2 Search Results for "Böhm, Stanislav"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.39
Weighted One-Deterministic-Counter Automata

Authors: Prince Mathew, Vincent Penelle, Prakash Saivasan, and A.V. Sreejith

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract
We introduce weighted one-deterministic-counter automata (odca). These are weighted one-counter automata (oca) with the property of counter-determinacy, meaning that all paths labelled by a given word starting from the initial configuration have the same counter-effect. Weighted odcas are a strict extension of weighted visibly ocas, which are weighted ocas where the input alphabet determines the actions on the counter. We present a novel problem called the co-VS (complement to a vector space) reachability problem for weighted odcas over fields, which seeks to determine if there exists a run from a given configuration of a weighted odca to another configuration whose weight vector lies outside a given vector space. We establish two significant properties of witnesses for co-VS reachability: they satisfy a pseudo-pumping lemma, and the lexicographically minimal witness has a special form. It follows that the co-VS reachability problem is in 𝖯. These reachability problems help us to show that the equivalence problem of weighted odcas over fields is in 𝖯 by adapting the equivalence proof of deterministic real-time ocas [Stanislav Böhm and Stefan Göller, 2011] by Böhm et al. This is a step towards resolving the open question of the equivalence problem of weighted ocas. Finally, we demonstrate that the regularity problem, the problem of checking whether an input weighted odca over a field is equivalent to some weighted automaton, is in 𝖯. We also consider boolean odcas and show that the equivalence problem for (non-deterministic) boolean odcas is in PSPACE, whereas it is undecidable for (non-deterministic) boolean ocas.
Cite as

Prince Mathew, Vincent Penelle, Prakash Saivasan, and A.V. Sreejith. Weighted One-Deterministic-Counter Automata. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 39:1-39:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mathew_et_al:LIPIcs.FSTTCS.2023.39,
  author =	{Mathew, Prince and Penelle, Vincent and Saivasan, Prakash and Sreejith, A.V.},
  title =	{{Weighted One-Deterministic-Counter Automata}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{39:1--39:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.39},
  URN =		{urn:nbn:de:0030-drops-194129},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.39},
  annote =	{Keywords: One-counter automata, Equivalence, Weighted automata, Reachability}
}
Document
DOI: 10.4230/LIPIcs.STACS.2017.14
On Büchi One-Counter Automata

Authors: Stanislav Böhm, Stefan Göller, Simon Halfon, and Piotr Hofman

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Abstract
Equivalence of deterministic pushdown automata is a famous problem in theoretical computer science whose decidability has been shown by Sénizergues. Our first result shows that decidability no longer holds when moving from finite words to infinite words. This solves an open problem that has recently been raised by Löding. In fact, we show that already the equivalence problem for deterministic Büchi one-counter automata is undecidable. Hence, the decidability border is rather tight when taking into account a recent result by Löding and Repke that equivalence of deterministic weak parity pushdown automata (a subclass of deterministic Büchi pushdown automata) is decidable. Another known result on finite words is that the universality problem for vector addition systems is decidable. We show undecidability when moving to infinite words. In fact, we prove that already the universality problem for nondeterministic Büchi one-counter nets (or equivalently vector addition systems with one unbounded dimension) is undecidable.
Cite as

Stanislav Böhm, Stefan Göller, Simon Halfon, and Piotr Hofman. On Büchi One-Counter Automata. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 14:1-14:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bohm_et_al:LIPIcs.STACS.2017.14,
  author =	{B\"{o}hm, Stanislav and G\"{o}ller, Stefan and Halfon, Simon and Hofman, Piotr},
  title =	{{On B\"{u}chi One-Counter Automata}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{14:1--14:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.14},
  URN =		{urn:nbn:de:0030-drops-70194},
  doi =		{10.4230/LIPIcs.STACS.2017.14},
  annote =	{Keywords: infinite words, deterministic pushdown automata}
}
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