6 Search Results for "Terauchi, Tachio"

Document
DOI: 10.4230/LIPIcs.CPM.2026.11
Matching Regular-Typed Pattern Languages: Quadratic-Time Algorithms

Authors: Yuya Uezato

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract
Pattern languages (PAT) are a class of languages generated by expressions called patterns that may contain variables. In a pattern, each variable can be instantiated with an arbitrary string. Typed pattern languages extend PAT by associating a type (constraint) with each variable that restricts the domain of allowed substitutions. In this paper, we study regular-typed PAT (PATwRT), where all types are represented either by a regular expression or by an ε-NFA. We consider the PATwRT matching problem for patterns with a single repeated variable of the form P = α₁ β α₂ β ⋯ β α_K. We present simple algorithms whose running time is linear in K and quadratic in the input length N, with polynomial dependence on the sizes of the type representations. Our results extend previous quadratic-time work in two directions: (1) the quadratic-time algorithm for untyped PAT of Fernau et al. (STACS 2015), and (2) the quadratic-time algorithm for the restricted PATwRT K = 3, i.e., α₁ β α₂ β α₃ of Nogami and Terauchi (MFCS 2025).
Cite as

Yuya Uezato. Matching Regular-Typed Pattern Languages: Quadratic-Time Algorithms. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{uezato:LIPIcs.CPM.2026.11,
  author =	{Uezato, Yuya},
  title =	{{Matching Regular-Typed Pattern Languages: Quadratic-Time Algorithms}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.11},
  URN =		{urn:nbn:de:0030-drops-259374},
  doi =		{10.4230/LIPIcs.CPM.2026.11},
  annote =	{Keywords: Pattern languages, Regular expressions, String algorithms}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.45
Reasoning About Quality in Hyperproperties

Authors: Samuel Graepler, Benjamin Monmege, and Jean-Marc Talbot

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Hyperproperties allow one to specify properties of systems that inherently involve not single executions of the system, but several of them at once: observational determinism and non-inference are two examples of such properties used to study the security of systems. Logics like HyperLTL have been studied in the past to model check hyperproperties of systems. However, most of the time, requiring strict security properties is actually ineffective as systems do not meet such requirements. To overcome this issue, we introduce qualitative reasoning in HyperLTL, inspired by a similar work on LTL by Almagor, Boker and Kupferman [Almagor et al., 2016] where a formula has a value in the interval [0, 1], obtained by considering either a propositional quality (how much the specification is satisfied), or a temporal quality (when the specification is satisfied). We show decidability of the approximated model checking problem, as well as the model checking of large fragments.
Cite as

Samuel Graepler, Benjamin Monmege, and Jean-Marc Talbot. Reasoning About Quality in Hyperproperties. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 45:1-45:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{graepler_et_al:LIPIcs.CSL.2026.45,
  author =	{Graepler, Samuel and Monmege, Benjamin and Talbot, Jean-Marc},
  title =	{{Reasoning About Quality in Hyperproperties}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{45:1--45:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.45},
  URN =		{urn:nbn:de:0030-drops-254704},
  doi =		{10.4230/LIPIcs.CSL.2026.45},
  annote =	{Keywords: Hyperlogics, Automata-based model checking, Quantitative verification}
}
Artifact
Software
DOI: 10.4230/artifacts.24325
nogamita/MFCS2025

Authors: Taisei Nogami and Tachio Terauchi

Abstract
Cite as

Taisei Nogami, Tachio Terauchi. nogamita/MFCS2025 (Software, Analysis Script). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{analysis_script,
   title = {{nogamita/MFCS2025}}, 
   author = {Nogami, Taisei and Terauchi, Tachio},
   note = {Software, JSPS KAKENHI Grant Numbers JP25KJ2137, JP23K24826, and JP20K20625 (visited on 2025-08-20)},
   url = {https://github.com/nogamita/MFCS2025},
   doi = {10.4230/artifacts.24325},
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.81
Efficient Matching of Some Fundamental Regular Expressions with Backreferences

Authors: Taisei Nogami and Tachio Terauchi

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Regular expression matching is of practical importance due to its widespread use in real-world applications. In practical use, regular expressions are often used with real-world extensions. Accordingly, the matching problem of regular expressions with real-world extensions has been actively studied in recent years, yielding steady progress. However, backreference, a popular extension supported by most modern programming languages such as Java, Python, JavaScript and others in their standard libraries for string processing, is an exception to this positive trend. In fact, it is known that the matching problem of regular expressions with backreferences (rewbs) is theoretically hard and the existence of an asymptotically fast matching algorithm for arbitrary rewbs seems unlikely. Even among currently known partial solutions, the balance between efficiency and generality remains unsatisfactory. To bridge this gap, we present an efficient matching algorithm for rewbs of the form e_0 (e)_1 e_1 \1 e_2 where e_0, e, e_1, e_2 are pure regular expressions, which are fundamental and frequently used in practical applications. It runs in quadratic time with respect to the input string length, substantially improving the best-known cubic time complexity for these rewbs. Our algorithm combines ideas from both stringology and automata theory in a novel way. We leverage two techniques from automata theory, injection and summarization, to simultaneously examine matches whose backreferenced substrings are either a fixed right-maximal repeat or its extendable prefixes, which are concepts from stringology. By further utilizing a subtle property of extendable prefixes, our algorithm correctly decides the matching problem while achieving the quadratic-time complexity.
Cite as

