3 Search Results for "Karandikar, Prateek"


Document
Track B: Automata, Logic, Semantics, and Theory of Programming
On the Length of Strongly Monotone Descending Chains over ℕ^d

Authors: Sylvain Schmitz and Lia Schütze

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)


Abstract
A recent breakthrough by Künnemann, Mazowiecki, Schütze, Sinclair-Banks, and Węgrzycki (ICALP 2023) bounds the running time for the coverability problem in d-dimensional vector addition systems under unary encoding to n^{2^{O(d)}}, improving on Rackoff’s n^{2^{O(dlg d)}} upper bound (Theor. Comput. Sci. 1978), and provides conditional matching lower bounds. In this paper, we revisit Lazić and Schmitz' "ideal view" of the backward coverability algorithm (Inform. Comput. 2021) in the light of this breakthrough. We show that the controlled strongly monotone descending chains of downwards-closed sets over ℕ^d that arise from the dual backward coverability algorithm of Lazić and Schmitz on d-dimensional unary vector addition systems also enjoy this tight n^{2^{O(d)}} upper bound on their length, and that this also translates into the same bound on the running time of the backward coverability algorithm. Furthermore, our analysis takes place in a more general setting than that of Lazić and Schmitz, which allows to show the same results and improve on the 2EXPSPACE upper bound derived by Benedikt, Duff, Sharad, and Worrell (LICS 2017) for the coverability problem in invertible affine nets.

Cite as

Sylvain Schmitz and Lia Schütze. On the Length of Strongly Monotone Descending Chains over ℕ^d. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 153:1-153:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{schmitz_et_al:LIPIcs.ICALP.2024.153,
  author =	{Schmitz, Sylvain and Sch\"{u}tze, Lia},
  title =	{{On the Length of Strongly Monotone Descending Chains over \mathbb{N}^d}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{153:1--153:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.153},
  URN =		{urn:nbn:de:0030-drops-202964},
  doi =		{10.4230/LIPIcs.ICALP.2024.153},
  annote =	{Keywords: Vector addition system, coverability, well-quasi-order, order ideal, affine net}
}
Document
The Height of Piecewise-Testable Languages with Applications in Logical Complexity

Authors: Prateek Karandikar and Philippe Schnoebelen

Published in: LIPIcs, Volume 62, 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)


Abstract
The height of a piecewise-testable language L is the maximum length of the words needed to define L by excluding and requiring given subwords. The height of L is an important descriptive complexity measure that has not yet been investigated in a systematic way. This paper develops a series of new techniques for bounding the height of finite languages and of languages obtained by taking closures by subwords, superwords and related operations. As an application of these results, we show that FO^2(A^*, subword), the two-variable fragment of the first-order logic of sequences with the subword ordering, can only express piecewise-testable properties and has elementary complexity.

Cite as

Prateek Karandikar and Philippe Schnoebelen. The Height of Piecewise-Testable Languages with Applications in Logical Complexity. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 37:1-37:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{karandikar_et_al:LIPIcs.CSL.2016.37,
  author =	{Karandikar, Prateek and Schnoebelen, Philippe},
  title =	{{The Height of Piecewise-Testable Languages with Applications in Logical Complexity}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{37:1--37:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Talbot, Jean-Marc and Regnier, Laurent},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2016.37},
  URN =		{urn:nbn:de:0030-drops-65776},
  doi =		{10.4230/LIPIcs.CSL.2016.37},
  annote =	{Keywords: Descriptive complexity}
}
Document
Decidability in the Logic of Subsequences and Supersequences

Authors: Prateek Karandikar and Philippe Schnoebelen

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)


Abstract
We consider first-order logics of sequences ordered by the subsequence ordering, aka sequence embedding. We show that the Sigma_2 theory is undecidable, answering a question left open by Kuske. Regarding fragments with a bounded number of variables, we show that the FO^2 theory is decidable while the FO^3 theory is undecidable.

Cite as

Prateek Karandikar and Philippe Schnoebelen. Decidability in the Logic of Subsequences and Supersequences. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 84-97, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{karandikar_et_al:LIPIcs.FSTTCS.2015.84,
  author =	{Karandikar, Prateek and Schnoebelen, Philippe},
  title =	{{Decidability in the Logic of Subsequences and Supersequences}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{84--97},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.84},
  URN =		{urn:nbn:de:0030-drops-56428},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.84},
  annote =	{Keywords: subsequence, subword, logic, first-order logic, decidability, piecewise- testability, Simon’s congruence}
}
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