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Documents authored by Krishna, Shankara Narayanan

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.
Cite as

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,∞}.
Cite as

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.
Cite as

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.
Cite as

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}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2018.8
Verification of Timed Asynchronous Programs

Authors: Parosh Aziz Abdulla, Mohamed Faouzi Atig, Shankara Narayanan Krishna, and Shaan Vaidya

Published in: LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

Abstract
In this paper, we address the verification problem for timed asynchronous programs. We associate to each task, a deadline for its execution. We first show that the control state reachability problem for such class of systems is decidable while the configuration reachability problem is undecidable. Then, we consider the subclass of timed asynchronous programs where tasks are always being executed from the same state. For this subclass, we show that the control state reachability problem is PSPACE-complete. Furthermore, we show the decidability for the configuration reachability problem for the subclass.
Cite as

Parosh Aziz Abdulla, Mohamed Faouzi Atig, Shankara Narayanan Krishna, and Shaan Vaidya. Verification of Timed Asynchronous Programs. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{abdulla_et_al:LIPIcs.FSTTCS.2018.8,
  author =	{Abdulla, Parosh Aziz and Atig, Mohamed Faouzi and Krishna, Shankara Narayanan and Vaidya, Shaan},
  title =	{{Verification of Timed Asynchronous Programs}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Ganguly, Sumit and Pandya, Paritosh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.8},
  URN =		{urn:nbn:de:0030-drops-99076},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.8},
  annote =	{Keywords: Reachability, Timed Automata, Asynchronous programs}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2018.39
Logics Meet 1-Clock Alternating Timed Automata

Authors: Shankara Narayanan Krishna, Khushraj Madnani, and Paritosh K. Pandya

Published in: LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

Abstract
This paper investigates a decidable and highly expressive real time logic QkMSO which is obtained by extending MSO[<] with guarded quantification using block of less than k metric quantifiers. The resulting logic is shown to be expressively equivalent to 1-clock ATA where loops are without clock resets, as well as, RatMTL, a powerful extension of MTL[U_I] with regular expressions. We also establish 4-variable property for QkMSO and characterize the expressive power of its 2-variable fragment. Thus, the paper presents progress towards expressively complete logics for 1-clock ATA.
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Shankara Narayanan Krishna, Khushraj Madnani, and Paritosh K. Pandya. Logics Meet 1-Clock Alternating Timed Automata. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{krishna_et_al:LIPIcs.CONCUR.2018.39,
  author =	{Krishna, Shankara Narayanan and Madnani, Khushraj and Pandya, Paritosh K.},
  title =	{{Logics Meet 1-Clock Alternating Timed Automata}},
  booktitle =	{29th International Conference on Concurrency Theory (CONCUR 2018)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Schewe, Sven and Zhang, Lijun},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.39},
  URN =		{urn:nbn:de:0030-drops-95779},
  doi =		{10.4230/LIPIcs.CONCUR.2018.39},
  annote =	{Keywords: Metric Temporal Logic, Alternating Timed Automata, MSO, Regular Expressions, Expressive Completeness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.77
Making Metric Temporal Logic Rational

Authors: Shankara Narayanan Krishna, Khushraj Madnani, and Paritosh K. Pandya

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

Abstract
We study an extension of MTL in pointwise time with regular expression guarded modality Reg_I(re) where re is a rational expression over subformulae. We study the decidability and expressiveness of this extension (MTL+Ureg+Reg), called RegMTL, as well as its fragment SfrMTL where only star-free rational expressions are allowed. Using the technique of temporal projections, we show that RegMTL has decidable satisfiability by giving an equisatisfiable reduction to MTL. We also identify a subclass MITL+UReg of RegMTL for which our equisatisfiable reduction gives rise to formulae of MITL, yielding elementary decidability. As our second main result, we show a tight automaton-logic connection between SfrMTL and partially ordered (or very weak) 1-clock alternating timed automata.
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Shankara Narayanan Krishna, Khushraj Madnani, and Paritosh K. Pandya. Making Metric Temporal Logic Rational. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 77:1-77:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{krishna_et_al:LIPIcs.MFCS.2017.77,
  author =	{Krishna, Shankara Narayanan and Madnani, Khushraj and Pandya, Paritosh K.},
  title =	{{Making Metric Temporal Logic Rational}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{77:1--77:14},
  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.2017.77},
  URN =		{urn:nbn:de:0030-drops-81112},
  doi =		{10.4230/LIPIcs.MFCS.2017.77},
  annote =	{Keywords: Metric Temporal Logic, Timed Automata, Regular Expression, Equisatisfiability, Expressiveness}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2017.39
Towards an Efficient Tree Automata Based Technique for Timed Systems

