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Documents authored by Ranzato, Francesco

Document
DOI: 10.4230/LIPIcs.CONCUR.2021.3
Inclusion Testing of Büchi Automata Based on Well-Quasiorders

Authors: Kyveli Doveri, Pierre Ganty, Francesco Parolini, and Francesco Ranzato

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
We introduce an algorithmic framework to decide whether inclusion holds between languages of infinite words over a finite alphabet. Our approach falls within the class of Ramsey-based methods and relies on a least fixpoint characterization of ω-languages leveraging ultimately periodic infinite words of type uv^ω, with u a finite prefix and v a finite period of an infinite word. We put forward an inclusion checking algorithm between Büchi automata, called BAInc, designed as a complete abstract interpretation using a pair of well-quasiorders on finite words. BAInc is quite simple: it consists of two least fixpoint computations (one for prefixes and the other for periods) manipulating finite sets (of pairs) of states compared by set inclusion, so that language inclusion holds when the sets (of pairs) of states of the fixpoints satisfy some basic conditions. We implemented BAInc in a tool called BAIT that we experimentally evaluated against the state-of-the-art. We gathered, in addition to existing benchmarks, a large number of new case studies stemming from program verification and word combinatorics, thereby significantly expanding both the scope and size of the available benchmark set. Our experimental results show that BAIT advances the state-of-the-art on an overwhelming majority of these benchmarks. Finally, we demonstrate the generality of our algorithmic framework by instantiating it to the inclusion problem of Büchi pushdown automata into Büchi automata.
Cite as

Kyveli Doveri, Pierre Ganty, Francesco Parolini, and Francesco Ranzato. Inclusion Testing of Büchi Automata Based on Well-Quasiorders. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{doveri_et_al:LIPIcs.CONCUR.2021.3,
  author =	{Doveri, Kyveli and Ganty, Pierre and Parolini, Francesco and Ranzato, Francesco},
  title =	{{Inclusion Testing of B\"{u}chi Automata Based on Well-Quasiorders}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{3:1--3:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.3},
  URN =		{urn:nbn:de:0030-drops-143802},
  doi =		{10.4230/LIPIcs.CONCUR.2021.3},
  annote =	{Keywords: B\"{u}chi (Pushdown) Automata, \omega-Language Inclusion, Well-quasiorders}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.117
A Rice’s Theorem for Abstract Semantics

Authors: Paolo Baldan, Francesco Ranzato, and Linpeng Zhang

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
Classical results in computability theory, notably Rice’s theorem, focus on the extensional content of programs, namely, on the partial recursive functions that programs compute. Later and more recent work investigated intensional generalisations of such results that take into account the way in which functions are computed, thus affected by the specific programs computing them. In this paper, we single out a novel class of program semantics based on abstract domains of program properties that are able to capture nonextensional aspects of program computations, such as their asymptotic complexity or logical invariants, and allow us to generalise some foundational computability results such as Rice’s Theorem and Kleene’s Second Recursion Theorem to these semantics. In particular, it turns out that for this class of abstract program semantics, any nontrivial abstract property is undecidable and every decidable overapproximation necessarily includes an infinite set of false positives which covers all values of the semantic abstract domain.
Cite as

Paolo Baldan, Francesco Ranzato, and Linpeng Zhang. A Rice’s Theorem for Abstract Semantics. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 117:1-117:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{baldan_et_al:LIPIcs.ICALP.2021.117,
  author =	{Baldan, Paolo and Ranzato, Francesco and Zhang, Linpeng},
  title =	{{A Rice’s Theorem for Abstract Semantics}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{117:1--117:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.117},
  URN =		{urn:nbn:de:0030-drops-141860},
  doi =		{10.4230/LIPIcs.ICALP.2021.117},
  annote =	{Keywords: Computability Theory, Recursive Function, Rice’s Theorem, Kleene’s Second Recursion Theorem, Program Analysis, Affine Program Invariants}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.30
Decidability and Synthesis of Abstract Inductive Invariants

Authors: Francesco Ranzato

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
Decidability and synthesis of inductive invariants ranging in a given domain play an important role in software verification. We consider here inductive invariants belonging to an abstract domain A as defined in abstract interpretation, namely, ensuring the existence of the best approximation in A of any system property. In this setting, we study the decidability of the existence of abstract inductive invariants in A of transition systems and their corresponding algorithmic synthesis. Our model relies on some general results which relate the existence of abstract inductive invariants with least fixed points of best correct approximations in A of the transfer functions of transition systems and their completeness properties. This approach allows us to derive decidability and synthesis results for abstract inductive invariants which are applied to the well-known Karr’s numerical abstract domain of affine equalities. Moreover, we show that a recent general algorithm for synthesizing inductive invariants in domains of logical formulae can be systematically derived from our results and generalized to a range of algorithms for computing abstract inductive invariants.
Cite as

Francesco Ranzato. Decidability and Synthesis of Abstract Inductive Invariants. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 30:1-30:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ranzato:LIPIcs.CONCUR.2020.30,
  author =	{Ranzato, Francesco},
  title =	{{Decidability and Synthesis of Abstract Inductive Invariants}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{30:1--30:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.30},
  URN =		{urn:nbn:de:0030-drops-128429},
  doi =		{10.4230/LIPIcs.CONCUR.2020.30},
  annote =	{Keywords: Inductive invariant, program verification, abstract interpretation}
}
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