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Volume

LIPIcs, Volume 284

43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

FSTTCS 2023, December 18-20, 2023, IIIT Hyderabad, Telangana, India

Editors: Patricia Bouyer and Srikanth Srinivasan

Document

DOI: 10.4230/LIPIcs.CCC.2024.1

A Technique for Hardness Amplification Against AC⁰

Authors: William M. Hoza

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

We study hardness amplification in the context of two well-known "moderate" average-case hardness results for AC⁰ circuits. First, we investigate the extent to which AC⁰ circuits of depth d can approximate AC⁰ circuits of some larger depth d + k. The case k = 1 is resolved by Håstad, Rossman, Servedio, and Tan’s celebrated average-case depth hierarchy theorem (JACM 2017). Our contribution is a significantly stronger correlation bound when k ≥ 3. Specifically, we show that there exists a linear-size AC⁰_{d + k} circuit h : {0, 1}ⁿ → {0, 1} such that for every AC⁰_d circuit g, either g has size exp(n^{Ω(1/d)}), or else g agrees with h on at most a (1/2 + ε)-fraction of inputs where ε = exp(-(1/d) ⋅ Ω(log n)^{k-1}). For comparison, Håstad, Rossman, Servedio, and Tan’s result has ε = n^{-Θ(1/d)}. Second, we consider the majority function. It is well known that the majority function is moderately hard for AC⁰ circuits (and stronger classes). Our contribution is a stronger correlation bound for the XOR of t copies of the n-bit majority function, denoted MAJ_n^{⊕ t}. We show that if g is an AC⁰_d circuit of size S, then g agrees with MAJ_n^{⊕ t} on at most a (1/2 + ε)-fraction of inputs, where ε = (O(log S)^{d - 1} / √n)^t. To prove these results, we develop a hardness amplification technique that is tailored to a specific type of circuit lower bound proof. In particular, one way to show that a function h is moderately hard for AC⁰ circuits is to (a) design some distribution over random restrictions or random projections, (b) show that AC⁰ circuits simplify to shallow decision trees under these restrictions/projections, and finally (c) show that after applying the restriction/projection, h is moderately hard for shallow decision trees with respect to an appropriate distribution. We show that (roughly speaking) if h can be proven to be moderately hard by a proof with that structure, then XORing multiple copies of h amplifies its hardness. Our analysis involves a new kind of XOR lemma for decision trees, which might be of independent interest.

Cite as

William M. Hoza. A Technique for Hardness Amplification Against AC⁰. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hoza:LIPIcs.CCC.2024.1,
  author =	{Hoza, William M.},
  title =	{{A Technique for Hardness Amplification Against AC⁰}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.1},
  URN =		{urn:nbn:de:0030-drops-203977},
  doi =		{10.4230/LIPIcs.CCC.2024.1},
  annote =	{Keywords: Bounded-depth circuits, average-case lower bounds, hardness amplification, XOR lemmas}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.18

Pseudorandomness, Symmetry, Smoothing: I

Authors: Harm Derksen, Peter Ivanov, Chin Ho Lee, and Emanuele Viola

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

We prove several new results about bounded uniform and small-bias distributions. A main message is that, small-bias, even perturbed with noise, does not fool several classes of tests better than bounded uniformity. We prove this for threshold tests, small-space algorithms, and small-depth circuits. In particular, we obtain small-bias distributions that - achieve an optimal lower bound on their statistical distance to any bounded-uniform distribution. This closes a line of research initiated by Alon, Goldreich, and Mansour in 2003, and improves on a result by O'Donnell and Zhao. - have heavier tail mass than the uniform distribution. This answers a question posed by several researchers including Bun and Steinke. - rule out a popular paradigm for constructing pseudorandom generators, originating in a 1989 work by Ajtai and Wigderson. This again answers a question raised by several researchers. For branching programs, our result matches a bound by Forbes and Kelley. Our small-bias distributions above are symmetric. We show that the xor of any two symmetric small-bias distributions fools any bounded function. Hence our examples cannot be extended to the xor of two small-bias distributions, another popular paradigm whose power remains unknown. We also generalize and simplify the proof of a result of Bazzi.

