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Documents authored by Yamakami, Tomoyuki

Document
DOI: 10.4230/LIPIcs.MFCS.2020.33
Synchronizing Deterministic Push-Down Automata Can Be Really Hard

Authors: Henning Fernau, Petra Wolf, and Tomoyuki Yamakami

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time. In this paper, we extend this algorithmic question to deterministic automata beyond finite automata. We prove that the question of synchronizability becomes undecidable even when looking at deterministic one-counter automata. This is also true for another classical mild extension of regularity, namely that of deterministic one-turn push-down automata. However, when we combine both restrictions, we arrive at scenarios with a PSPACE-complete (and hence decidable) synchronizability problem. Likewise, we arrive at a decidable synchronizability problem for (partially) blind deterministic counter automata. There are several interpretations of what synchronizability should mean for deterministic push-down automata. This is depending on the role of the stack: should it be empty on synchronization, should it be always the same or is it arbitrary? For the automata classes studied in this paper, the complexity or decidability status of the synchronizability problem is mostly independent of this technicality, but we also discuss one class of automata where this makes a difference.
Cite as

Henning Fernau, Petra Wolf, and Tomoyuki Yamakami. Synchronizing Deterministic Push-Down Automata Can Be Really Hard. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 33:1-33:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fernau_et_al:LIPIcs.MFCS.2020.33,
  author =	{Fernau, Henning and Wolf, Petra and Yamakami, Tomoyuki},
  title =	{{Synchronizing Deterministic Push-Down Automata Can Be Really Hard}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{33:1--33:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.33},
  URN =		{urn:nbn:de:0030-drops-127008},
  doi =		{10.4230/LIPIcs.MFCS.2020.33},
  annote =	{Keywords: Synchronizing automaton, Reset sequence, Real-time deterministic push-down automaton, Finite-turn push-down automaton, Computability, Computational complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.62
The 2CNF Boolean Formula Satisfiability Problem and the Linear Space Hypothesis

Authors: Tomoyuki Yamakami

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
We aim at investigating the solvability/insolvability of nondeterministic logarithmic-space (NL) decision, search, and optimization problems parameterized by size parameters using simultaneously polynomial time and sub-linear space on multi-tape deterministic Turing machines. We are particularly focused on a special NL-complete problem, 2SAT - the 2CNF Boolean formula satisfiability problem-parameterized by the number of Boolean variables. It is shown that 2SAT with n variables and m clauses can be solved simultaneously polynomial time and (n/2^{c sqrt{log(n)}}) polylog(m+n) space for an absolute constant c>0. This fact inspires us to propose a new, practical working hypothesis, called the linear space hypothesis (LSH), which states that 2SAT_3-a restricted variant of 2SAT in which each variable of a given 2CNF formula appears as literals in at most 3 clauses-cannot be solved simultaneously in polynomial time using strictly "sub-linear" (i.e., n^{epsilon} polylog(n) for a certain constant epsilon in (0,1)) space. An immediate consequence of this working hypothesis is L neq NL. Moreover, we use our hypothesis as a plausible basis to lead to the insolvability of various NL search problems as well as the nonapproximability of NL optimization problems. For our investigation, since standard logarithmic-space reductions may no longer preserve polynomial-time sub-linear-space complexity, we need to introduce a new, practical notion of "short reduction." It turns out that overline{2SAT}_3 is complete for a restricted version of NL, called Syntactic NL or simply SNL, under such short reductions. This fact supports the legitimacy of our working hypothesis.
Cite as

Tomoyuki Yamakami. The 2CNF Boolean Formula Satisfiability Problem and the Linear Space Hypothesis. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 62:1-62:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{yamakami:LIPIcs.MFCS.2017.62,
  author =	{Yamakami, Tomoyuki},
  title =	{{The 2CNF Boolean Formula Satisfiability Problem and the Linear Space Hypothesis}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{62:1--62:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.62},
  URN =		{urn:nbn:de:0030-drops-81344},
  doi =		{10.4230/LIPIcs.MFCS.2017.62},
  annote =	{Keywords: sub-linear space, linear space hypothesis, short reduction, Boolean formula satisfiability problem, NL search, NL optimization, Syntactic NL}
}
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