Authors: S. Akshay, Paul Gastin, Shankara Narayanan Krishna, and Ilias Sarkar

Published in: LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Abstract
The focus of this paper is the analysis of real-time systems with recursion, through the development of good theoretical techniques which are implementable. Time is modeled using clock variables, and recursion using stacks. Our technique consists of modeling the behaviours of the timed system as graphs, and interpreting these graphs on tree terms by showing a bound on their tree-width. We then build a tree automaton that accepts exactly those tree terms that describe realizable runs of the timed system. The emptiness of the timed system thus boils down to emptiness of a finite tree automaton that accepts these tree terms. This approach helps us in obtaining an optimal complexity, not just in theory (as done in earlier work e.g.[concur16]), but also in going towards an efficient implementation of our technique. To do this, we make several improvements in the theory and exploit these to build a first prototype tool that can analyze timed systems with recursion.
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S. Akshay, Paul Gastin, Shankara Narayanan Krishna, and Ilias Sarkar. Towards an Efficient Tree Automata Based Technique for Timed Systems. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 39:1-39:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{akshay_et_al:LIPIcs.CONCUR.2017.39,
  author =	{Akshay, S. and Gastin, Paul and Krishna, Shankara Narayanan and Sarkar, Ilias},
  title =	{{Towards an Efficient Tree Automata Based Technique for Timed Systems}},
  booktitle =	{28th International Conference on Concurrency Theory (CONCUR 2017)},
  pages =	{39:1--39:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-048-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{85},
  editor =	{Meyer, Roland and Nestmann, Uwe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.39},
  URN =		{urn:nbn:de:0030-drops-78017},
  doi =		{10.4230/LIPIcs.CONCUR.2017.39},
  annote =	{Keywords: Timed automata, tree automata, pushdown systems, tree-width}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2016.12
FO-Definable Transformations of Infinite Strings

Authors: Vrunda Dave, Shankara Narayanan Krishna, and Ashutosh Trivedi

Published in: LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)

Abstract
The theory of regular and aperiodic transformations of finite strings has recently received a lot of interest. These classes can be equivalently defined using logic (Monadic second-order logic and first-order logic), two-way machines (regular two-way and aperiodic two-way transducers), and one-way register machines (regular streaming string and aperiodic streaming string transducers). These classes are known to be closed under operations such as sequential composition and regular (star-free) choice; and problems such as functional equivalence and type checking, are decidable for these classes. On the other hand, for infinite strings these results are only known for regular transformations: Alur, Filiot, and Trivedi studied transformations of infinite strings and introduced an extension of streaming string transducers over infinte strings and showed that they capture monadic second-order definable transformations for infinite strings. In this paper we extend their work to recover connection for infinite strings among first-order logic definable transformations, aperiodic two-way transducers, and aperiodic streaming string transducers.
Cite as

Vrunda Dave, Shankara Narayanan Krishna, and Ashutosh Trivedi. FO-Definable Transformations of Infinite Strings. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{dave_et_al:LIPIcs.FSTTCS.2016.12,
  author =	{Dave, Vrunda and Krishna, Shankara Narayanan and Trivedi, Ashutosh},
  title =	{{FO-Definable Transformations of Infinite Strings}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.12},
  URN =		{urn:nbn:de:0030-drops-68476},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.12},
  annote =	{Keywords: Transducers, FO-definability, Infinite Strings}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2016.44
Mean-Payoff Games on Timed Automata

Authors: Shibashis Guha, Marcin Jurdzinski, Shankara Narayanan Krishna, and Ashutosh Trivedi

Published in: LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)

