Rewriting-related Techniques and Applications

We investigate solving methods for equational and membership constraints, generalization techniques in various theories, and calculi for conditional rule-based transformations. The developed algorithms and procedures are useful for equational reasoning, program analysis, and declarative programming. Our research interests also include rewriting-based deduction, models of computation, and computer security.

Rewriting has been playing an important role in symbolic computation and automated deduction. We are interested in fundamental algorithmic problems for rewriting-based techniques as well as in applications of rewriting-related frameworks in programming and reasoning.

Unification and matching are fundamental computational techniques for automated reasoning, term rewriting, and declarative programming. Essentially, they can be seen as methods for solving equations between terms. The difficulty of an unification problem depends on many parameters, e.g., the background equational theory, the order of the language, the presence of sorts, the representation of objects, etc. We have been investigating this problem under various combinations of those parameters, developing solving procedures, proving their properties, providing prototype implementations, identifying well-behaved special cases, and studying practical applications. Some of those algorithms have been included in the mathematical assistant system Theorema and in the rule-based programming tool PρLog. See also the Web page of the SToUT project.

Anti-unification is yet another fundamental technique originating from inductive reasoning. Its goal is to find an object which generalizes the given objects: retaining similarities between them as much as possible, and abstracting over the differences by variables. Unification and anti-unification are considered as dual methods in the following sense: solutions of an unification problem give most general common instance of the given expressions, while anti-unification computes their least general common generalization. We are interested in designing new anti-unification algorithms for various first- and higher-order theories, proving their properties, investigating complexity, providing implementations, and applying them in software code clone detection, program synthesis, and natural language processing. We have been developing an open-source online library of unification and anti-unification algorithms. See also the Web page of the GALA project.

We have contributed in the development of a calculus for conditional sequence transformations by strategies, called ρLog, which forms the theoretical basis of the rule-based programming tool PρLog. It deals with term sequences (also called hedges), transforming them by conditional rules. Transformations are nondeterministic and may yield several results. Strategies provide a control on rule applications in a declarative way. The transformation rules are combined with logic programming. See more details on the PρLog Web page.

Our other interests include equational reasoning, pattern calculi, and runtime verification. See the publication list below for relevant references.

Members

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Ongoing Projects

Software

Unification and Anti-Unification Algorithm Library

This library contains unification, matching, and anti-unification algorithms in various theories developed at RISC. Unification with sequence variables. Context sequence matching. Rigid anti-unification for unranked terms and hedges and its experimental extension with commutative symbols. Unranked second-order anti-unification and its ...

Authors: Teimuraz Kutsia, Alexander Baumgartner, David Cerna
MoreSoftware Website

Publications

2023

[Cerna]

Anti-unification and Generalization: a Survey

David Cerna, Temur Kutsia

In: Proceedings of IJCAI 2023 - 32nd International Joint Conference on Artifical Intelligence, Edith Elkind (ed.), pp. 6563-6573. 2023. ijcai.org, ISBN 978-1-956792-03-4 . [doi]
[bib]
@inproceedings{RISC6743,
author = {David Cerna and Temur Kutsia},
title = {{Anti-unification and Generalization: a Survey}},
booktitle = {{Proceedings of IJCAI 2023 - 32nd International Joint Conference on Artifical Intelligence}},
language = {english},
pages = {6563--6573},
publisher = {ijcai.org},
isbn_issn = {ISBN 978-1-956792-03-4 },
year = {2023},
editor = {Edith Elkind},
refereed = {yes},
length = {11},
url = {https://doi.org/10.24963/ijcai.2023/736}
}
[Kutsia]

Nominal AC-Matching

Mauricio Ayala-Rincón, Maribel Fernández, Gabriel Ferreira Silva, Temur Kutsia, and Daniele Nantes-Sobrinho

In: Proceedings of the 16th International Conference on Intelligent Computer Mathematics, CICM 2023, Catherine Dubois and Manfred Kerber (ed.), Lecture Notes in Aritificial Intelligence 14101, pp. 53-68. 2023. Springer, ISBN 978-3-031-42752-7. [doi]
[bib]
@inproceedings{RISC6744,
author = {Mauricio Ayala-Rincón and Maribel Fernández and Gabriel Ferreira Silva and Temur Kutsia and and Daniele Nantes-Sobrinho},
title = {{Nominal AC-Matching}},
booktitle = {{Proceedings of the 16th International Conference on Intelligent Computer Mathematics, CICM 2023}},
language = {english},
series = {Lecture Notes in Aritificial Intelligence},
volume = {14101},
pages = {53--68},
publisher = {Springer},
isbn_issn = {ISBN 978-3-031-42752-7},
year = {2023},
editor = {Catherine Dubois and Manfred Kerber},
refereed = {yes},
length = {16},
url = {https://doi.org/10.1007/978-3-031-42753-4_4}
}

