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Documents authored by Madhusudan, P.

Found 2 Possible Name Variants:

Madhusudan, P.

Document
DOI: 10.4230/LIPIcs.CSL.2018.31
A Decidable Fragment of Second Order Logic With Applications to Synthesis

Authors: P. Madhusudan, Umang Mathur, Shambwaditya Saha, and Mahesh Viswanathan

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an exists^*forall^* quantifier prefix (over variables, functions and relations) making EQSMT conducive for modeling synthesis problems. Moreover, EQSMT allows reasoning using a combination of background theories provided that they have a decidable satisfiability problem for the exists^*forall^* FO-fragment (e.g., linear arithmetic). Our decision procedure reduces the satisfiability of EQSMT formulae to satisfiability queries of exists^*forall^* formulae of each individual background theory, allowing us to use existing efficient SMT solvers supporting exists^*forall^* reasoning for these theories; hence our procedure can be seen as effectively quantified SMT (EQSMT) reasoning.
Cite as

P. Madhusudan, Umang Mathur, Shambwaditya Saha, and Mahesh Viswanathan. A Decidable Fragment of Second Order Logic With Applications to Synthesis. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{madhusudan_et_al:LIPIcs.CSL.2018.31,
  author =	{Madhusudan, P. and Mathur, Umang and Saha, Shambwaditya and Viswanathan, Mahesh},
  title =	{{A Decidable Fragment of Second Order Logic With Applications to Synthesis}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.31},
  URN =		{urn:nbn:de:0030-drops-96987},
  doi =		{10.4230/LIPIcs.CSL.2018.31},
  annote =	{Keywords: second order logic, synthesis, decidable fragment}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.18
Lagrange's Theorem for Binary Squares

Authors: P. Madhusudan, Dirk Nowotka, Aayush Rajasekaran, and Jeffrey Shallit

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
We show how to prove theorems in additive number theory using a decision procedure based on finite automata. Among other things, we obtain the following analogue of Lagrange's theorem: every natural number > 686 is the sum of at most 4 natural numbers whose canonical base-2 representation is a binary square, that is, a string of the form xx for some block of bits x. Here the number 4 is optimal. While we cannot embed this theorem itself in a decidable theory, we show that stronger lemmas that imply the theorem can be embedded in decidable theories, and show how automated methods can be used to search for these stronger lemmas.
Cite as

P. Madhusudan, Dirk Nowotka, Aayush Rajasekaran, and Jeffrey Shallit. Lagrange's Theorem for Binary Squares. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{madhusudan_et_al:LIPIcs.MFCS.2018.18,
  author =	{Madhusudan, P. and Nowotka, Dirk and Rajasekaran, Aayush and Shallit, Jeffrey},
  title =	{{Lagrange's Theorem for Binary Squares}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.18},
  URN =		{urn:nbn:de:0030-drops-96003},
  doi =		{10.4230/LIPIcs.MFCS.2018.18},
  annote =	{Keywords: binary square, theorem-proving, finite automaton, decision procedure, decidable theory, additive number theory}
}

Madhusudan, Parthasarathy

Document
DOI: 10.4230/LIPIcs.CSL.2011.428
Synthesizing Reactive Programs

Authors: Parthasarathy Madhusudan

Published in: LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011)

Abstract
Current theoretical solutions to the classical Church's synthesis problem are focused on synthesizing transition systems and not programs. Programs are compact and often the true aim in many synthesis problems, while the transition systems that correspond to them are often large and not very useful as synthesized artefacts. Consequently, current practical techniques first synthesize a transition system, and then extract a more compact representation from it. We reformulate the synthesis of reactive systems directly in terms of program synthesis, and develop a theory to show that the problem of synthesizing programs over a fixed set of Boolean variables in a simple imperative programming language is decidable for regular omega-specifications. We also present results for synthesizing programs with recursion against both regular specifications as well as visibly-pushdown language specifications. Finally, we show applications to program repair, and conclude with open problems in synthesizing distributed programs.
Cite as

Parthasarathy Madhusudan. Synthesizing Reactive Programs. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 428-442, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{madhusudan:LIPIcs.CSL.2011.428,
  author =	{Madhusudan, Parthasarathy},
  title =	{{Synthesizing Reactive Programs}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{428--442},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Bezem, Marc},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.428},
  URN =		{urn:nbn:de:0030-drops-32479},
  doi =		{10.4230/LIPIcs.CSL.2011.428},
  annote =	{Keywords: program synthesis, boolean programs, automata theory, temporal logics}
}
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