Cite as

Harm Derksen, Peter Ivanov, Chin Ho Lee, and Emanuele Viola. Pseudorandomness, Symmetry, Smoothing: I. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 18:1-18:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{derksen_et_al:LIPIcs.CCC.2024.18,
  author =	{Derksen, Harm and Ivanov, Peter and Lee, Chin Ho and Viola, Emanuele},
  title =	{{Pseudorandomness, Symmetry, Smoothing: I}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{18:1--18:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.18},
  URN =		{urn:nbn:de:0030-drops-204144},
  doi =		{10.4230/LIPIcs.CCC.2024.18},
  annote =	{Keywords: pseudorandomness, k-wise uniform distributions, small-bias distributions, noise, symmetric tests, thresholds, Krawtchouk polynomials}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.20

Lower Bounds for Set-Multilinear Branching Programs

Authors: Prerona Chatterjee, Deepanshu Kush, Shubhangi Saraf, and Amir Shpilka

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

In this paper, we prove super-polynomial lower bounds for the model of sum of ordered set-multilinear algebraic branching programs, each with a possibly different ordering (∑smABP). Specifically, we give an explicit nd-variate polynomial of degree d such that any ∑smABP computing it must have size n^ω(1) for d as low as ω(log n). Notably, this constitutes the first such lower bound in the low degree regime. Moreover, for d = poly(n), we demonstrate an exponential lower bound. This result generalizes the seminal work of Nisan (STOC, 1991), which proved an exponential lower bound for a single ordered set-multilinear ABP. The significance of our lower bounds is underscored by the recent work of Bhargav, Dwivedi, and Saxena (TAMC, 2024), which showed that super-polynomial lower bounds against a sum of ordered set-multilinear branching programs - for a polynomial of sufficiently low degree - would imply super-polynomial lower bounds against general ABPs, thereby resolving Valiant’s longstanding conjecture that the permanent polynomial can not be computed efficiently by ABPs. More precisely, their work shows that if one could obtain such lower bounds when the degree is bounded by O(log n/ log log n), then it would imply super-polynomial lower bounds against general ABPs. Our results strengthen the works of Arvind & Raja (Chic. J. Theor. Comput. Sci., 2016) and Bhargav, Dwivedi & Saxena (TAMC, 2024), as well as the works of Ramya & Rao (Theor. Comput. Sci., 2020) and Ghoshal & Rao (International Computer Science Symposium in Russia, 2021), each of which established lower bounds for related or restricted versions of this model. They also strongly answer a question from the former two, which asked to prove super-polynomial lower bounds for general ∑smABP.

Cite as

Prerona Chatterjee, Deepanshu Kush, Shubhangi Saraf, and Amir Shpilka. Lower Bounds for Set-Multilinear Branching Programs. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chatterjee_et_al:LIPIcs.CCC.2024.20,
  author =	{Chatterjee, Prerona and Kush, Deepanshu and Saraf, Shubhangi and Shpilka, Amir},
  title =	{{Lower Bounds for Set-Multilinear Branching Programs}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.20},
  URN =		{urn:nbn:de:0030-drops-204167},
  doi =		{10.4230/LIPIcs.CCC.2024.20},
  annote =	{Keywords: Lower Bounds, Algebraic Branching Programs, Set-multilinear polynomials}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.31

