25 Search Results for "Krishna, Shankara Narayanan"

Document
DOI: 10.4230/LIPIcs.CSL.2026.33
Deciding the Value of Two-Clock Almost Non-Zeno Weighted Timed Games

Authors: Isa Vialard

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

Abstract
The Value Problem for weighted timed games (wtgs) consists in determining, given a two-player weighted timed game with a reachability objective and a rational threshold, whether or not the value of the game exceeds the threshold. When restrained to wtgs with non-negative weight, this problem is known to be undecidable for weighted timed games with three or more clocks, and decidable for one-clock wtgs. The Value Problem for two-clock non-negative wtgs, which remained stubbornly open for a decade, was recently shown to be undecidable. In this paper, we show that the Value Problem is decidable when considering two-clock almost non-Zeno wtgs.
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Isa Vialard. Deciding the Value of Two-Clock Almost Non-Zeno Weighted Timed Games. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{vialard:LIPIcs.CSL.2026.33,
  author =	{Vialard, Isa},
  title =	{{Deciding the Value of Two-Clock Almost Non-Zeno Weighted Timed Games}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{33:1--33:21},
  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.2026.33},
  URN =		{urn:nbn:de:0030-drops-254580},
  doi =		{10.4230/LIPIcs.CSL.2026.33},
  annote =	{Keywords: Weighted timed games, decidability, real-time systems}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2025.2
Unboundedness Problems for Formal Languages (Invited Talk)

Authors: Georg Zetzsche

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

Abstract
Informally, unboundedness problems are decision problems that ask about the existence of infinitely many words (satisfying certain properties) in a formal language. For example: Is a given language infinite? Or: Does a given language have super-polynomial growth? These came into focus in recent years because of their connections to downward closure computation and separability problems. Although unboundedness problems may seem difficult at first, it turns out that there are techniques that are at the same time conceptually very simple, but also apply to a surprisingly wide variety of language classes. The talk will survey recent results (and techniques) concerning unboundedness problems.
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Georg Zetzsche. Unboundedness Problems for Formal Languages (Invited Talk). 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. 2:1-2:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zetzsche:LIPIcs.FSTTCS.2025.2,
  author =	{Zetzsche, Georg},
  title =	{{Unboundedness Problems for Formal Languages}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{2:1--2:10},
  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.2025.2},
  URN =		{urn:nbn:de:0030-drops-250810},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.2},
  annote =	{Keywords: Decidability, formal languages, unifying frameworks, downward closure, separability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.50
Lexicographic Transductions of Finite Words

Authors: Emmanuel Filiot, Nathan Lhote, and Pierre-Alain Reynier

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

Abstract
Regular transductions over finite words have linear input-to-output growth. This class of transductions enjoys many characterizations, such as transductions computable by two-way transducers as well as transductions definable in MSO (in the sense of Courcelle). Recently, regular transductions have been extended by Bojańczyk to polyregular transductions, which have polynomial growth, and are characterized by pebble transducers and MSO interpretations. Another class of interest is that of transductions defined by streaming string transducers or marble transducers, which have exponential growth and are incomparable with polyregular transductions. In this paper, we consider MSO set interpretations (MSOSI) over finite words, that were introduced by Colcombet and Loeding. MSOSI are a natural candidate for the class of "regular transductions with exponential growth", and are rather well behaved. However, MSOSI for now lacks two desirable properties that regular and polyregular transductions have. The first property is to have an automata description. This property is closely related to a second property, that of being regularity preserving, meaning preserving regular languages under inverse image. We first show that if MSOSI are (effectively) regularity preserving then any automatic ω-word has a decidable MSO theory, an almost 20 years old conjecture of Bárány. Our main contribution is the introduction of a class of transductions of exponential growth, which we call lexicographic transductions. We provide three different presentations for this class: first, as the closure of simple transductions (recognizable transductions) under a single operator called maplex; second, as a syntactic fragment of MSOSI (but the regular languages are given by automata instead of formulas); and third, we give an automaton based model called nested marble transducers, which generalize both marble transducers and pebble transducers. We show that this class enjoys many nice properties including being regularity preserving.
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Emmanuel Filiot, Nathan Lhote, and Pierre-Alain Reynier. Lexicographic Transductions of Finite Words. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{filiot_et_al:LIPIcs.MFCS.2025.50,
  author =	{Filiot, Emmanuel and Lhote, Nathan and Reynier, Pierre-Alain},
  title =	{{Lexicographic Transductions of Finite Words}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{50:1--50:18},
  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.2025.50},
  URN =		{urn:nbn:de:0030-drops-241572},
  doi =		{10.4230/LIPIcs.MFCS.2025.50},
  annote =	{Keywords: Transducers, Automata, MSO, Logical interpretations, Automatic structures}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.38
The Complexity of Separability for Semilinear Sets and Parikh Automata

