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.

Software

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 ...

MoreSoftware Website

Publications

2018

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}
}

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}
}

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}
}

Gröbner Bases of Modules and Faugère's F4 Algorithm in Isabelle/HOL

A. Maletzky, F. Immler

In: Intelligent Computer Mathematics (Proceedings of CICM 2018, Hagenberg, Austria, August 13-17), Florian Rabe and William Farmer and Grant Passmore and Abdou Youssef (ed.), Proceedings of CICM 2018, Lecture Notes in Computer Science 11006, pp. 178-193. 2018. Springer, ISBN 978-3-319-96811-7. The final publication is available at Springer via https://doi.org/10.1007/978-3-319-96812-4_16. [url]
[bib]
@inproceedings{RISC5733,
author = {A. Maletzky and F. Immler},
title = {{Gröbner Bases of Modules and Faugère's F4 Algorithm in Isabelle/HOL}},
booktitle = {{Intelligent Computer Mathematics (Proceedings of CICM 2018, Hagenberg, Austria, August 13-17)}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {11006},
pages = {178--193},
publisher = {Springer},
isbn_issn = {ISBN 978-3-319-96811-7},
year = {2018},
note = {The final publication is available at Springer via https://doi.org/10.1007/978-3-319-96812-4_16},
editor = {Florian Rabe and William Farmer and Grant Passmore and Abdou Youssef},
refereed = {yes},
length = {16},
conferencename = {CICM 2018},
url = {https://doi.org/10.1007/978-3-319-96812-4_16}
}

Proximity-Based Generalization

Temur Kutsia, Cleo Pau

In: 32nd International Workshop on Unification, UNIF 2018, Mauricio Ayala-Rincon and Philippe Balbiani (ed.), pp. - . 2018. [pdf]
[bib]
@inproceedings{RISC5713,
author = {Temur Kutsia and Cleo Pau},
title = {{Proximity-Based Generalization}},
booktitle = {{32nd International Workshop on Unification, UNIF 2018}},
language = {english},
pages = { -- },
isbn_issn = { },
year = {2018},
editor = {Mauricio Ayala-Rincon and Philippe Balbiani},
refereed = {yes},
length = {0}
}

2017

Unranked Second-Order Anti-Unification

Alexander Baumgartner, Temur Kutsia

Information and Computation 255(2), pp. 262-286. 2017. ISSN: 0890-5401. [url]
[bib]
@article{RISC5192,
author = {Alexander Baumgartner and Temur Kutsia},
title = {{Unranked Second-Order Anti-Unification}},
language = {english},
journal = {Information and Computation},
volume = {255},
number = {2},
pages = {262--286},
isbn_issn = {ISSN: 0890-5401},
year = {2017},
refereed = {yes},
length = {25},
url = {http://doi.org/10.1016/j.ic.2017.01.005}
}

Higher-Order Pattern Anti-Unification in Linear Time

Alexander Baumgartner, Temur Kutsia, Jordi Levy, Mateu Villaret

Journal of Automated Reasoning 58(2), pp. 293-310. 2017. ISSN 0168-7433. [url]
[bib]
@article{RISC5337,
author = {Alexander Baumgartner and Temur Kutsia and Jordi Levy and Mateu Villaret},
title = {{Higher-Order Pattern Anti-Unification in Linear Time}},
language = {english},
journal = { Journal of Automated Reasoning},
volume = {58},
number = {2},
pages = {293--310},
isbn_issn = {ISSN 0168-7433},
year = {2017},
refereed = {yes},
length = {18},
url = {http://dx.doi.org/10.1007/s10817-016-9383-3}
}

Gröbner Bases Computation by Triangularizing Macaulay Matrices

Bruno Buchberger

Advanced Studies in Pure Mathematics (The 50th Anniversary of Gröbner Bases) 75, pp. 1-9. 2017. Mathematical Society of Japan, 0.
[bib]
@article{RISC5586,
author = {Bruno Buchberger},
title = {{Gröbner Bases Computation by Triangularizing Macaulay Matrices}},
language = {english},
journal = {Advanced Studies in Pure Mathematics (The 50th Anniversary of Gröbner Bases)},
volume = {75},
pages = {1--9},
publisher = {Mathematical Society of Japan},
isbn_issn = {0},
year = {2017},
refereed = {no},
length = {9}
}

Satisfiability Checking and Symbolic Computation

Abraham Erika , Abbott John , Becker Bernd , Bigatti Anna Maria , Brain Martin , Buchberger Bruno , Cimatti Alessandro , Davenport James , England Matthew , Fontaine Pascal , Forrest Stephen , Griggio Alberto , Kröning Daniel , Seiler Werner M. , Sturm

ACM Communications in Computer Algebra 50(4), pp. 145-147. 2017. 0.
[bib]
@article{RISC5587,
author = { Abraham Erika and Abbott John and Becker Bernd and Bigatti Anna Maria and Brain Martin and Buchberger Bruno and Cimatti Alessandro and Davenport James and England Matthew and Fontaine Pascal and Forrest Stephen and Griggio Alberto and Kröning Daniel and Seiler Werner M. and Sturm },
title = {{Satisfiability Checking and Symbolic Computation}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {50},
number = {4},
pages = {145--147},
isbn_issn = {0},
year = {2017},
refereed = {no},
length = {3}
}

