59 Search Results for "Pandya, Paritosh"

Volume

LIPIcs, Volume 122

38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

FSTTCS 2018, December 11-13, 2018, Ahmedabad, India

Editors: Sumit Ganguly and Paritosh Pandya

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.56
Efficient Polynomial Identity Testing over Nonassociative Algebras

Authors: Partha Mukhopadhyay, C. Ramya, and Pratik Shastri

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We design the first efficient polynomial identity testing algorithms over the nonassociative polynomial algebra. In particular, multiplication among the formal variables is commutative but it is not associative. This complements the strong lower bound results obtained over this algebra by Hrubeš, Yehudayoff, and Wigderson [Pavel Hrubes et al., 2010] and Fijalkow, Lagarde, Ohlmann, and Serre [Fijalkow et al., 2021] from the identity testing perspective. Our main results are the following: - We construct nonassociative algebras (both commutative and noncommutative) which have no low degree identities. As a result, we obtain the first Amitsur-Levitzki type theorems [A. S. Amitsur and J. Levitzki, 1950] over nonassociative polynomial algebras. As a direct consequence, we obtain randomized polynomial-time black-box PIT algorithms for nonassociative polynomials which allow evaluation over such algebras. - On the derandomization side, we give a deterministic polynomial-time identity testing algorithm for nonassociative polynomials given by arithmetic circuits in the white-box setting. Previously, such an algorithm was known with the additional restriction of noncommutativity [Vikraman Arvind et al., 2017]. - In the black-box setting, we construct a hitting set of quasipolynomial-size for nonassociative polynomials computed by arithmetic circuits of small depth. Understanding the black-box complexity of identity testing, even in the randomized setting, was open prior to our work.
Cite as

Partha Mukhopadhyay, C. Ramya, and Pratik Shastri. Efficient Polynomial Identity Testing over Nonassociative Algebras. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 56:1-56:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mukhopadhyay_et_al:LIPIcs.APPROX/RANDOM.2025.56,
  author =	{Mukhopadhyay, Partha and C. Ramya and Shastri, Pratik},
  title =	{{Efficient Polynomial Identity Testing over Nonassociative Algebras}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{56:1--56:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.56},
  URN =		{urn:nbn:de:0030-drops-244224},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.56},
  annote =	{Keywords: Polynomial identity testing, nonassociative algebra, arithmetic circuits, black-box algorithms, white-box algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.22
On the Reachability Problem for Two-Dimensional Branching VASS

Authors: Clotilde Bizière, Thibault Hilaire, Jérôme Leroux, and Grégoire Sutre

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

Abstract
Vectors addition systems with states (VASS), or equivalently Petri nets, are arguably one of the most studied formalisms for the modeling and analysis of concurrent systems. A central decision problem for VASS is reachability: whether there exists a run from an initial configuration to a final one. This problem has been known to be decidable for over forty years, and its complexity has recently been precisely characterized. Our work concerns the reachability problem for BVASS, a branching generalization of VASS. In dimension one, the exact complexity of this problem is known. In this paper, we prove that the reachability problem for 2-dimensional BVASS is decidable. In fact, we even show that the reachability set admits a computable semilinear presentation. The decidability status of the reachability problem for BVASS remains open in higher dimensions.
Cite as

Clotilde Bizière, Thibault Hilaire, Jérôme Leroux, and Grégoire Sutre. On the Reachability Problem for Two-Dimensional Branching VASS. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{biziere_et_al:LIPIcs.MFCS.2025.22,
  author =	{Bizi\`{e}re, Clotilde and Hilaire, Thibault and Leroux, J\'{e}r\^{o}me and Sutre, Gr\'{e}goire},
  title =	{{On the Reachability Problem for Two-Dimensional Branching VASS}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.22},
  URN =		{urn:nbn:de:0030-drops-241294},
  doi =		{10.4230/LIPIcs.MFCS.2025.22},
  annote =	{Keywords: Vector addition systems, Reachability problem, Semilinear sets, Verification}
}
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
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.162
Positive and Monotone Fragments of FO and LTL