2022

[Dundua]

Unranked Nominal Unification

Besik Dundua, Temur Kutsia, Mikheil Rukhaia

In: Proceedings of TbiLLC 2019 - 13th International Tbilisi Symposium on Logic, Language, and Computation, Aybüke Özgün and Yulia Zinova (ed.), Proceedings of 13th International Tbilisi Symposium on Logic, Language, and Computation, Lecture Notes in Computer Science 13206, pp. 279-296. 2022. Springer, ISBN 978-3-030-98478-6. [doi] [pdf]
[bib]
@inproceedings{RISC6498,
author = {Besik Dundua and Temur Kutsia and Mikheil Rukhaia},
title = {{Unranked Nominal Unification}},
booktitle = {{Proceedings of TbiLLC 2019 - 13th International Tbilisi Symposium on Logic, Language, and Computation}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {13206},
pages = {279--296},
publisher = {Springer},
isbn_issn = {ISBN 978-3-030-98478-6},
year = {2022},
editor = {Aybüke Özgün and Yulia Zinova},
refereed = {yes},
length = {17},
conferencename = {13th International Tbilisi Symposium on Logic, Language, and Computation},
url = {https://doi.org/10.1007/978-3-030-98479-3_14}
}
[Kutsia]

Nominal Unification and Matching of Higher Order Expressions with Recursive Let

Manfred Schmidt-Schauß, Temur Kutsia, Jordi Levy, Mateu Villaret, Yunus Kutz

Fundamenta Informaticae 185(3), pp. 247-283. 2022. IOS Press, ISSN 1875-8681. [url]
[bib]
@article{RISC6506,
author = {Manfred Schmidt-Schauß and Temur Kutsia and Jordi Levy and Mateu Villaret and Yunus Kutz},
title = {{Nominal Unification and Matching of Higher Order Expressions with Recursive Let}},
language = {english},
journal = {Fundamenta Informaticae},
volume = {185},
number = {3},
pages = {247--283},
publisher = {IOS Press},
isbn_issn = {ISSN 1875-8681},
year = {2022},
refereed = {yes},
length = {37},
url = {https://arxiv.org/abs/2102.08146v4}
}
[Kutsia]

Work-in-progress papers presented at the 15th Conference on Intelligent Computer Mathematics, CICM 2022 (Informal Proceedings)

Kevin Buzzard and Temur Kutsia

, 2022. [url] [pdf]
[bib]
@techreport{RISC6584,
author = {Kevin Buzzard and Temur Kutsia},
title = {{Work-in-progress papers presented at the 15th Conference on Intelligent Computer Mathematics, CICM 2022 (Informal Proceedings)}},
language = {english},
year = {2022},
institution = { },
length = {77},
url = {https://cicm-conference.org/2022/cicm.php}
}
[Pau]

Matching and Generalization Modulo Proximity and Tolerance Relations

Temur Kutsia, Cleo Pau

In: Proceedings of TbiLLC 2019 - 13th International Tbilisi Symposium on Logic, Language, and Computation, Aybüke Özgün and Yulia Zinova (ed.), Lecture Notes in Computer Science 13206, pp. 323-342. 2022. Springer, ISBN 978-3-030-98478-6. [doi] [pdf]
[bib]
@inproceedings{RISC6491,
author = {Temur Kutsia and Cleo Pau},
title = {{Matching and Generalization Modulo Proximity and Tolerance Relations}},
booktitle = {{Proceedings of TbiLLC 2019 - 13th International Tbilisi Symposium on Logic, Language, and Computation}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {13206},
pages = {323--342},
publisher = {Springer},
isbn_issn = {ISBN 978-3-030-98478-6},
year = {2022},
editor = {Aybüke Özgün and Yulia Zinova},
refereed = {yes},
length = {20},
url = {https://doi.org/10.1007/978-3-030-98479-3_16}
}
[Pau]