An overview of PρLog

Besik Dundua, Temur Kutsia, Klaus Reisenberger-Hagmayr

In: Proceedings of the 19th International Symposium on Practical Aspects of Declarative Languages, PADL 2017, Y. Lierler and W. Taha (ed.), Lecture Notes in Computer Science 10137, pp. 34-49. 2017. Springer, ISBN 978-3-319-51675-2. [pdf]
[bib]
@inproceedings{RISC5416,
author = {Besik Dundua and Temur Kutsia and Klaus Reisenberger-Hagmayr},
title = {{An overview of PρLog}},
booktitle = {{ Proceedings of the 19th International Symposium on Practical Aspects of Declarative Languages, PADL 2017}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {10137},
pages = {34--49},
publisher = {Springer},
isbn_issn = {ISBN 978-3-319-51675-2},
year = {2017},
editor = {Y. Lierler and W. Taha},
refereed = {yes},
length = {16}
}

Rewriting Logic from a ρLog Point of View

Mauricio Ayala-Rincon, Besik Dundua, Temur Kutsia, Mircea Marin

In: Proceedings of the 12th Workshop on Logical and Semantic Frameworks with Applications (LSFA 2017) , Sandra Alves and Renata Wasserman (ed.), pp. -. 2017. [pdf]
[bib]
@inproceedings{RISC5473,
author = {Mauricio Ayala-Rincon and Besik Dundua and Temur Kutsia and Mircea Marin},
title = {{Rewriting Logic from a ρLog Point of View}},
booktitle = {{Proceedings of the 12th Workshop on Logical and Semantic Frameworks with Applications (LSFA 2017) }},
language = {english},
pages = {--},
isbn_issn = { },
year = {2017},
editor = {Sandra Alves and Renata Wasserman},
refereed = {yes},
length = {16}
}

Pattern-Based Calculi with Finitary Matching

Sandra Alves, Besik Dundua, Mario Florido, Temur Kutsia

Logic Journal of the IGPL, pp. -. 2017. Oxford University Press, ISSN 1367-0751. To appear. [url]
[bib]
@article{RISC5517,
author = {Sandra Alves and Besik Dundua and Mario Florido and Temur Kutsia},
title = {{Pattern-Based Calculi with Finitary Matching}},
language = {english},
journal = {Logic Journal of the IGPL},
pages = {--},
publisher = {Oxford University Press},
isbn_issn = {ISSN 1367-0751},
year = {2017},
note = {To appear},
refereed = {yes},
length = {41},
url = {https://doi.org/10.1093/JIGPAL/jzx059}
}

Adapting Cylindrical Algebraic Decomposition for Proof Specific Tasks

E. Abraham, T. Jebelean

In: ICAI 2017: 10th International Conference on Applied Informatics, G. Kusper (ed.), Proceedings of ICAI 2017: 10th International Conference on Applied Informatics, pp. 0-0. 2017. ISBN 0. In print. [url] [pdf]
[bib]
@inproceedings{RISC5546,
author = {E. Abraham and T. Jebelean},
title = {{Adapting Cylindrical Algebraic Decomposition for Proof Specific Tasks}},
booktitle = {{ICAI 2017: 10th International Conference on Applied Informatics}},
language = {English},
abstract = {We develop a case study on using quantifier elimination and cylindrical algebraic decomposition for the purpose of finding specific terms for the automation of proving mathematical properties in elementary analysis.Real--life proofs in specific mathematical domains are difficult to automate because of the high number of assumptions necessary for the prover to succeed. In particular, in elementary analysis, it is allmost impossible to find automatically the appropriate terms for the instantiation of universal assumptions and for witnessing the existential goals. We aim at developing such proofs in natural style, in the frame of the{\em Theorema} system.Finding such terms is actually possible by using quantifier elimination (QE) based on cylindrical algebraic decomposition (CAD). However, the current straightforward approach lacks in efficiency, because several redundant calls may be necessary, and because the nature of the problem is slightly different.We study some natural--style proofs, the necessary special terms, and the corresponding usage of the QE/CAD, and identify specific techniques for adapting these algorithms in order to increase their efficiency.The experiments are performed partially in {\em Mathematica} and partially in {\tt SMT-RAT}, the latter used as ``white--box'', which allows to inspect the intermediate results and to adapt certain parts of the algorithms.},
pages = {0--0},
isbn_issn = {ISBN 0},
year = {2017},
note = {In print},
editor = {G. Kusper},
refereed = {yes},
length = {0},
conferencename = {ICAI 2017: 10th International Conference on Applied Informatics},
url = {https://icai.uni-eszterhazy.hu/}
}