Authors: Simon Iosti, Denis Kuperberg, and Quentin Moreau

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

Abstract
We study the positive logic FO^+ on finite words, and its fragments, pursuing and refining the work initiated in [Denis Kuperberg, 2023]. First, we transpose notorious logic equivalences into positive first-order logic: FO^+ is equivalent to LTL^+, and its two-variable fragment FO^{2+} with (resp. without) successor available is equivalent to UTL^+ with (resp. without) the "next" operator X available. This shows that despite previous negative results, the class of FO^+-definable languages exhibits some form of robustness. We then exhibit an example of an FO-definable monotone language on one predicate, that is not FO^+-definable, refining the example from [Denis Kuperberg, 2023] with 3 predicates. Moreover, we show that such a counter-example cannot be FO²-definable. Finally, we provide a new example distinguishing the positive and monotone versions of FO² without quantifier alternation. This does not rely on a variant of the previously known counter-example, and witnesses a new phenomenon.
Cite as

Simon Iosti, Denis Kuperberg, and Quentin Moreau. Positive and Monotone Fragments of FO and LTL. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 162:1-162:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{iosti_et_al:LIPIcs.ICALP.2025.162,
  author =	{Iosti, Simon and Kuperberg, Denis and Moreau, Quentin},
  title =	{{Positive and Monotone Fragments of FO and LTL}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{162:1--162:17},
  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.2025.162},
  URN =		{urn:nbn:de:0030-drops-235398},
  doi =		{10.4230/LIPIcs.ICALP.2025.162},
  annote =	{Keywords: Positive logic, LTL, separation, first-order, monotone}
}
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
Complete Volume
DOI: 10.4230/LIPIcs.FSTTCS.2018
LIPIcs, Volume 122, FSTTCS'18, Complete Volume

Authors: Sumit Ganguly and Paritosh Pandya

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

Abstract
LIPIcs, Volume 122, FSTTCS'18, Complete Volume
Cite as

38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Proceedings{ganguly_et_al:LIPIcs.FSTTCS.2018,
  title =	{{LIPIcs, Volume 122, FSTTCS'18, Complete Volume}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  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},
  URN =		{urn:nbn:de:0030-drops-100240},
  doi =		{10.4230/LIPIcs.FSTTCS.2018},
  annote =	{Keywords: Theory of Computation}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.FSTTCS.2018.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Sumit Ganguly and Paritosh Pandya

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

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 0:i-0:xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ganguly_et_al:LIPIcs.FSTTCS.2018.0,
  author =	{Ganguly, Sumit and Pandya, Paritosh},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{0:i--0:xiv},
  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.2018.0},
  URN =		{urn:nbn:de:0030-drops-98992},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.FSTTCS.2018.1
Random Testing for Distributed Systems with Theoretical Guarantees (Invited Paper)

Authors: Rupak Majumdar

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

Abstract
Random testing has proven to be an effective way to catch bugs in concurrent and distributed systems. This is surprising, as the space of executions is enormous and conventional formal methods intuition would suggest that bad behaviors would only be found by extremely unlikely coincidences. Empirically, many bugs in distributed systems can be explained by interactions among only a small number of features. Thus, one can attempt to explain the effectiveness of random testing under various "small depth" hypotheses. In particular, it may be possible to test all interactions of k features for a small constant k by executing a family of tests that is exponentially or even doubly-exponentially smaller than the family of all tests. Moreover, under certain conditions, a randomly chosen small set of tests is sufficient to cover all k-wise interactions with high probability. I will describe two concrete scenarios. First, I will describe bugs in distributed systems caused by network partition faults. In many practical instances, these bugs occur due to two or three key nodes, such as leaders or replicas, not being able to communicate, or because the leading node finds itself in a block of the partition without quorum. In this case, I will show using the probabilistic method that a small set of randomly chosen tests will cover all "small partition" scenarios with high probability. Second, I will consider bugs that arise due to unexpected schedules (interleavings) of concurrent events. Again, many bugs depend only on the relative ordering of a small number of events (the "bug depth" of the bug). In this case, I will show a testing algorithm that prioritizes low depth interleavings and a randomized testing algorithm that bounds the probability of sampling any behavior of bug depth k for a fixed k. The testing algorithm is based on combinatorial insights from the theory of partial orders, such as the notion of dimension and its generalization to d-hitting families as well as results on online chain partitioning. Beyond the potential for designing or explaining random testing procedures, the technical arguments show the potential of combining "Theory A" and "Theory B" results to the important domain of software testing. This is joint work primarily with Filip Niksic [Filip Niksic, 2018], and with Dmitry Chistikov, Simin Oraee, Burcu Kulahcioglu Özkan, Mitra Tabaei Befrouei, and Georg Weissenbacher. This work was partially funded by an ERC Synergy Award (ImPACT).
Cite as