Authors: Elias Rojas Collins, Chris Köcher, and Georg Zetzsche

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

Abstract
In a separability problem, we are given two sets K and L from a class 𝒞, and we want to decide whether there exists a set S from a class 𝒮 such that K ⊆ S and S ∩ L = ∅. In this case, we speak of separability of sets in 𝒞 by sets in 𝒮. We study two types of separability problems. First, we consider separability of semilinear sets (i.e. subsets of ℕ^d for some d) by sets definable by quantifier-free monadic Presburger formulas (or equivalently, the recognizable subsets of ℕ^d). Here, a formula is monadic if each atom uses at most one variable. Second, we consider separability of languages of Parikh automata by regular languages. A Parikh automaton is a machine with access to counters that can only be incremented, and have to meet a semilinear constraint at the end of the run. Both of these separability problems are known to be decidable with elementary complexity. Our main results are that both problems are coNP-complete. In the case of semilinear sets, coNP-completeness holds regardless of whether the input sets are specified by existential Presburger formulas, quantifier-free formulas, or semilinear representations. Our results imply that recognizable separability of rational subsets of Σ* × ℕ^d (shown decidable by Choffrut and Grigorieff) is coNP-complete as well. Another application is that regularity of deterministic Parikh automata (where the target set is specified using a quantifier-free Presburger formula) is coNP-complete as well.
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Elias Rojas Collins, Chris Köcher, and Georg Zetzsche. The Complexity of Separability for Semilinear Sets and Parikh Automata. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{collins_et_al:LIPIcs.MFCS.2025.38,
  author =	{Collins, Elias Rojas and K\"{o}cher, Chris and Zetzsche, Georg},
  title =	{{The Complexity of Separability for Semilinear Sets and Parikh Automata}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{38:1--38:21},
  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.2025.38},
  URN =		{urn:nbn:de:0030-drops-241457},
  doi =		{10.4230/LIPIcs.MFCS.2025.38},
  annote =	{Keywords: Vector Addition System, Separability, Regular Language}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.72
One-Parametric Presburger Arithmetic Has Quantifier Elimination

Authors: Alessio Mansutti and Mikhail R. Starchak

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

Abstract
We give a quantifier elimination procedure for one-parametric Presburger arithmetic, the extension of Presburger arithmetic with the function x ↦ t ⋅ x, where t is a fixed free variable ranging over the integers. This resolves an open problem proposed in [Bogart et al., Discrete Analysis, 2017]. As conjectured in [Goodrick, Arch. Math. Logic, 2018], quantifier elimination is obtained for the extended structure featuring all integer division functions x ↦ ⌊x/(f(t))⌋, one for each integer polynomial f. Our algorithm works by iteratively eliminating blocks of existential quantifiers. The elimination of a block builds on two sub-procedures, both running in non-deterministic polynomial time. The first one is an adaptation of a recently developed and efficient quantifier elimination procedure for Presburger arithmetic, modified to handle formulae with coefficients over the ring ℤ[t] of univariate polynomials. The second is reminiscent of the so-called "base t division method" used by Bogart et al. As a result, we deduce that the satisfiability problem for the existential fragment of one-parametric Presburger arithmetic (which encompasses a broad class of non-linear integer programs) is in NP, and that the smallest solution to a satisfiable formula in this fragment is of polynomial bit size.
Cite as

