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Documents authored by Genet, Thomas

Document
DOI: 10.4230/LIPIcs.FSCD.2023.7
Automata-Based Verification of Relational Properties of Functions over Algebraic Data Structures

Authors: Théo Losekoot, Thomas Genet, and Thomas Jensen

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
This paper is concerned with automatically proving properties about the input-output relation of functional programs operating over algebraic data types. Recent results show how to approximate the image of a functional program using a regular tree language. Though expressive, those techniques cannot prove properties relating the input and the output of a function, e.g., proving that the output of a function reversing a list has the same length as the input list. In this paper, we built upon those results and define a procedure to compute or over-approximate such a relation. Instead of representing the image of a function by a regular set of terms, we represent (an approximation of) the input-output relation by a regular set of tuples of terms. Regular languages of tuples of terms are recognized using a tree automaton recognizing convolutions of terms, where a convolution transforms a tuple of terms into a term built on tuples of symbols. Both the program and the properties are transformed into predicates and Constrained Horn clauses (CHCs). Then, using an Implication Counter Example procedure (ICE), we infer a model of the clauses, associating to each predicate a regular relation. In this ICE procedure, checking if a given model satisfies the clauses is undecidable in general. We overcome undecidability by proposing an incomplete but sound inference procedure for such relational regular properties. Though the procedure is incomplete, its implementation performs well on 120 examples. It efficiently proves non-trivial relational properties or finds counter-examples.
Cite as

Théo Losekoot, Thomas Genet, and Thomas Jensen. Automata-Based Verification of Relational Properties of Functions over Algebraic Data Structures. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{losekoot_et_al:LIPIcs.FSCD.2023.7,
  author =	{Losekoot, Th\'{e}o and Genet, Thomas and Jensen, Thomas},
  title =	{{Automata-Based Verification of Relational Properties of Functions over Algebraic Data Structures}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.7},
  URN =		{urn:nbn:de:0030-drops-179915},
  doi =		{10.4230/LIPIcs.FSCD.2023.7},
  annote =	{Keywords: Formal verification, Tree automata, Constrained Horn Clauses, Model inference, Relational properties, Algebraic datatypes}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2018.16
Completeness of Tree Automata Completion

Authors: Thomas Genet

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)

Abstract
We consider rewriting of a regular language with a left-linear term rewriting system. We show a completeness theorem on equational tree automata completion stating that, if there exists a regular over-approximation of the set of reachable terms, then equational completion can compute it (or safely under-approximate it). A nice corollary of this theorem is that, if the set of reachable terms is regular, then equational completion can also compute it. This was known to be true for some term rewriting system classes preserving regularity, but was still an open question in the general case. The proof is not constructive because it depends on the regularity of the set of reachable terms, which is undecidable. To carry out those proofs we generalize and improve two results of completion: the Termination and the Upper-Bound theorems. Those theoretical results provide an algorithmic way to safely explore regular approximations with completion. This has been implemented in Timbuk and used to verify safety properties, automatically and efficiently, on first-order and higher-order functional programs.
Cite as

Thomas Genet. Completeness of Tree Automata Completion. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{genet:LIPIcs.FSCD.2018.16,
  author =	{Genet, Thomas},
  title =	{{Completeness of Tree Automata Completion}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{16:1--16:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.16},
  URN =		{urn:nbn:de:0030-drops-91868},
  doi =		{10.4230/LIPIcs.FSCD.2018.16},
  annote =	{Keywords: term rewriting systems, regularity preservation, over-approximation, completeness, tree automata, tree automata completion}
}
Document
DOI: 10.4230/LIPIcs.RTA.2015.177
Reachability Analysis of Innermost Rewriting

Authors: Thomas Genet and Yann Salmon

Published in: LIPIcs, Volume 36, 26th International Conference on Rewriting Techniques and Applications (RTA 2015)

Abstract
We consider the problem of inferring a grammar describing the output of a functional program given a grammar describing its input. Solutions to this problem are helpful for detecting bugs or proving safety properties of functional programs and, several rewriting tools exist for solving this problem. However, known grammar inference techniques are not able to take evaluation strategies of the program into account. This yields very imprecise results when the evaluation strategy matters. In this work, we adapt the Tree Automata Completion algorithm to approximate accurately the set of terms reachable by rewriting under the innermost strategy. We prove that the proposed technique is sound and precise w.r.t. innermost rewriting. The proposed algorithm has been implemented in the Timbuk reachability tool. Experiments show that it noticeably improves the accuracy of static analysis for functional programs using the call-by-value evaluation strategy.
Cite as

Thomas Genet and Yann Salmon. Reachability Analysis of Innermost Rewriting. In 26th International Conference on Rewriting Techniques and Applications (RTA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 36, pp. 177-193, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{genet_et_al:LIPIcs.RTA.2015.177,
  author =	{Genet, Thomas and Salmon, Yann},
  title =	{{Reachability Analysis of Innermost Rewriting}},
  booktitle =	{26th International Conference on Rewriting Techniques and Applications (RTA 2015)},
  pages =	{177--193},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-85-9},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{36},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2015.177},
  URN =		{urn:nbn:de:0030-drops-51968},
  doi =		{10.4230/LIPIcs.RTA.2015.177},
  annote =	{Keywords: term rewriting systems, strategy, innermost strategy, tree automata, functiona l program, static analysis}
}
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