Rupak Majumdar. Random Testing for Distributed Systems with Theoretical Guarantees (Invited Paper). In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{majumdar:LIPIcs.FSTTCS.2018.1,
  author =	{Majumdar, Rupak},
  title =	{{Random Testing for Distributed Systems with Theoretical Guarantees}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{1:1--1:1},
  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.2018.1},
  URN =		{urn:nbn:de:0030-drops-99000},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.1},
  annote =	{Keywords: Random testing, Hitting families}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.FSTTCS.2018.2
Model Checking Randomized Security Protocols (Invited Paper)

Authors: A. Prasad Sistla

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

Abstract
The design of security protocols is extremely subtle and is prone to serious faults. Many tools for automatic analysis of such protocols have been developed. However, none of them have the ability to model protocols that use explicit randomization. Such randomized protocols are being increasingly used in systems to provide privacy and anonymity guarantees. In this talk we consider the problem of automatic verification of randomized security protocols. We consider verification of secrecy and indistinguishability properties under a powerful threat model of Dolev-Yao adversary. We present some complexity bounds on verification of these properties. We also describe practical algorithms for checking indistinguishability. These algorithms have been implemented in the tool SPAN and have been experimentally evaluated. The talk concludes with future challenges. (Joint work with: Matt Bauer, Rohit Chadha and Mahesh Viswanathan)
Cite as

A. Prasad Sistla. Model Checking Randomized Security Protocols (Invited Paper). In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{sistla:LIPIcs.FSTTCS.2018.2,
  author =	{Sistla, A. Prasad},
  title =	{{Model Checking Randomized Security Protocols}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{2:1--2:1},
  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.2018.2},
  URN =		{urn:nbn:de:0030-drops-99018},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.2},
  annote =	{Keywords: Randomized Protocols, Verification}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.FSTTCS.2018.3
Algorithms for the Asymmetric Traveling Salesman Problem (Invited Paper)

Authors: Ola Svensson

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

Abstract
The traveling salesman problem is one of the most fundamental optimization problems. Given n cities and pairwise distances, it is the problem of finding a tour of minimum total distance that visits each city once. In spite of significant research efforts, current techniques seem insufficient for settling the approximability of the traveling salesman problem. The gap in our understanding is especially large in the general asymmetric setting where the distance from city i to j is not assumed to equal the distance from j to i. Indeed, until recently, it remained an open problem to design an algorithm with any constant approximation guarantee. This status is particularly intriguing as the standard linear programming relaxation is believed to give a constant-factor approximation algorithm, where the constant may in fact be as small as 2. In this talk, we will give an overview of old and new approaches for settling this question. We shall, in particular, talk about our new approach that gives the first constant-factor approximation algorithm for the asymmetric traveling salesman problem. Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality gap of that relaxation. The main idea of our approach is to first give a generic reduction to structured instances and on those instances we then solve an easier problem (but equivalent in terms of constant-factor approximation) obtained by relaxing the general connectivity requirements into local connectivity conditions. This is based on joint work with Jakub Tarnawski and László A. Végh.
Cite as

Ola Svensson. Algorithms for the Asymmetric Traveling Salesman Problem (Invited Paper). In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{svensson:LIPIcs.FSTTCS.2018.3,
  author =	{Svensson, Ola},
  title =	{{Algorithms for the Asymmetric Traveling Salesman Problem}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{3:1--3:1},
  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.2018.3},
  URN =		{urn:nbn:de:0030-drops-99024},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.3},
  annote =	{Keywords: Approximation algorithms, combinatorial optimization, linear programming, traveling salesman problem}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.FSTTCS.2018.4
Continuous Algorithms (Invited Paper)