Alessio Mansutti and Mikhail R. Starchak. One-Parametric Presburger Arithmetic Has Quantifier Elimination. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 72:1-72:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mansutti_et_al:LIPIcs.MFCS.2025.72,
  author =	{Mansutti, Alessio and Starchak, Mikhail R.},
  title =	{{One-Parametric Presburger Arithmetic Has Quantifier Elimination}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{72:1--72:18},
  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.2025.72},
  URN =		{urn:nbn:de:0030-drops-241794},
  doi =		{10.4230/LIPIcs.MFCS.2025.72},
  annote =	{Keywords: decision procedures, quantifier elimination, non-linear integer arithmetic}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.26
Optimal Concolic Dynamic Partial Order Reduction

Authors: Mohammad Hossein Khoshechin Jorshari, Michalis Kokologiannakis, Rupak Majumdar, and Srinidhi Nagendra

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
Stateless model checking (SMC) software implementations requires exploring both concurrency- and data nondeterminism. Unfortunately, most SMC algorithms focus on efficient exploration of concurrency nondeterminism, thereby neglecting an important source of bugs. We present ConDpor, an SMC algorithm for unmodified Java programs that combines optimal dynamic partial order reduction (DPOR) for concurrency nondeterminism, with concolic execution for data nondeterminism. ConDpor is sound, complete, optimal, and parametric w.r.t. the memory consistency model. Our experiments confirm that ConDpor is exponentially faster than DPOR with small-domain enumeration. Overall, ConDpor opens the door for efficient exploration of concurrent programs with data nondeterminism.
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Mohammad Hossein Khoshechin Jorshari, Michalis Kokologiannakis, Rupak Majumdar, and Srinidhi Nagendra. Optimal Concolic Dynamic Partial Order Reduction. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{khoshechinjorshari_et_al:LIPIcs.CONCUR.2025.26,
  author =	{Khoshechin Jorshari, Mohammad Hossein and Kokologiannakis, Michalis and Majumdar, Rupak and Nagendra, Srinidhi},
  title =	{{Optimal Concolic Dynamic Partial Order Reduction}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{26:1--26:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.26},
  URN =		{urn:nbn:de:0030-drops-239765},
  doi =		{10.4230/LIPIcs.CONCUR.2025.26},
  annote =	{Keywords: Stateless model checking, dynamic symbolic execution}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.24
Expressive Equivalence Between Decidable Freeze and Metric Timed Temporal Logics.

Authors: Hsi-Ming Ho, Shankara Narayanan Krishna, Khushraj Madnani, Rupak Majumdar, and Paritosh Pandya

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
We demonstrate a surprising and first-of-its-kind expressive equivalence between decidable metric and freeze logics over timed words in pointwise semantics. Our main result states that Metric Interval Temporal Logic with future, past and Pnueli modalities, MITPPL, and full unilateral timed propositional temporal logic with both future and past temporal modalities, UPTL, have identical expressiveness. One of the highlights of this paper, which allows for this equivalence, is to prove that UPTL formulas admit monadic decomposition. Our result also implies that several decidable logics for real-time specifications, such as one-variable UPTL, unilateral MITPPL, and Q2MLO, are all expressively equivalent, and the reductions between them are effective. Hence, our result unifies the fragmented expressiveness boundary of timed temporal logics. As corollaries, we resolve the open question of the decidability for full UPTL, and the variable or clock hierarchy problem for the future fragment of UPTL.
Cite as