Low-Depth Algebraic Circuit Lower Bounds over Any Field

Authors: Michael A. Forbes

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

The recent breakthrough of Limaye, Srinivasan and Tavenas [Limaye et al., 2022] (LST) gave the first super-polynomial lower bounds against low-depth algebraic circuits, for any field of zero (or sufficiently large) characteristic. It was an open question to extend this result to small-characteristic ([Limaye et al., 2022; Govindasamy et al., 2022; Fournier et al., 2023]), which in particular is relevant for an approach to prove superpolynomial AC⁰[p]-Frege lower bounds ([Govindasamy et al., 2022]). In this work, we prove super-polynomial algebraic circuit lower bounds against low-depth algebraic circuits over any field, with the same parameters as LST (or even matching the improved parameters of Bhargav, Dutta, and Saxena [Bhargav et al., 2022]). We give two proofs. The first is logical, showing that even though the proof of LST naively fails in small characteristic, the proof is sufficiently algebraic that generic transfer results imply the result over characteristic zero implies the result over all fields. Motivated by this indirect proof, we then proceed to give a second constructive proof, replacing the field-dependent set-multilinearization result of LST with a set-multilinearization that works over any field, by using the Binet-Minc identity [Minc, 1979].

Cite as

Michael A. Forbes. Low-Depth Algebraic Circuit Lower Bounds over Any Field. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{forbes:LIPIcs.CCC.2024.31,
  author =	{Forbes, Michael A.},
  title =	{{Low-Depth Algebraic Circuit Lower Bounds over Any Field}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.31},
  URN =		{urn:nbn:de:0030-drops-204271},
  doi =		{10.4230/LIPIcs.CCC.2024.31},
  annote =	{Keywords: algebraic circuits, lower bounds, low-depth circuits, positive characteristic}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.16

NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials

Authors: Omkar Baraskar, Agrim Dewan, Chandan Saha, and Pulkit Sinha

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

Abstract

An s-sparse polynomial has at most s monomials with nonzero coefficients. The Equivalence Testing problem for sparse polynomials (ETsparse) asks to decide if a given polynomial f is equivalent to (i.e., in the orbit of) some s-sparse polynomial. In other words, given f ∈ 𝔽[𝐱] and s ∈ ℕ, ETsparse asks to check if there exist A ∈ GL(|𝐱|, 𝔽) and 𝐛 ∈ 𝔽^|𝐱| such that f(A𝐱 + 𝐛) is s-sparse. We show that ETsparse is NP-hard over any field 𝔽, if f is given in the sparse representation, i.e., as a list of nonzero coefficients and exponent vectors. This answers a question posed by Gupta, Saha and Thankey (SODA 2023) and also, more explicitly, by Baraskar, Dewan and Saha (STACS 2024). The result implies that the Minimum Circuit Size Problem (MCSP) is NP-hard for a dense subclass of depth-3 arithmetic circuits if the input is given in sparse representation. We also show that approximating the smallest s₀ such that a given s-sparse polynomial f is in the orbit of some s₀-sparse polynomial to within a factor of s^{1/3 - ε} is NP-hard for any ε > 0; observe that s-factor approximation is trivial as the input is s-sparse. Finally, we show that for any constant σ ≥ 6, checking if a polynomial (given in sparse representation) is in the orbit of some support-σ polynomial is NP-hard. Support of a polynomial f is the maximum number of variables present in any monomial of f. These results are obtained via direct reductions from the 3-SAT problem.

Cite as

Omkar Baraskar, Agrim Dewan, Chandan Saha, and Pulkit Sinha. NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baraskar_et_al:LIPIcs.ICALP.2024.16,
  author =	{Baraskar, Omkar and Dewan, Agrim and Saha, Chandan and Sinha, Pulkit},
  title =	{{NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{16:1--16:21},
  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.2024.16},
  URN =		{urn:nbn:de:0030-drops-201598},
  doi =		{10.4230/LIPIcs.ICALP.2024.16},
  annote =	{Keywords: Equivalence testing, MCSP, sparse polynomials, 3SAT}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.136

Improved Algorithm for Reachability in d-VASS

Authors: Yuxi Fu, Qizhe Yang, and Yangluo Zheng

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

Abstract

An 𝖥_{d} upper bound for the reachability problem in vector addition systems with states (VASS) in fixed dimension is given, where 𝖥_d is the d-th level of the Grzegorczyk hierarchy of complexity classes. The new algorithm combines the idea of the linear path scheme characterization of the reachability in the 2-dimension VASSes with the general decomposition algorithm by Mayr, Kosaraju and Lambert. The result improves the 𝖥_{d + 4} upper bound due to Leroux and Schmitz (LICS 2019).