Authors: Santosh Vempala

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

Abstract
While the design of algorithms is traditionally a discrete endeavour, in recent years many advances have come from continuous perspectives. Typically, a continuous process, deterministic or randomized, is designed and shown to have desirable properties, such as approaching an optimal solution or a target distribution, and an algorithm is derived from this by appropriate discretization. We will discuss examples of this for optimization (gradient descent, interior-point method) and sampling (Brownian motion, Hamiltonian Monte Carlo), with applications to learning. In some interesting and rather general settings, the current fastest methods have been obtained via this approach.
Cite as

Santosh Vempala. Continuous Algorithms (Invited Paper). In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{vempala:LIPIcs.FSTTCS.2018.4,
  author =	{Vempala, Santosh},
  title =	{{Continuous Algorithms}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{4:1--4:1},
  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.2018.4},
  URN =		{urn:nbn:de:0030-drops-99037},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.4},
  annote =	{Keywords: Algorithms}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2018.5
On the Probabilistic Degree of OR over the Reals

Authors: Siddharth Bhandari, Prahladh Harsha, Tulasimohan Molli, and Srikanth Srinivasan

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

Abstract
We study the probabilistic degree over R of the OR function on n variables. For epsilon in (0,1/3), the epsilon-error probabilistic degree of any Boolean function f:{0,1}^n -> {0,1} over R is the smallest non-negative integer d such that the following holds: there exists a distribution of polynomials Pol in R[x_1,...,x_n] entirely supported on polynomials of degree at most d such that for all z in {0,1}^n, we have Pr_{P ~ Pol}[P(z) = f(z)] >= 1- epsilon. It is known from the works of Tarui (Theoret. Comput. Sci. 1993) and Beigel, Reingold, and Spielman (Proc. 6th CCC 1991), that the epsilon-error probabilistic degree of the OR function is at most O(log n * log(1/epsilon)). Our first observation is that this can be improved to O{log (n atop <= log(1/epsilon))}, which is better for small values of epsilon. In all known constructions of probabilistic polynomials for the OR function (including the above improvement), the polynomials P in the support of the distribution Pol have the following special structure: P(x_1,...,x_n) = 1 - prod_{i in [t]} (1- L_i(x_1,...,x_n)), where each L_i(x_1,..., x_n) is a linear form in the variables x_1,...,x_n, i.e., the polynomial 1-P(bar{x}) is a product of affine forms. We show that the epsilon-error probabilistic degree of OR when restricted to polynomials of the above form is Omega(log (n over <= log(1/epsilon))/log^2 (log (n over <= log(1/epsilon))})), thus matching the above upper bound (up to polylogarithmic factors).
Cite as

Siddharth Bhandari, Prahladh Harsha, Tulasimohan Molli, and Srikanth Srinivasan. On the Probabilistic Degree of OR over the Reals. 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. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bhandari_et_al:LIPIcs.FSTTCS.2018.5,
  author =	{Bhandari, Siddharth and Harsha, Prahladh and Molli, Tulasimohan and Srinivasan, Srikanth},
  title =	{{On the Probabilistic Degree of OR over the Reals}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{5:1--5:12},
  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.2018.5},
  URN =		{urn:nbn:de:0030-drops-99044},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.5},
  annote =	{Keywords: Polynomials over reals, probabilistic polynomials, probabilistic degree, OR polynomial}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2018.6
Quasipolynomial Hitting Sets for Circuits with Restricted Parse Trees