A framework for approximate generalization in quantitative theories

Temur Kutsia, Cleo Pau

Technical report no. 22-04 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). May 2022. Licensed under CC BY 4.0 International. [doi] [pdf]
[bib]
@techreport{RISC6505,
author = {Temur Kutsia and Cleo Pau},
title = {{A framework for approximate generalization in quantitative theories}},
language = {english},
abstract = {Anti-unification aims at computing generalizations for given terms, retaining their common structure and abstracting differences by variables. We study quantitative anti-unification where the notion of the common structure is relaxed into "proximal'' up to the given degree with respect to the given fuzzy proximity relation. Proximal symbols may have different names and arities. We develop a generic set of rules for computing minimal complete sets of approximate generalizations and study their properties. Depending on the characterizations of proximities between symbols and the desired forms of solutions, these rules give rise to different versions of concrete algorithms.},
number = {22-04},
year = {2022},
month = {May},
keywords = {Generalization, anti-unification, quantiative theories, fuzzy proximity relations},
length = {22},
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)}
}
[Pau]

Symbolic Techniques for Approximate Reasoning

Cleo Pau

RISC, JKU. PhD Thesis. 2022. [pdf]
[bib]
@phdthesis{RISC6513,
author = {Cleo Pau},
title = {{Symbolic Techniques for Approximate Reasoning}},
language = {english},
year = {2022},
translation = {0},
school = {RISC, JKU},
length = {202}
}
[Pau]

A Framework for Approximate Generalization in Quantitative Theories

Temur Kutsia and Cleo Pau

In: Automated Reasoning, Jasmin Blanchette, Laura Kovács, and Dirk Pattinson (ed.), Proceedings of 11th International Joint Conference, IJCAR 2022, Haifa, Israel, August 8-10, 2022, Lecture Notes in Artificial Intelligence 13385, pp. 578-596. 2022. Springer, ISBN 978-3-031-10768-9. [doi]
[bib]
@inproceedings{RISC6631,
author = {Temur Kutsia and Cleo Pau},
title = {{A Framework for Approximate Generalization in Quantitative Theories}},
booktitle = {{Automated Reasoning}},
language = {english},
series = {Lecture Notes in Artificial Intelligence},
volume = {13385},
pages = {578--596},
publisher = {Springer},
isbn_issn = {ISBN 978-3-031-10768-9},
year = {2022},
editor = {Jasmin Blanchette and Laura Kovács and and Dirk Pattinson},
refereed = {yes},
sponsor = {FWF},
length = {19},
conferencename = {11th International Joint Conference, IJCAR 2022, Haifa, Israel, August 8-10, 2022},
url = {https://doi.org/10.1007/978-3-031-10769-6}
}

2021

[Cerna]

A Special Case of Schematic Syntactic Unification

David M. Cerna

CAS ICS / RISC. Technical report, 2021. [pdf]
[bib]
@techreport{RISC6349,
author = {David M. Cerna},
title = {{A Special Case of Schematic Syntactic Unification}},
language = {english},
abstract = {We present a unification problem based on first-order syntactic unification which ask whether every problemin a schematically-defined sequence of unification problems isunifiable, so called loop unification. Alternatively, our problemmay be formulated as a recursive procedure calling first-ordersyntactic unification on certain bindings occurring in the solvedform resulting from unification. Loop unification is closely relatedto Narrowing as the schematic constructions can be seen as arewrite rule applied during unification, and primal grammars, aswe deal with recursive term constructions. However, loop unifi-cation relaxes the restrictions put on variables as fresh as wellas used extra variables may be introduced by rewriting. In thiswork we consider an important special case, so called semiloopunification. We provide a sufficient condition for unifiability of theentire sequence based on the structure of a sufficiently long initialsegment. It remains an open question whether this conditionis also necessary for semiloop unification and how it may beextended to loop unification.},
year = {2021},
institution = {CAS ICS / RISC},
length = {8}
}
[Dramnesc]