Abstract
Mean-payoff games on timed automata are played on the infinite weighted graph of configurations of priced timed automata between two players - Player Min and Player Max - by moving a token along the states of the graph to form an infinite run. The goal of Player Min is to minimize the limit average weight of the run, while the goal of the Player Max is the opposite. Brenguier, Cassez, and Raskin recently studied a variation of these games and showed that mean-payoff games are undecidable for timed automata with five or more clocks. We refine this result by proving the undecidability of mean-payoff games with three clocks. On a positive side, we show the decidability of mean-payoff games on one-clock timed automata with binary price-rates. A key contribution of this paper is the application of dynamic programming based proof techniques applied in the context of average reward optimization on an uncountable state and action space.
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Shibashis Guha, Marcin Jurdzinski, Shankara Narayanan Krishna, and Ashutosh Trivedi. Mean-Payoff Games on Timed Automata. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{guha_et_al:LIPIcs.FSTTCS.2016.44,
  author =	{Guha, Shibashis and Jurdzinski, Marcin and Krishna, Shankara Narayanan and Trivedi, Ashutosh},
  title =	{{Mean-Payoff Games on Timed Automata}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.44},
  URN =		{urn:nbn:de:0030-drops-68797},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.44},
  annote =	{Keywords: Timed Automata, Mean-Payoff Games, Controller-Synthesis}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2016.27
Analyzing Timed Systems Using Tree Automata

Authors: S. Akshay, Paul Gastin, and Shankara Narayanan Krishna

Published in: LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

Abstract
Timed systems, such as timed automata, are usually analyzed using their operational semantics on timed words. The classical region abstraction for timed automata reduces them to (untimed) finite state automata with the same time-abstract properties, such as state reachability. We propose a new technique to analyze such timed systems using finite tree automata instead of finite word automata. The main idea is to consider timed behaviors as graphs with matching edges capturing timing constraints. Such graphs can be interpreted in trees opening the way to tree automata based techniques which are more powerful than analysis based on word automata. The technique is quite general and applies to many timed systems. In this paper, as an example, we develop the technique on timed pushdown systems, which have recently received considerable attention. Further, we also demonstrate how we can use it on timed automata and timed multi-stack pushdown systems (with boundedness restrictions).
Cite as

S. Akshay, Paul Gastin, and Shankara Narayanan Krishna. Analyzing Timed Systems Using Tree Automata. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{akshay_et_al:LIPIcs.CONCUR.2016.27,
  author =	{Akshay, S. and Gastin, Paul and Krishna, Shankara Narayanan},
  title =	{{Analyzing Timed Systems Using Tree Automata}},
  booktitle =	{27th International Conference on Concurrency Theory (CONCUR 2016)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-017-0},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{59},
  editor =	{Desharnais, Jos\'{e}e and Jagadeesan, Radha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.27},
  URN =		{urn:nbn:de:0030-drops-61775},
  doi =		{10.4230/LIPIcs.CONCUR.2016.27},
  annote =	{Keywords: Timed automata, tree automata, pushdown systems, tree-width}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.8
Stochastic Timed Games Revisited

Authors: S. Akshay, Patricia Bouyer, Shankara Narayanan Krishna, Lakshmi Manasa, and Ashutosh Trivedi

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
Stochastic timed games (STGs), introduced by Bouyer and Forejt, naturally generalize both continuous-time Markov chains and timed automata by providing a partition of the locations between those controlled by two players (Player Box and Player Diamond) with competing objectives and those governed by stochastic laws. Depending on the number of players - 2, 1, or 0 - subclasses of stochastic timed games are often classified as 2 1/2-player, 1 1/2-player, and 1/2-player games where the 1/2 symbolizes the presence of the stochastic "nature" player. For STGs with reachability objectives it is known that 1 1/2-player one-clock STGs are decidable for qualitative objectives, and that 2 1/2-player three-clock STGs are undecidable for quantitative reachability objectives. This paper further refines the gap in this decidability spectrum. We show that quantitative reachability objectives are already undecidable for 1 1/2 player four-clock STGs, and even under the time-bounded restriction for 2 1/2-player five-clock STGs. We also obtain a class of 1 1/2, 2 1/2 player STGs for which the quantitative reachability problem is decidable.
Cite as