Hsi-Ming Ho, Shankara Narayanan Krishna, Khushraj Madnani, Rupak Majumdar, and Paritosh Pandya. Expressive Equivalence Between Decidable Freeze and Metric Timed Temporal Logics.. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 24:1-24:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ho_et_al:LIPIcs.CONCUR.2025.24,
  author =	{Ho, Hsi-Ming and Krishna, Shankara Narayanan and Madnani, Khushraj and Majumdar, Rupak and Pandya, Paritosh},
  title =	{{Expressive Equivalence Between Decidable Freeze and Metric Timed Temporal Logics.}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{24:1--24:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.24},
  URN =		{urn:nbn:de:0030-drops-239744},
  doi =		{10.4230/LIPIcs.CONCUR.2025.24},
  annote =	{Keywords: Timed Propositional Temporal Logic, Expressiveness, Metric Interval Temporal Logic, Satisfiability, Decidability}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.20
A Formal Language Perspective on Factorized Representations

Authors: Benny Kimelfeld, Wim Martens, and Matthias Niewerth

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
Factorized representations (FRs) are a well-known tool to succinctly represent results of join queries and have been originally defined using the named database perspective. We define FRs in the unnamed database perspective and use them to establish several new connections. First, unnamed FRs can be exponentially more succinct than named FRs, but this difference can be alleviated by imposing a disjointness condition on columns. Conversely, named FRs can also be exponentially more succinct than unnamed FRs. Second, unnamed FRs are the same as (i.e., isomorphic to) context-free grammars for languages in which each word has the same length. This tight connection allows us to transfer a wide range of results on context-free grammars to database factorization; of which we offer a selection in the paper. Third, when we generalize unnamed FRs to arbitrary sets of tuples, they become a generalization of path multiset representations, a formalism that was recently introduced to succinctly represent sets of paths in the context of graph database query evaluation.
Cite as

Benny Kimelfeld, Wim Martens, and Matthias Niewerth. A Formal Language Perspective on Factorized Representations. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kimelfeld_et_al:LIPIcs.ICDT.2025.20,
  author =	{Kimelfeld, Benny and Martens, Wim and Niewerth, Matthias},
  title =	{{A Formal Language Perspective on Factorized Representations}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.20},
  URN =		{urn:nbn:de:0030-drops-229614},
  doi =		{10.4230/LIPIcs.ICDT.2025.20},
  annote =	{Keywords: Databases, relational databases, graph databases, factorized databases, regular path queries, compact representations}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.18
A Framework for Extraction and Transformation of Documents

Authors: Cristian Riveros, Markus L. Schmid, and Nicole Schweikardt

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
We present a theoretical framework for the extraction and transformation of text documents as a two-phase process: The first phase uses document spanners to extract information from the input document. The second phase transforms the extracted information into a suitable output. To support several reasonable extract-transform scenarios, we propose for the first phase an extension of document spanners from span-tuples to so-called multispan-tuples, where variables are mapped to sets of spans instead of only single spans. We focus on multispanners described by regex formulas, and we prove that these have the same desirable properties as standard regular spanners. To formalize the second phase, we consider transformations that map every pair document-tuple, where each tuple comes from the (multi)span-relation extracted in the first phase, into a new output document. The specification of the two phases is what we call an extract-transform (ET) program, which covers practically relevant extract-transform tasks. In this paper, our main technical goal is to identify a broad class of ET programs that can be evaluated efficiently. We specifically focus on the scenario of regular ET programs: the extraction phase is given by a regex multispanner and the transformation phase is given by a regular string-to-string function. We show that for any regular ET program, given an input document, we can enumerate all final output documents with output-linear delay after linear preprocessing. As a side effect, we characterize the expressive power of regular ET programs and also show that they have desirable properties, like being closed under composition.
Cite as