Taisei Nogami and Tachio Terauchi. Efficient Matching of Some Fundamental Regular Expressions with Backreferences. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 81:1-81:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nogami_et_al:LIPIcs.MFCS.2025.81,
  author =	{Nogami, Taisei and Terauchi, Tachio},
  title =	{{Efficient Matching of Some Fundamental Regular Expressions with Backreferences}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{81:1--81:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.81},
  URN =		{urn:nbn:de:0030-drops-241886},
  doi =		{10.4230/LIPIcs.MFCS.2025.81},
  annote =	{Keywords: Regular expressions, Backreferences, Regex matching, NFA simulation, Suffix arrays, Right-maximal repeats}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.71
On the Expressive Power of Regular Expressions with Backreferences

Authors: Taisei Nogami and Tachio Terauchi

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
A rewb is a regular expression extended with a feature called backreference. It is broadly known that backreference is a practical extension of regular expressions, and is supported by most modern regular expression engines, such as those in the standard libraries of Java, Python, and more. Meanwhile, indexed languages are the languages generated by indexed grammars, a formal grammar class proposed by A.V.Aho. We show that these two models' expressive powers are related in the following way: every language described by a rewb is an indexed language. As the smallest formal grammar class previously known to contain rewbs is the class of context sensitive languages, our result strictly improves the known upper-bound. Moreover, we prove the following two claims: there exists a rewb whose language does not belong to the class of stack languages, which is a proper subclass of indexed languages, and the language described by a rewb without a captured reference is in the class of nonerasing stack languages, which is a proper subclass of stack languages. Finally, we show that the hierarchy investigated in a prior study, which separates the expressive power of rewbs by the notion of nested levels, is within the class of nonerasing stack languages.
Cite as

Taisei Nogami and Tachio Terauchi. On the Expressive Power of Regular Expressions with Backreferences. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 71:1-71:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{nogami_et_al:LIPIcs.MFCS.2023.71,
  author =	{Nogami, Taisei and Terauchi, Tachio},
  title =	{{On the Expressive Power of Regular Expressions with Backreferences}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{71:1--71:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.71},
  URN =		{urn:nbn:de:0030-drops-186055},
  doi =		{10.4230/LIPIcs.MFCS.2023.71},
  annote =	{Keywords: Regular expressions, Backreferences, Expressive power}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.15
On Lookaheads in Regular Expressions with Backreferences

Authors: Nariyoshi Chida and Tachio Terauchi

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
Many modern regular expression engines employ various extensions to give more expressive support for real-world usages. Among the major extensions employed by many of the modern regular expression engines are backreferences and lookaheads. A question of interest about these extended regular expressions is their expressive power. Previous works have shown that (i) the extension by lookaheads does not enhance the expressive power, i.e., the expressive power of regular expressions with lookaheads is still regular, and that (ii) the extension by backreferences enhances the expressive power, i.e., the expressive power of regular expressions with backreferences (abbreviated as rewb) is no longer regular. This raises the following natural question: Does the extension of regular expressions with backreferences by lookaheads enhance the expressive power of regular expressions with backreferences? This paper answers the question positively by proving that adding either positive lookaheads or negative lookaheads increases the expressive power of rewb (the former abbreviated as rewbl_p and the latter as rewbl_n). A consequence of our result is that neither the class of finite state automata nor that of memory automata (MFA) of Schmid [Markus L. Schmid, 2016] (which corresponds to regular expressions with backreferenes but without lookaheads) corresponds to rewbl_p or rewbl_n. To fill the void, as a first step toward building such automata, we propose a new class of automata called memory automata with positive lookaheads (PLMFA) that corresponds to rewbl_p. The key idea of PLMFA is to extend MFA with a new kind of memories, called positive-lookahead memory, that is used to simulate the backtracking behavior of positive lookaheads. Interestingly, our positive-lookahead memories are almost perfectly symmetric to the capturing-group memories of MFA. Therefore, our PLMFA can be seen as a natural extension of MFA that can be obtained independently of its original intended purpose of simulating rewbl_p.
Cite as

Nariyoshi Chida and Tachio Terauchi. On Lookaheads in Regular Expressions with Backreferences. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chida_et_al:LIPIcs.FSCD.2022.15,
  author =	{Chida, Nariyoshi and Terauchi, Tachio},
  title =	{{On Lookaheads in Regular Expressions with Backreferences}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.15},
  URN =		{urn:nbn:de:0030-drops-162965},
  doi =		{10.4230/LIPIcs.FSCD.2022.15},
  annote =	{Keywords: Regular expressions, Lookaheads, Backreferences, Memory automata}
}
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