S. Akshay, Patricia Bouyer, Shankara Narayanan Krishna, Lakshmi Manasa, and Ashutosh Trivedi. Stochastic Timed Games Revisited. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{akshay_et_al:LIPIcs.MFCS.2016.8,
  author =	{Akshay, S. and Bouyer, Patricia and Krishna, Shankara Narayanan and Manasa, Lakshmi and Trivedi, Ashutosh},
  title =	{{Stochastic Timed Games Revisited}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.8},
  URN =		{urn:nbn:de:0030-drops-64985},
  doi =		{10.4230/LIPIcs.MFCS.2016.8},
  annote =	{Keywords: timed automata, stochastic games, two-counter machines}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2015.261
Revisiting Robustness in Priced Timed Games

Authors: Shibashis Guha, Shankara Narayanan Krishna, Lakshmi Manasa, and Ashutosh Trivedi

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

Abstract
Priced timed games are optimal-cost reachability games played between two players---the controller and the environment---by moving a token along the edges of infinite graphs of configurations of priced timed automata. The goal of the controller is to reach a given set of target locations as cheaply as possible, while the goal of the environment is the opposite. Priced timed games are known to be undecidable for timed automata with 3 or more clocks, while they are known to be decidable for automata with 1 clock. In an attempt to recover decidability for priced timed games Bouyer, Markey, and Sankur studied robust priced timed games where the environment has the power to slightly perturb delays proposed by the controller. Unfortunately, however, they showed that the natural problem of deciding the existence of optimal limit-strategy---optimal strategy of the controller where the perturbations tend to vanish in the limit---is undecidable with 10 or more clocks. In this paper we revisit this problem and improve our understanding of the decidability of these games. We show that the limit-strategy problem is already undecidable for a subclass of robust priced timed games with 5 or more clocks. On a positive side, we show the decidability of the existence of almost optimal strategies for the same subclass of one-clock robust priced timed games by adapting a classical construction by Bouyer at al. for one-clock priced timed games.
Cite as

Shibashis Guha, Shankara Narayanan Krishna, Lakshmi Manasa, and Ashutosh Trivedi. Revisiting Robustness in Priced Timed Games. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 261-277, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{guha_et_al:LIPIcs.FSTTCS.2015.261,
  author =	{Guha, Shibashis and Krishna, Shankara Narayanan and Manasa, Lakshmi and Trivedi, Ashutosh},
  title =	{{Revisiting Robustness in Priced Timed Games}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{261--277},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.261},
  URN =		{urn:nbn:de:0030-drops-56440},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.261},
  annote =	{Keywords: Priced Timed Games, Decidability, Optimal strategies, Robustness}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2014.147
First-order Definable String Transformations

Authors: Emmanuel Filiot, Shankara Narayanan Krishna, and Ashutosh Trivedi

Published in: LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

Abstract
The connection between languages defined by computational models and logic for languages is well-studied. Monadic second-order logic and finite automata are shown to closely correspond to each-other for the languages of strings, trees, and partial-orders. Similar connections are shown for first-order logic and finite automata with certain aperiodicity restriction. Courcelle in 1994 proposed a way to use logic to define functions over structures where the output structure is defined using logical formulas interpreted over the input structure. Engelfriet and Hoogeboom discovered the corresponding "automata connection" by showing that two-way generalised sequential machines capture the class of monadic-second order definable transformations. Alur and Cerny further refined the result by proposing a one-way deterministic transducer model with string variables - called the streaming string transducers - to capture the same class of transformations. In this paper we establish a transducer-logic correspondence for Courcelle's first-order definable string transformations. We propose a new notion of transition monoid for streaming string transducers that involves structural properties of both underlying input automata and variable dependencies. By putting an aperiodicity restriction on the transition monoids, we define a class of streaming string transducers that captures exactly the class of first-order definable transformations.
Cite as

Emmanuel Filiot, Shankara Narayanan Krishna, and Ashutosh Trivedi. First-order Definable String Transformations. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 147-159, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{filiot_et_al:LIPIcs.FSTTCS.2014.147,
  author =	{Filiot, Emmanuel and Krishna, Shankara Narayanan and Trivedi, Ashutosh},
  title =	{{First-order Definable String Transformations}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{147--159},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Raman, Venkatesh and Suresh, S. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.147},
  URN =		{urn:nbn:de:0030-drops-48393},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.147},
  annote =	{Keywords: First-order logic, streaming string transducers}
}
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