Cristian Riveros, Markus L. Schmid, and Nicole Schweikardt. A Framework for Extraction and Transformation of Documents. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{riveros_et_al:LIPIcs.ICDT.2025.18,
  author =	{Riveros, Cristian and Schmid, Markus L. and Schweikardt, Nicole},
  title =	{{A Framework for Extraction and Transformation of Documents}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{18:1--18:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.18},
  URN =		{urn:nbn:de:0030-drops-229593},
  doi =		{10.4230/LIPIcs.ICDT.2025.18},
  annote =	{Keywords: Information extraction, Document spanners, Transducers, Query evaluation}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.142
An Efficient Quantifier Elimination Procedure for Presburger Arithmetic

Authors: Christoph Haase, Shankara Narayanan Krishna, Khushraj Madnani, Om Swostik Mishra, and Georg Zetzsche

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

Abstract
All known quantifier elimination procedures for Presburger arithmetic require doubly exponential time for eliminating a single block of existentially quantified variables. It has even been claimed in the literature that this upper bound is tight. We observe that this claim is incorrect and develop, as the main result of this paper, a quantifier elimination procedure eliminating a block of existentially quantified variables in singly exponential time. As corollaries, we can establish the precise complexity of numerous problems. Examples include deciding (i) monadic decomposability for existential formulas, (ii) whether an existential formula defines a well-quasi ordering or, more generally, (iii) certain formulas of Presburger arithmetic with Ramsey quantifiers. Moreover, despite the exponential blowup, our procedure shows that under mild assumptions, even NP upper bounds for decision problems about quantifier-free formulas can be transferred to existential formulas. The technical basis of our results is a kind of small model property for parametric integer programming that generalizes the seminal results by von zur Gathen and Sieveking on small integer points in convex polytopes.
Cite as

Christoph Haase, Shankara Narayanan Krishna, Khushraj Madnani, Om Swostik Mishra, and Georg Zetzsche. An Efficient Quantifier Elimination Procedure for Presburger Arithmetic. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 142:1-142:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{haase_et_al:LIPIcs.ICALP.2024.142,
  author =	{Haase, Christoph and Krishna, Shankara Narayanan and Madnani, Khushraj and Mishra, Om Swostik and Zetzsche, Georg},
  title =	{{An Efficient Quantifier Elimination Procedure for Presburger Arithmetic}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{142:1--142:17},
  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.2024.142},
  URN =		{urn:nbn:de:0030-drops-202856},
  doi =		{10.4230/LIPIcs.ICALP.2024.142},
  annote =	{Keywords: Presburger arithmetic, quantifier elimination, parametric integer programming, convex geometry}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.42
Counter Machines with Infrequent Reversals

Authors: Alain Finkel, Shankara Narayanan Krishna, Khushraj Madnani, Rupak Majumdar, and Georg Zetzsche

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

Abstract
Bounding the number of reversals in a counter machine is one of the most prominent restrictions to achieve decidability of the reachability problem. Given this success, we explore whether this notion can be relaxed while retaining decidability. To this end, we introduce the notion of an f-reversal-bounded counter machine for a monotone function f: ℕ → ℕ. In such a machine, every run of length n makes at most f(n) reversals. Our first main result is a dichotomy theorem: We show that for every monotone function f, one of the following holds: Either (i) f grows so slowly that every f-reversal bounded counter machine is already k-reversal bounded for some constant k or (ii) f belongs to Ω(log(n)) and reachability in f-reversal bounded counter machines is undecidable. This shows that classical reversal bounding already captures the decidable cases of f-reversal bounding for any monotone function f. The key technical ingredient is an analysis of the growth of small solutions of iterated compositions of Presburger-definable constraints. In our second contribution, we investigate whether imposing f-reversal boundedness improves the complexity of the reachability problem in vector addition systems with states (VASS). Here, we obtain an analogous dichotomy: We show that either (i) f grows so slowly that every f-reversal-bounded VASS is already k-reversal-bounded for some constant k or (ii) f belongs to Ω(n) and the reachability problem for f-reversal-bounded VASS remains Ackermann-complete. This result is proven using run amalgamation in VASS. Overall, our results imply that classical restriction of reversal boundedness is a robust one.
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Alain Finkel, Shankara Narayanan Krishna, Khushraj Madnani, Rupak Majumdar, and Georg Zetzsche. Counter Machines with Infrequent Reversals. 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. 42:1-42:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{finkel_et_al:LIPIcs.FSTTCS.2023.42,
  author =	{Finkel, Alain and Krishna, Shankara Narayanan and Madnani, Khushraj and Majumdar, Rupak and Zetzsche, Georg},
  title =	{{Counter Machines with Infrequent Reversals}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{42:1--42:17},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.42},
  URN =		{urn:nbn:de:0030-drops-194152},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.42},
  annote =	{Keywords: Counter machines, reversal-bounded, reachability, decidability, complexity}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.23
Satisfiability Checking of Multi-Variable TPTL with Unilateral Intervals Is PSPACE-Complete