Nominal Unification of Higher Order Expressions with Recursive Let

Manfred Schmidt-Schauss, Temur Kutsia, Jordy Levy, Mateu Villaret

In: Proceedings of the 26th International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR 2016, M. Hermenegildo and P. Lopez-Garcia (ed.), LNCS 10184, pp. 328-344. 2017. Springer, ISBN 978-3-319-63138-7. [pdf]
[bib]
@inproceedings{RISC5438,
author = {Manfred Schmidt-Schauss and Temur Kutsia and Jordy Levy and Mateu Villaret},
title = {{Nominal Unification of Higher Order Expressions with Recursive Let}},
booktitle = {{ Proceedings of the 26th International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR 2016}},
language = {english},
series = {LNCS},
volume = {10184},
pages = {328--344},
publisher = {Springer},
isbn_issn = {ISBN 978-3-319-63138-7},
year = {2017},
editor = {M. Hermenegildo and P. Lopez-Garcia},
refereed = {yes},
length = {17}
}

Mathematical Aspects of Computer and Information Sciences

Johannes Blömer, Ilias Kotsireas, Temur Kutsia, Dimitris E. Simos, editors

Lecture Notes in Computer Science 10693, 2017. Springer, ISBN 978-3-319-72452-2. [url]
[bib]
@booklet{RISC5518,
author = {Johannes Blömer and Ilias Kotsireas and Temur Kutsia and Dimitris E. Simos and editors},
title = {{Mathematical Aspects of Computer and Information Sciences}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {10693},
publisher = {Springer},
isbn_issn = {ISBN 978-3-319-72452-2},
year = {2017},
edition = { },
translation = {0},
length = {462},
url = {https://doi.org/10.1007/978-3-319-72453-9}
}

The Formalization of Vickrey Auctions: A Comparison of Two Approaches in Isabelle and Theorema

A. Maletzky, W. Windsteiger

In: Intelligent Computer Mathematics: 10th International Conference, CICM 2017, Edinburgh, UK, July 17-21, H. Geuvers, M. England, O. Hasan, F. Rabe, O. Teschke (ed.), Lecture Notes in Computer Science 10383, pp. 25-39. 2017. Springer, ISBN 978-3-319-62075-6. doi 10.1007/978-3-319-62075-6_3. [url] [pdf]
[bib]
@inproceedings{RISC4536,
author = {A. Maletzky and W. Windsteiger},
title = {{The Formalization of Vickrey Auctions: A Comparison of Two Approaches in Isabelle and Theorema}},
booktitle = {{Intelligent Computer Mathematics: 10th International Conference, CICM 2017, Edinburgh, UK, July 17-21}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {10383},
pages = {25--39},
publisher = {Springer},
isbn_issn = {ISBN 978-3-319-62075-6},
year = {2017},
note = {doi 10.1007/978-3-319-62075-6_3},
editor = {H. Geuvers and M. England and O. Hasan and F. Rabe and O. Teschke},
refereed = {yes},
length = {15},
url = {https://link.springer.com/chapter/10.1007/978-3-319-62075-6_3}
}

2016

Stam's Identities Collection: A Case Study for Math Knowledge Bases

Bruno Buchberger

In: Mathematical Software - ICMS 2016: 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings, Gert-Martin Greuel, Thorsten Koch, Peter Paule and Andrew Sommese (ed.), pp. 437-442. 2016. Springer International Publishing, Cham, 978-3-319-42432-3. [url] [pdf]
[bib]
@inproceedings{RISC5324,
author = {Bruno Buchberger},
title = {{Stam's Identities Collection: A Case Study for Math Knowledge Bases}},
booktitle = {{Mathematical Software - ICMS 2016: 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings}},
language = {english},
pages = {437--442},
publisher = {Springer International Publishing},
address = {Cham},
isbn_issn = {978-3-319-42432-3},
year = {2016},
editor = {Gert-Martin Greuel and Thorsten Koch and Peter Paule and Andrew Sommese},
refereed = {no},
length = {6},
url = {http://dx.doi.org/10.1007/978-3-319-42432-3_55}
}

The GDML and EuKIM Projects: Short Report on the Initiative

Bruno Buchberger

In: Mathematical Software - ICMS 2016: 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings, Gert-Martin Greuel, Thorsten Koch, Peter Paule and Andrew Sommese (ed.), pp. 443-446. 2016. Springer International Publishing, Cham, 978-3-319-42432-3. [url] [pdf]
[bib]
@inproceedings{RISC5325,
author = {Bruno Buchberger},
title = {{The GDML and EuKIM Projects: Short Report on the Initiative}},
booktitle = {{Mathematical Software - ICMS 2016: 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings}},
language = {english},
pages = {443--446},
publisher = {Springer International Publishing},
address = {Cham},
isbn_issn = {978-3-319-42432-3},
year = {2016},
editor = {Gert-Martin Greuel and Thorsten Koch and Peter Paule and Andrew Sommese},
refereed = {no},
length = {4},
url = {http://dx.doi.org/10.1007/978-3-319-42432-3_56}
}

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