7 Search Results for "Raha, Ritam"

Document
DOI: 10.4230/LIPIcs.STACS.2026.5
On the Complexity of Language Membership for Probabilistic Words

Authors: Antoine Amarilli, Mikaël Monet, Paul Raphaël, and Sylvain Salvati

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We study the membership problem to context-free languages L (CFLs) on probabilistic words, that specify for each position a probability distribution on the letters (assuming independence across positions). Our task is to compute, given a probabilistic word, what is the probability that a word drawn according to the distribution belongs to L. This problem generalizes the problem of counting how many words of length n belong to L, or of counting how many completions of a partial word belong to L. We show that this problem is in polynomial time for unambiguous context-free languages (uCFLs), but can be #P-hard already for unions of two linear uCFLs. More generally, we show that the problem is in polynomial time for so-called poly-slicewise-unambiguous languages, where given a length n we can tractably compute an uCFL for the words of length n in the language. This class includes some inherently ambiguous languages, and implies the tractability of bounded CFLs and of languages recognized by unambiguous polynomial-time counter automata; but we show that the problem can be #P-hard for nondeterministic counter automata, even for Parikh automata with a single counter. We then introduce classes of circuits from knowledge compilation which we use for tractable counting, and show that this covers the tractability of poly-slicewise-unambiguous languages and of some CFLs that are not poly-slicewise-unambiguous. Extending these circuits with negation further allows us to show tractability for the language of primitive words, and for the language of concatenations of two palindromes. We finally show the conditional undecidability of the meta-problem that asks, given a CFG, whether the probabilistic membership problem for that CFG is tractable or #P-hard.
Cite as

Antoine Amarilli, Mikaël Monet, Paul Raphaël, and Sylvain Salvati. On the Complexity of Language Membership for Probabilistic Words. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{amarilli_et_al:LIPIcs.STACS.2026.5,
  author =	{Amarilli, Antoine and Monet, Mika\"{e}l and Rapha\"{e}l, Paul and Salvati, Sylvain},
  title =	{{On the Complexity of Language Membership for Probabilistic Words}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.5},
  URN =		{urn:nbn:de:0030-drops-254943},
  doi =		{10.4230/LIPIcs.STACS.2026.5},
  annote =	{Keywords: Automaton, probabilistic words, context-free grammar, membership problem}
}
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.
Cite as

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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.71
Faster All-Pairs Optimal Electric Car Routing

Authors: Dani Dorfman, Haim Kaplan, Robert E. Tarjan, Mikkel Thorup, and Uri Zwick

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We present a randomized Õ(n^{3.5})-time algorithm for computing optimal energetic paths for an electric car between all pairs of vertices in an n-vertex directed graph with positive and negative costs, or gains, which are defined to be the negatives of the costs. The optimal energetic paths are finite and well-defined even if the graph contains negative-cost, or equivalently, positive-gain, cycles. This makes the problem much more challenging than standard shortest paths problems. More specifically, for every two vertices s and t in the graph, the algorithm computes α_B(s,t), the maximum amount of charge the car can reach t with, if it starts at s with full battery, i.e., with charge B, where B is the capacity of the battery. The algorithm also outputs a concise description of the optimal energetic paths that achieve these values. In the presence of positive-gain cycles, optimal paths are not necessarily simple. For dense graphs, our new Õ(n^{3.5}) time algorithm improves on a previous Õ(mn²)-time algorithm of Dorfman et al. [ESA 2023] for the problem. The gain of an arc is the amount of charge added to the battery of the car when traversing the arc. The charge in the battery can never exceed the capacity B of the battery and can never be negative. An arc of positive gain may correspond, for example, to a downhill road segment, while an arc with a negative gain may correspond to an uphill segment. A positive-gain cycle, if one exists, can be used in certain cases to charge the battery to its capacity. This makes the problem more interesting and more challenging. As mentioned, optimal energetic paths are well-defined even in the presence of positive-gain cycles. Positive-gain cycles may arise when certain road segments have magnetic charging strips, or when the electric car has solar panels. Combined with a result of Dorfman et al. [SOSA 2024], this also provides a randomized Õ(n^{3.5})-time algorithm for computing minimum-cost paths between all pairs of vertices in an n-vertex graph when the battery can be externally recharged, at varying costs, at intermediate vertices.
Cite as

Dani Dorfman, Haim Kaplan, Robert E. Tarjan, Mikkel Thorup, and Uri Zwick. Faster All-Pairs Optimal Electric Car Routing. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 71:1-71:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dorfman_et_al:LIPIcs.ICALP.2025.71,
  author =	{Dorfman, Dani and Kaplan, Haim and Tarjan, Robert E. and Thorup, Mikkel and Zwick, Uri},
  title =	{{Faster All-Pairs Optimal Electric Car Routing}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{71:1--71:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.71},
  URN =		{urn:nbn:de:0030-drops-234486},
  doi =		{10.4230/LIPIcs.ICALP.2025.71},
  annote =	{Keywords: EV routing, Shortest Paths, Shortcuts, Sampling}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.19
The Complexity of Learning LTL, CTL and ATL Formulas

Authors: Benjamin Bordais, Daniel Neider, and Rajarshi Roy

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We consider the problem of learning temporal logic formulas from examples of system behavior. Learning temporal properties has crystallized as an effective means to explain complex temporal behaviors. Several efficient algorithms have been designed for learning temporal formulas. However, the theoretical understanding of the complexity of the learning decision problems remains largely unexplored. To address this, we study the complexity of the passive learning problems of three prominent temporal logics, Linear Temporal Logic (LTL), Computation Tree Logic (CTL) and Alternating-time Temporal Logic (ATL) and several of their fragments. We show that learning formulas with unbounded occurrences of binary operators is NP-complete for all of these logics. On the other hand, when investigating the complexity of learning formulas with bounded occurrences of binary operators, we exhibit discrepancies between the complexity of learning LTL, CTL and ATL formulas (with a varying number of agents).
Cite as