Authors: Shankara Narayanan Krishna, Khushraj Nanik Madnani, Rupak Majumdar, and Paritosh Pandya

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
We investigate the decidability of the {0,∞} fragment of Timed Propositional Temporal Logic (TPTL). We show that the satisfiability checking of TPTL^{0,∞} is PSPACE-complete. Moreover, even its 1-variable fragment (1-TPTL^{0,∞}) is strictly more expressive than Metric Interval Temporal Logic (MITL) for which satisfiability checking is EXPSPACE complete. Hence, we have a strictly more expressive logic with computationally easier satisfiability checking. To the best of our knowledge, TPTL^{0,∞} is the first multi-variable fragment of TPTL for which satisfiability checking is decidable without imposing any bounds/restrictions on the timed words (e.g. bounded variability, bounded time, etc.). The membership in PSPACE is obtained by a reduction to the emptiness checking problem for a new "non-punctual’’ subclass of Alternating Timed Automata with multiple clocks called Unilateral Very Weak Alternating Timed Automata (VWATA^{0,∞}) which we prove to be in PSPACE. We show this by constructing a simulation equivalent non-deterministic timed automata whose number of clocks is polynomial in the size of the given VWATA^{0,∞}.
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Shankara Narayanan Krishna, Khushraj Nanik Madnani, Rupak Majumdar, and Paritosh Pandya. Satisfiability Checking of Multi-Variable TPTL with Unilateral Intervals Is PSPACE-Complete. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{krishna_et_al:LIPIcs.CONCUR.2023.23,
  author =	{Krishna, Shankara Narayanan and Madnani, Khushraj Nanik and Majumdar, Rupak and Pandya, Paritosh},
  title =	{{Satisfiability Checking of Multi-Variable TPTL with Unilateral Intervals Is PSPACE-Complete}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.23},
  URN =		{urn:nbn:de:0030-drops-190171},
  doi =		{10.4230/LIPIcs.CONCUR.2023.23},
  annote =	{Keywords: TPTL, Satisfiability, Non-Punctuality, Decidability, Expressiveness, ATA}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.16
On the Separability Problem of String Constraints

Authors: Parosh Aziz Abdulla, Mohamed Faouzi Atig, Vrunda Dave, and Shankara Narayanan Krishna

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
We address the separability problem for straight-line string constraints. The separability problem for languages of a class C by a class S asks: given two languages A and B in C, does there exist a language I in S separating A and B (i.e., I is a superset of A and disjoint from B)? The separability of string constraints is the same as the fundamental problem of interpolation for string constraints. We first show that regular separability of straight line string constraints is undecidable. Our second result is the decidability of the separability problem for straight-line string constraints by piece-wise testable languages, though the precise complexity is open. In our third result, we consider the positive fragment of piece-wise testable languages as a separator, and obtain an ExpSpace algorithm for the separability of a useful class of straight-line string constraints, and a Pspace-hardness result.
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Parosh Aziz Abdulla, Mohamed Faouzi Atig, Vrunda Dave, and Shankara Narayanan Krishna. On the Separability Problem of String Constraints. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{abdulla_et_al:LIPIcs.CONCUR.2020.16,
  author =	{Abdulla, Parosh Aziz and Atig, Mohamed Faouzi and Dave, Vrunda and Krishna, Shankara Narayanan},
  title =	{{On the Separability Problem of String Constraints}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{16:1--16:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.16},
  URN =		{urn:nbn:de:0030-drops-128286},
  doi =		{10.4230/LIPIcs.CONCUR.2020.16},
  annote =	{Keywords: string constraints, separability, interpolants}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.43
Synthesis of Computable Regular Functions of Infinite Words