AlCons: Deductive Synthesis of Sorting Algorithms in Theorema

I. Dramnesc, T. Jebelean

In: Theoretical Aspects of Computing - ICTAC 2021, A. Cerone, P. Csaba Ölveczky (ed.), Proceedings of 18th International Colloquium on Theoretical Aspects of Computing - ICTAC, Nur-Sultan, Kazakhstan, LNCS 12819, pp. 314-333. September 2021. Springer, 978-3-030-85315-0. [pdf]
[bib]
@inproceedings{RISC6478,
author = {I. Dramnesc and T. Jebelean},
title = {{AlCons: Deductive Synthesis of Sorting Algorithms in Theorema}},
booktitle = {{Theoretical Aspects of Computing - ICTAC 2021}},
language = {english},
abstract = {We describe the principles and the implementation of AlCons (em Algorithm Constructor), a system for the automatic proof--based synthesis of sorting algorithms on lists and on binary trees, in the frame of the Theorema system. The core of the system is a dedicated prover based on specific inference rules and strategies for constructive proofs over the domains of lists and of binary trees, aimed at the automatic synthesis of sorting algorithms and their auxiliary functions from logical specifications. The specific distinctive feature of our approach is the use of multisets for expressing the fact that two lists (trees) have the same elements. This allows a more natural expression of the properties related to sorting, compared to the classical approach using the permutation relation (a list is a permutation of another). Moreover, the use of multisets leads to special inference rules and strategies which make the proofs more efficient, as for instance: expand/compress multiset terms and solve meta-variables using multiset equalities. Additionally we use a Noetherian induction strategy based on the relation induced by the strict inclusion of multisets, which facilitates the synthesis of arbitrary recursion structures, without having to indicate the recursion schemes in advance. The necessary auxiliary algorithms (like, e.g., for insertion and merging) are generated by the same principles from the synthesis conjectures that are automatically produced during the main proof, using a ``cascading" method, which in fact contributes to the automation of theory exploration. The prover is implemented in the frame of the Theorema system and works in natural style, while the generated algorithms can be immediately tested in the same system.},
series = {LNCS},
volume = {12819},
pages = {314--333},
publisher = {Springer},
isbn_issn = {978-3-030-85315-0},
year = {2021},
month = {September },
editor = {A. Cerone and P. Csaba Ölveczky},
refereed = {yes},
length = {20},
conferencename = {18th International Colloquium on Theoretical Aspects of Computing - ICTAC, Nur-Sultan, Kazakhstan}
}
[Dundua]

Variadic equational matching in associative and commutative theories

Besik Dundua, Temur Kutsia, Mircea Marin

Journal of Symbolic Computation 106, pp. 78-109. 2021. Elsevier, ISSN 0747-7171. [doi] [pdf]
[bib]
@article{RISC6260,
author = {Besik Dundua and Temur Kutsia and Mircea Marin},
title = {{Variadic equational matching in associative and commutative theories}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {106},
pages = {78--109},
publisher = {Elsevier},
isbn_issn = {ISSN 0747-7171},
year = {2021},
refereed = {yes},
length = {32},
url = {https://doi.org/10.1016/j.jsc.2021.01.001}
}
[Kutsia]

9th International Symposium on Symbolic Computation in Software Science (SCSS 2021), short and work-in-progress papers

Temur Kutsia (editor)

Technical report no. 21-16 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). August 2021. Licensed under CC BY 4.0 International. [doi] [pdf]
[bib]
@techreport{RISC6359,
author = {Temur Kutsia (editor)},
title = {{9th International Symposium on Symbolic Computation in Software Science (SCSS 2021), short and work-in-progress papers}},
language = {english},
abstract = {This collection contains short and work-in-progress papers presented at the 9th International Symposium on Symbolic Computation in Software Science, SCSS 2021.},
number = {21-16},
year = {2021},
month = {August},
keywords = {Symbolic computation, software science, artificial intelligence},
length = {56},
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)}
}
[Pau]

Proximity-Based Unification and Matching for Full Fuzzy Signatures

Temur Kutsia, Cleo Pau

Technical report no. 21-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). April 2021. [doi] [pdf]
[bib]
@techreport{RISC6296,
author = {Temur Kutsia and Cleo Pau},
title = {{Proximity-Based Unification and Matching for Full Fuzzy Signatures}},
language = {english},
abstract = {Proximity relations are binary fuzzy relations, which are reflexiveand symmetric, but not transitive. We propose proximity-based unification and matching algorithms in fuzzy languages whose signaturestolerate mismatches in function symbol names, arity, and in the arguments order (so called full fuzzy signatures). This work generalizeson the one hand, proximity-based unification to full fuzzy signatures,and on the other hand, similarity-based unification over a full fuzzysignature by extending similarity to proximity.},
number = {21-08},
year = {2021},
month = {April},
keywords = {Fuzzy proximity relations, Unification Matching, Arity mismatch},
length = {15},
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)}
}
[Pau]

Generalization Algorithms with Proximity Relations in Full Fuzzy Signatures

Temur Kutsia, Cleo Pau

Technical report no. 21-09 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). April 2021. [doi] [pdf]
[bib]
@techreport{RISC6297,
author = {Temur Kutsia and Cleo Pau},
title = {{Generalization Algorithms with Proximity Relations in Full Fuzzy Signatures}},
language = {english},
abstract = {Anti-unification aims at computing generalizations for given terms,retaining their common structure and abstracting differences by variables. We study anti-unification for full fuzzy signatures, where thenotion of common structure is relaxed into a ``proximal'' one with re-spect to a given proximity relation. Mismatches between both symbolnames and their arities are permitted. We develop algorithms for different cases of the problem and study their properties.},
number = {21-09},
year = {2021},
month = {April},
keywords = {Fuzzy proximity relations, Generalization, Anti-unification, Arity mismatch},
length = {15},
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)}
}
[Pau]

