3 Search Results for "Ko, Sang-Ki"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.12
Explorability in Pushdown Automata

Authors: Ayaan Bedi and Karoliina Lehtinen

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We study explorability, a measure of nondeterminism in pushdown automata, which generalises history-determinism. An automaton is k-explorable if, while reading the input, it suffices to follow k concurrent runs, built step-by-step based only on the input seen so far, to construct an accepting one, if it exists. We show that the class of explorable PDAs lies strictly between history-deterministic and fully nondeterministic PDAs in terms of both expressiveness and succinctness. In fact increasing explorability induces an infinite hierarchy: each level k defines a strictly more expressive class than level k-1, yet the entire class remains less expressive than general nondeterministic PDAs. We then introduce a parameterized notion of explorability, where the number of runs may depend on input length, and show that exponential explorability precisely captures the context-free languages. Finally, we prove that explorable PDAs can be doubly exponentially more succinct than history-deterministic ones, and that the succinctness gap between deterministic and 2-explorable PDAs is not recursively enumerable. These results position explorability as a robust and operationally meaningful measure of nondeterminism for pushdown systems.
Cite as

Ayaan Bedi and Karoliina Lehtinen. Explorability in Pushdown Automata. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bedi_et_al:LIPIcs.FSTTCS.2025.12,
  author =	{Bedi, Ayaan and Lehtinen, Karoliina},
  title =	{{Explorability in Pushdown Automata}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.12},
  URN =		{urn:nbn:de:0030-drops-250921},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.12},
  annote =	{Keywords: Pushdown automata, nondeterminism, explorability, history-determinism}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.60
Simon’s Congruence Pattern Matching

Authors: Sungmin Kim, Sang-Ki Ko, and Yo-Sub Han

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
Testing Simon’s congruence asks whether two strings have the same set of subsequences of length no greater than a given integer. In the light of the recent discovery of an optimal linear algorithm for testing Simon’s congruence, we solve the Simon’s congruence pattern matching problem. The problem requires finding all substrings of a text that are congruent to a pattern under the Simon’s congruence. Our algorithm efficiently solves the problem in linear time in the length of the text by reusing results from previous computations with the help of new data structures called X-trees and Y-trees. Moreover, we define and solve variants of the Simon’s congruence pattern matching problem. They require finding the longest and shortest substring of the text as well as the shortest subsequence of the text which is congruent to the pattern under the Simon’s congruence. Two more variants which ask for the longest congruent subsequence of the text and optimizing the pattern matching problem are left as open problems.
Cite as

Sungmin Kim, Sang-Ki Ko, and Yo-Sub Han. Simon’s Congruence Pattern Matching. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 60:1-60:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kim_et_al:LIPIcs.ISAAC.2022.60,
  author =	{Kim, Sungmin and Ko, Sang-Ki and Han, Yo-Sub},
  title =	{{Simon’s Congruence Pattern Matching}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{60:1--60:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.60},
  URN =		{urn:nbn:de:0030-drops-173456},
  doi =		{10.4230/LIPIcs.ISAAC.2022.60},
  annote =	{Keywords: pattern matching, Simon’s congruence, string algorithm, data structure}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.132
On the Identity Problem for the Special Linear Group and the Heisenberg Group

Authors: Sang-Ki Ko, Reino Niskanen, and Igor Potapov

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We study the identity problem for matrices, i.e., whether the identity matrix is in a semigroup generated by a given set of generators. In particular we consider the identity problem for the special linear group following recent NP-completeness result for SL(2,Z) and the undecidability for SL(4,Z) generated by 48 matrices. First we show that there is no embedding from pairs of words into 3 x3 integer matrices with determinant one, i.e., into SL{(3,Z)} extending previously known result that there is no embedding into C^{2 x 2}. Apart from theoretical importance of the result it can be seen as a strong evidence that the computational problems in SL{(3,Z)} are decidable. The result excludes the most natural possibility of encoding the Post correspondence problem into SL{(3,Z)}, where the matrix products extended by the right multiplication correspond to the Turing machine simulation. Then we show that the identity problem is decidable in polynomial time for an important subgroup of SL(3,Z), the Heisenberg group H(3,Z). Furthermore, we extend the decidability result for H(n,Q) in any dimension n. Finally we are tightening the gap on decidability question for this long standing open problem by improving the undecidability result for the identity problem in SL{(4,Z)} substantially reducing the bound on the size of the generator set from 48 to 8 by developing a novel reduction technique.
Cite as

Sang-Ki Ko, Reino Niskanen, and Igor Potapov. On the Identity Problem for the Special Linear Group and the Heisenberg Group. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 132:1-132:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ko_et_al:LIPIcs.ICALP.2018.132,
  author =	{Ko, Sang-Ki and Niskanen, Reino and Potapov, Igor},
  title =	{{On the Identity Problem for the Special Linear Group and the Heisenberg Group}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{132:1--132:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.132},
  URN =		{urn:nbn:de:0030-drops-91367},
  doi =		{10.4230/LIPIcs.ICALP.2018.132},
  annote =	{Keywords: matrix semigroup, identity problem, special linear group, Heisenberg group, decidability}
}
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