Authors: Vrunda Dave, Emmanuel Filiot, Shankara Narayanan Krishna, and Nathan Lhote

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming ω-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the latter transducers define the class of rational functions. Even though regular functions are robustly characterised by several finite-state devices, even the subclass of rational functions may contain functions which are not computable (by a Turing machine with infinite input). This paper proposes a decision procedure for the following synthesis problem: given a regular function f (equivalently specified by one of the aforementioned transducer model), is f computable and if it is, synthesize a Turing machine computing it. For regular functions, we show that computability is equivalent to continuity, and therefore the problem boils down to deciding continuity. We establish a generic characterisation of continuity for functions preserving regular languages under inverse image (such as regular functions). We exploit this characterisation to show the decidability of continuity (and hence computability) of rational and regular functions. For rational functions, we show that this can be done in NLogSpace (it was already known to be in PTime by Prieur). In a similar fashion, we also effectively characterise uniform continuity of regular functions, and relate it to the notion of uniform computability, which offers stronger efficiency guarantees.
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Vrunda Dave, Emmanuel Filiot, Shankara Narayanan Krishna, and Nathan Lhote. Synthesis of Computable Regular Functions of Infinite Words. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dave_et_al:LIPIcs.CONCUR.2020.43,
  author =	{Dave, Vrunda and Filiot, Emmanuel and Krishna, Shankara Narayanan and Lhote, Nathan},
  title =	{{Synthesis of Computable Regular Functions of Infinite Words}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{43:1--43:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.43},
  URN =		{urn:nbn:de:0030-drops-128554},
  doi =		{10.4230/LIPIcs.CONCUR.2020.43},
  annote =	{Keywords: transducers, infinite words, computability, continuity, synthesis}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.69
On Synthesis of Resynchronizers for Transducers

Authors: Sougata Bose, Shankara Narayanan Krishna, Anca Muscholl, Vincent Penelle, and Gabriele Puppis

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We study two formalisms that allow to compare transducers over words under origin semantics: rational and regular resynchronizers, and show that the former are captured by the latter. We then consider some instances of the following synthesis problem: given transducers T_1,T_2, construct a rational (resp. regular) resynchronizer R, if it exists, such that T_1 is contained in R(T_2) under the origin semantics. We show that synthesis of rational resynchronizers is decidable for functional, and even finite-valued, one-way transducers, and undecidable for relational one-way transducers. In the two-way setting, synthesis of regular resynchronizers is shown to be decidable for unambiguous two-way transducers. For larger classes of two-way transducers, the decidability status is open.
Cite as

Sougata Bose, Shankara Narayanan Krishna, Anca Muscholl, Vincent Penelle, and Gabriele Puppis. On Synthesis of Resynchronizers for Transducers. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 69:1-69:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bose_et_al:LIPIcs.MFCS.2019.69,
  author =	{Bose, Sougata and Krishna, Shankara Narayanan and Muscholl, Anca and Penelle, Vincent and Puppis, Gabriele},
  title =	{{On Synthesis of Resynchronizers for Transducers}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{69:1--69:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.69},
  URN =		{urn:nbn:de:0030-drops-110133},
  doi =		{10.4230/LIPIcs.MFCS.2019.69},
  annote =	{Keywords: String transducers, resynchronizers, synthesis}
}
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