Proximity-Based Unification and Matching for Fully Fuzzy Signatures

Cleo Pau, Temur Kutsia

In: Proceedings of the 30th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2021, , pp. 1-6. 2021. IEEE, isbn 978-1-6654-4407-1. [doi] [pdf]
[bib]
@inproceedings{RISC6369,
author = {Cleo Pau and Temur Kutsia},
title = {{Proximity-Based Unification and Matching for Fully Fuzzy Signatures}},
booktitle = {{Proceedings of the 30th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2021}},
language = {english},
pages = {1--6},
publisher = {IEEE},
isbn_issn = {isbn 978-1-6654-4407-1},
year = {2021},
editor = { },
refereed = {yes},
length = {6},
url = {https://doi.org/10.1109/FUZZ45933.2021.9494438}
}

2020

[Cerna]

Idempotent Anti-unification

David Cerna, Temur Kutsia

ACM Transactions on Computational Logic (TOCL) 21(2), pp. 10:1-10:32. 2020. ACM Press, ISSN 1529-3785. [doi] [pdf]
[bib]
@article{RISC6023,
author = {David Cerna and Temur Kutsia},
title = {{Idempotent Anti-unification}},
language = {english},
journal = {ACM Transactions on Computational Logic (TOCL)},
volume = {21},
number = {2},
pages = {10:1--10:32},
publisher = {ACM Press},
isbn_issn = {ISSN 1529-3785},
year = {2020},
refereed = {yes},
length = {32},
url = {https://doi.org/10.1145/3359060}
}
[Cerna]

Unital Anti-Unification: Type and Algorithms

David M. Cerna, Temur Kutsia

In: Proceedings of the 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020), Zena M. Ariola (ed.), Leibniz International Proceedings in Informatics (LIPIcs) 167, pp. 26:1-26:20. 2020. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, ISBN 978-3-95977-155-9, ISSN 1868-8969. [url]
[bib]
@inproceedings{RISC6132,
author = {David M. Cerna and Temur Kutsia},
title = {{Unital Anti-Unification: Type and Algorithms}},
booktitle = {{Proceedings of the 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)}},
language = {english},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {167},
pages = {26:1--26:20},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum für Informatik},
isbn_issn = {ISBN 978-3-95977-155-9, ISSN 1868-8969},
year = {2020},
editor = {Zena M. Ariola},
refereed = {yes},
length = {20},
url = {https://drops.dagstuhl.de/opus/volltexte/2020/12352/}
}
[Cerna]

Higher-order pattern generalization modulo equational theories

David M. Cerna, Temur Kutsia

Mathematical Structures in Computer Science 30(6), pp. 627-663. 2020. ISSN 0960-1295. [url]
[bib]
@article{RISC6226,
author = {David M. Cerna and Temur Kutsia},
title = {{Higher-order pattern generalization modulo equational theories}},
language = {english},
journal = {Mathematical Structures in Computer Science},
volume = {30},
number = {6},
pages = {627--663},
isbn_issn = {ISSN 0960-1295},
year = {2020},
refereed = {yes},
length = {37},
url = {https://www.cambridge.org/core/services/aop-cambridge-core/content/view/88E26F155F0FD02B3EDD648971D9AD1B/S0960129520000110a.pdf/higher-order-pattern-generalization-modulo-equational-theories.pdf}
}
[Cerna]

Anti-unification and the Theory of Semirings

David M. Cerna

Theor. Comput. Sci. 848, pp. 133-139. 2020. RISC / CAS ICS, 0304-3975. [doi]
[bib]
@article{RISC6234,
author = {David M. Cerna},
title = {{Anti-unification and the Theory of Semirings}},
language = {english},
abstract = {It was recently shown that anti-unification over an equational theory consisting of only unitequations (more than one) is nullary. Such pure theories are artificial and are of little effect onpractical aspects of anti-unification. In this work, we extend these nullarity results to the theory ofsemirings, a heavily studied theory with many practical applications. Furthermore, our argumentholds over semirings with commutative multiplication and/or idempotent addition. We also cover afew open questions discussed in previous work.},
journal = {Theor. Comput. Sci.},
volume = {848},
pages = {133--139},
isbn_issn = {0304-3975},
year = {2020},
refereed = {yes},
institution = {RISC / CAS ICS},
length = {7},
url = {https://doi.org/10.1016/j.tcs.2020.10.020}
}

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