Benjamin Bordais, Daniel Neider, and Rajarshi Roy. The Complexity of Learning LTL, CTL and ATL Formulas. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 19:1-19:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bordais_et_al:LIPIcs.STACS.2025.19,
  author =	{Bordais, Benjamin and Neider, Daniel and Roy, Rajarshi},
  title =	{{The Complexity of Learning LTL, CTL and ATL Formulas}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{19:1--19:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.19},
  URN =		{urn:nbn:de:0030-drops-228441},
  doi =		{10.4230/LIPIcs.STACS.2025.19},
  annote =	{Keywords: Temporal logic, passive learning, complexity}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.34
On Continuous Pushdown VASS in One Dimension

Authors: Guillermo A. Pérez and Shrisha Rao

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
A pushdown vector addition system with states (PVASS) extends the model of vector addition systems with a pushdown stack. The algorithmic analysis of PVASS has applications such as static analysis of recursive programs manipulating integer variables. Unfortunately, reachability analysis, even for one-dimensional PVASS is not known to be decidable. So, we relax the model of one-dimensional PVASS to make the counter updates continuous and show that in this case reachability, coverability, and boundedness are decidable in polynomial time. In addition, for the extension of the model with lower-bound guards on the states, we show that coverability and reachability are NP-complete, and boundedness is coNP-complete.
Cite as

Guillermo A. Pérez and Shrisha Rao. On Continuous Pushdown VASS in One Dimension. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{perez_et_al:LIPIcs.CONCUR.2024.34,
  author =	{P\'{e}rez, Guillermo A. and Rao, Shrisha},
  title =	{{On Continuous Pushdown VASS in One Dimension}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{34:1--34:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.34},
  URN =		{urn:nbn:de:0030-drops-208065},
  doi =		{10.4230/LIPIcs.CONCUR.2024.34},
  annote =	{Keywords: Vector addition systems, Pushdown automata, Reachability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.30
Parikh One-Counter Automata

Authors: Michaël Cadilhac, Arka Ghosh, Guillermo A. Pérez, and Ritam Raha

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

Abstract
Counting abilities in finite automata are traditionally provided by two orthogonal extensions: adding a single counter that can be tested for zeroness at any point, or adding ℤ-valued counters that are tested for equality only at the end of runs. In this paper, finite automata extended with both types of counters are introduced. They are called Parikh One-Counter Automata (POCA): the "Parikh" part referring to the evaluation of counters at the end of runs, and the "One-Counter" part to the single counter that can be tested during runs. Their expressiveness, in the deterministic and nondeterministic variants, is investigated; it is shown in particular that there are deterministic POCA languages that cannot be expressed without nondeterminism in the original models. The natural decision problems are also studied; strikingly, most of them are no harder than in the original models. A parametric version of nonemptiness is also considered.
Cite as

Michaël Cadilhac, Arka Ghosh, Guillermo A. Pérez, and Ritam Raha. Parikh One-Counter Automata. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cadilhac_et_al:LIPIcs.MFCS.2023.30,
  author =	{Cadilhac, Micha\"{e}l and Ghosh, Arka and P\'{e}rez, Guillermo A. and Raha, Ritam},
  title =	{{Parikh One-Counter Automata}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{30:1--30:15},
  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.2023.30},
  URN =		{urn:nbn:de:0030-drops-185645},
  doi =		{10.4230/LIPIcs.MFCS.2023.30},
  annote =	{Keywords: Parikh automata, Context-free languages, One-counter automata}
}
Document
DOI: 10.4230/LIPIcs.CSL.2022.33
Revisiting Parameter Synthesis for One-Counter Automata

Authors: Guillermo A. Pérez and Ritam Raha

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

Abstract
We study the synthesis problem for one-counter automata with parameters. One-counter automata are obtained by extending classical finite-state automata with a counter whose value can range over non-negative integers and be tested for zero. The updates and tests applicable to the counter can further be made parametric by introducing a set of integer-valued variables called parameters. The synthesis problem for such automata asks whether there exists a valuation of the parameters such that all infinite runs of the automaton satisfy some ω-regular property. Lechner showed that (the complement of) the problem can be encoded in a restricted one-alternation fragment of Presburger arithmetic with divisibility. In this work (i) we argue that said fragment, called ∀∃_RPAD^+, is unfortunately undecidable. Nevertheless, by a careful re-encoding of the problem into a decidable restriction of ∀∃_RPAD^+, (ii) we prove that the synthesis problem is decidable in general and in 2NEXP for several fixed ω-regular properties. Finally, (iii) we give polynomial-space algorithms for the special cases of the problem where parameters can only be used in counter tests.
Cite as

Guillermo A. Pérez and Ritam Raha. Revisiting Parameter Synthesis for One-Counter Automata. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 33:1-33:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{perez_et_al:LIPIcs.CSL.2022.33,
  author =	{P\'{e}rez, Guillermo A. and Raha, Ritam},
  title =	{{Revisiting Parameter Synthesis for One-Counter Automata}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{33:1--33:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.33},
  URN =		{urn:nbn:de:0030-drops-157534},
  doi =		{10.4230/LIPIcs.CSL.2022.33},
  annote =	{Keywords: Parametric one-counter automata, Reachability, Software Verification}
}
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