@article{RISC5763,
author = {Sandra Alves and Besik Dundua and Mário Florido and Temur Kutsia},
title = {{Pattern-based calculi with finitary matching}},
language = {english},
journal = {Logic Journal of the IGPL},
volume = {26},
number = {2},
pages = {203--243},
isbn_issn = {ISSN 1367-0751},
year = {2018},
refereed = {yes},
length = {41},
url = {https://doi.org/10.1093/JIGPAL/jzx059}
}

Teaching the Formalization of Mathematical Theories and Algorithms via the Automatic Checking of Finite Models

Wolfgang Schreiner, Alexander Brunhuemer, Christoph Fürst

In: Post-Proceedings ThEdu'17, Pedro Quaresma and Walther Neuper (ed.), Proceedings of 6th International Workshop on Theorem proving components for Educational software (ThEdu'17), Gothenburg, Sweden, 6 Aug 2017, Electronic Proceedings in Theoretical Computer Science (EPTCS) 267, pp. 120-139. 2018. Open Publishing Association, ISSN 2075-2180. [url] [pdf]
[bib]
@inproceedings{RISC5531,
author = {Wolfgang Schreiner and Alexander Brunhuemer and Christoph Fürst},
title = {{Teaching the Formalization of Mathematical Theories and Algorithms via the Automatic Checking of Finite Models}},
booktitle = {{Post-Proceedings ThEdu'17}},
language = {english},
abstract = {Education in the practical applications of logic and proving such as the formalspecification and verification of computer programs is substantially hampered bythe fact that most time and effort that is invested in proving is actuallywasted in vain: because of errors in the specifications respectively algorithmsthat students have developed, their proof attempts are often pointless (becausethe proposition proved is actually not of interest) or a priori doomed to fail(because the proposition to be proved does actually not hold); this is afrequent source of frustration and gives formal methods a bad reputation. RISCAL(RISC Algorithm Language) is a formal specification language and associatedsoftware system that attempts to overcome this problem by making logicformalization fun rather than a burden. To this end, RISCAL allows students toeasily validate the correctness of instances of propositions respectivelyalgorithms by automatically evaluating/executing and checking them on (small)finite models. Thus many/most errors can be quickly detected and subsequentproof attempts can be focused on propositions that are more/most likely to beboth meaningful and true.},
series = {Electronic Proceedings in Theoretical Computer Science (EPTCS)},
volume = {267},
pages = {120--139},
publisher = {Open Publishing Association},
isbn_issn = {ISSN 2075-2180},
year = {2018},
editor = {Pedro Quaresma and Walther Neuper},
refereed = {yes},
keywords = {formal methods, program specification and verification, model checking, computer science education, logic},
sponsor = {Supported by the Johannes Kepler University Linz, Linz Institute of Technology (LIT), Project LOGTECHEDU "Logic Technology for Computer Science Education"},
length = {20},
conferencename = {6th International Workshop on Theorem proving components for Educational software (ThEdu'17), Gothenburg, Sweden, 6 Aug 2017},
url = {http://dx.doi.org/10.4204/EPTCS.267.8}
}

Rational General Solutions of Systems of First-Order Partial Differential Equations

Georg Grasegger, Alberto Lastra, J. Rafael Sendra, Franz Winkler

Journal of Computational and Applied Mathematics 331, pp. 88-103. 2018. ISSN: 0377-0427.
[bib]
@article{RISC5509,
author = {Georg Grasegger and Alberto Lastra and J. Rafael Sendra and Franz Winkler},
title = {{Rational General Solutions of Systems of First-Order Partial Differential Equations}},
language = {english},
journal = {Journal of Computational and Applied Mathematics},
volume = {331},
pages = {88--103},
isbn_issn = {ISSN: 0377-0427},
year = {2018},
refereed = {yes},
length = {16}
}

Deciding the Existence of Rational General Solutions for First-Order Algebraic ODEs

N.T. Vo, G. Grasegger, F. Winkler

Journal of Symbolic Computation 87, pp. 127-139. 2018. ISSN 0747-7171.
[bib]
@article{RISC5589,
author = {N.T. Vo and G. Grasegger and F. Winkler},
title = {{Deciding the Existence of Rational General Solutions for First-Order Algebraic ODEs}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {87},
pages = {127--139},
isbn_issn = {ISSN 0747-7171},
year = {2018},
refereed = {yes},
length = {12}
}

Construction of all Polynomial Relations among Dedekind Eta Functions of Level $N$

Ralf Hemmecke, Silviu Radu

Technical report no. 18-03 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. January 26 2018. Accepted for publication in the Journal of Symbolic Computation. [pdf]
[bib]
@techreport{RISC5561,
author = {Ralf Hemmecke and Silviu Radu},
title = {{Construction of all Polynomial Relations among Dedekind Eta Functions of Level $N$}},
language = {english},
abstract = {We describe an algorithm that, given a positive integer $N$,computes a Gr\"obner basis of the ideal of polynomial relations among Dedekind$\eta$-functions of level $N$, i.e., among the elements of$\{\eta(\delta_1\tau),\ldots,\eta(\delta_n\tau)\}$ where$1=\delta_1<\delta_2\dots<\delta_n=N$ are the positive divisors of$N$.More precisely, we find a finite generating set (which is also aGr\"obner basis of the ideal $\ker\phi$ where\begin{gather*} \phi:Q[E_1,\ldots,E_n] \to Q[\eta(\delta_1\tau),\ldots,\eta(\delta_n\tau)], \quad E_k\mapsto \eta(\delta_k\tau), \quad k=1,\ldots,n.\end{gather*}},
number = {18-03},
year = {2018},
month = {January 26},
note = {Accepted for publication in the Journal of Symbolic Computation},
keywords = {Dedekind $\eta$ function, modular functions, modular equations, ideal of relations, Groebner basis},
length = {18},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

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