Authors: Ramprasad Saptharishi and Anamay Tengse

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

Abstract
We study the class of non-commutative Unambiguous circuits or Unique-Parse-Tree (UPT) circuits, and a related model of Few-Parse-Trees (FewPT) circuits (which were recently introduced by Lagarde, Malod and Perifel [Guillaume Lagarde et al., 2016] and Lagarde, Limaye and Srinivasan [Guillaume Lagarde et al., 2017]) and give the following constructions: - An explicit hitting set of quasipolynomial size for UPT circuits, - An explicit hitting set of quasipolynomial size for FewPT circuits (circuits with constantly many parse tree shapes), - An explicit hitting set of polynomial size for UPT circuits (of known parse tree shape), when a parameter of preimage-width is bounded by a constant. The above three results are extensions of the results of [Manindra Agrawal et al., 2015], [Rohit Gurjar et al., 2015] and [Rohit Gurjar et al., 2016] to the setting of UPT circuits, and hence also generalize their results in the commutative world from read-once oblivious algebraic branching programs (ROABPs) to UPT-set-multilinear circuits. The main idea is to study shufflings of non-commutative polynomials, which can then be used to prove suitable depth reduction results for UPT circuits and thereby allow a careful translation of the ideas in [Manindra Agrawal et al., 2015], [Rohit Gurjar et al., 2015] and [Rohit Gurjar et al., 2016].
Cite as

Ramprasad Saptharishi and Anamay Tengse. Quasipolynomial Hitting Sets for Circuits with Restricted Parse Trees. 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. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{saptharishi_et_al:LIPIcs.FSTTCS.2018.6,
  author =	{Saptharishi, Ramprasad and Tengse, Anamay},
  title =	{{Quasipolynomial Hitting Sets for Circuits with Restricted Parse Trees}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{6:1--6:19},
  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.2018.6},
  URN =		{urn:nbn:de:0030-drops-99050},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.6},
  annote =	{Keywords: Unambiguous Circuits, Read-once Oblivious ABPs, Polynomial Identity Testing, Lower Bounds, Algebraic Circuit Complexity}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2018.7
Univariate Ideal Membership Parameterized by Rank, Degree, and Number of Generators

Authors: V. Arvind, Abhranil Chatterjee, Rajit Datta, and Partha Mukhopadhyay

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

Abstract
Let F[X] be the polynomial ring over the variables X={x_1,x_2, ..., x_n}. An ideal I= <p_1(x_1), ..., p_n(x_n)> generated by univariate polynomials {p_i(x_i)}_{i=1}^n is a univariate ideal. We study the ideal membership problem for the univariate ideals and show the following results. - Let f(X) in F[l_1, ..., l_r] be a (low rank) polynomial given by an arithmetic circuit where l_i : 1 <= i <= r are linear forms, and I=<p_1(x_1), ..., p_n(x_n)> be a univariate ideal. Given alpha in F^n, the (unique) remainder f(X) mod I can be evaluated at alpha in deterministic time d^{O(r)} * poly(n), where d=max {deg(f),deg(p_1)...,deg(p_n)}. This yields a randomized n^{O(r)} algorithm for minimum vertex cover in graphs with rank-r adjacency matrices. It also yields an n^{O(r)} algorithm for evaluating the permanent of a n x n matrix of rank r, over any field F. Over Q, an algorithm of similar run time for low rank permanent is due to Barvinok [Barvinok, 1996] via a different technique. - Let f(X)in F[X] be given by an arithmetic circuit of degree k (k treated as fixed parameter) and I=<p_1(x_1), ..., p_n(x_n)>. We show that in the special case when I=<x_1^{e_1}, ..., x_n^{e_n}>, we obtain a randomized O^*(4.08^k) algorithm that uses poly(n,k) space. - Given f(X)in F[X] by an arithmetic circuit and I=<p_1(x_1), ..., p_k(x_k)>, membership testing is W[1]-hard, parameterized by k. The problem is MINI[1]-hard in the special case when I=<x_1^{e_1}, ..., x_k^{e_k}>.
Cite as

V. Arvind, Abhranil Chatterjee, Rajit Datta, and Partha Mukhopadhyay. Univariate Ideal Membership Parameterized by Rank, Degree, and Number of Generators. 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. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{arvind_et_al:LIPIcs.FSTTCS.2018.7,
  author =	{Arvind, V. and Chatterjee, Abhranil and Datta, Rajit and Mukhopadhyay, Partha},
  title =	{{Univariate Ideal Membership Parameterized by Rank, Degree, and Number of Generators}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{7:1--7:18},
  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.2018.7},
  URN =		{urn:nbn:de:0030-drops-99068},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.7},
  annote =	{Keywords: Combinatorial Nullstellensatz, Ideal Membership, Parametric Hardness, Low Rank Permanent}
}
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