Cite as

Yuxi Fu, Qizhe Yang, and Yangluo Zheng. Improved Algorithm for Reachability in d-VASS. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 136:1-136:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fu_et_al:LIPIcs.ICALP.2024.136,
  author =	{Fu, Yuxi and Yang, Qizhe and Zheng, Yangluo},
  title =	{{Improved Algorithm for Reachability in d-VASS}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{136:1--136:18},
  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.2024.136},
  URN =		{urn:nbn:de:0030-drops-202799},
  doi =		{10.4230/LIPIcs.ICALP.2024.136},
  annote =	{Keywords: Petri net, vector addition system, reachability}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.FSTTCS.2023

LIPIcs, Volume 284, FSTTCS 2023, Complete Volume

Authors: Patricia Bouyer and Srikanth Srinivasan

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

Abstract

LIPIcs, Volume 284, FSTTCS 2023, Complete Volume

Cite as

43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 1-784, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Proceedings{bouyer_et_al:LIPIcs.FSTTCS.2023,
  title =	{{LIPIcs, Volume 284, FSTTCS 2023, Complete Volume}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{1--784},
  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},
  URN =		{urn:nbn:de:0030-drops-193724},
  doi =		{10.4230/LIPIcs.FSTTCS.2023},
  annote =	{Keywords: LIPIcs, Volume 284, FSTTCS 2023, Complete Volume}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.FSTTCS.2023.0

Front Matter, Table of Contents, Preface, Conference Organization

Authors: Patricia Bouyer and Srikanth Srinivasan

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

Abstract

Front Matter, Table of Contents, Preface, Conference Organization

Cite as

43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bouyer_et_al:LIPIcs.FSTTCS.2023.0,
  author =	{Bouyer, Patricia and Srinivasan, Srikanth},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{0:i--0:xvi},
  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.2023.0},
  URN =		{urn:nbn:de:0030-drops-193737},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.FSTTCS.2023.1

Reachability Games and Friends: A Journey Through the Lens of Memory and Complexity (Invited Talk)

Authors: Thomas Brihaye, Aline Goeminne, James C. A. Main, and Mickael Randour

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

Abstract

Reachability objectives are arguably the most basic ones in the theory of games on graphs (and beyond). But far from being bland, they constitute the cornerstone of this field. Reachability is everywhere, as are the tools we use to reason about it. In this invited contribution, we take the reader on a journey through a zoo of models that have reachability objectives at their core. Our goal is to illustrate how model complexity impacts the complexity of strategies needed to play optimally in the corresponding games and computational complexity.

Cite as

Thomas Brihaye, Aline Goeminne, James C. A. Main, and Mickael Randour. Reachability Games and Friends: A Journey Through the Lens of Memory and Complexity (Invited Talk). 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. 1:1-1:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{brihaye_et_al:LIPIcs.FSTTCS.2023.1,
  author =	{Brihaye, Thomas and Goeminne, Aline and Main, James C. A. and Randour, Mickael},
  title =	{{Reachability Games and Friends: A Journey Through the Lens of Memory and Complexity}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{1:1--1:26},
  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.2023.1},
  URN =		{urn:nbn:de:0030-drops-193747},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.1},
  annote =	{Keywords: Games on graphs, reachability, finite-memory strategies, complexity}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.FSTTCS.2023.2

On Measuring Average Case Complexity via Sum-Of-Squares Degree (Invited Talk)

Authors: Prasad Raghavendra

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

Abstract

Sum-of-squares semidefinite programming hierarchy is a sequence of increasingly complex semidefinite programs to reason about systems of polynomial inequalities. The k-th-level of the sum-of-squares SDP hierarchy is a semidefinite program that can be solved in time n^O(k). Sum-of-squares SDP hierarchies subsume fundamental algorithmic techniques such as linear programming and spectral methods. Many state-of-the-art algorithms for approximating NP-hard optimization problems are captured in the first few levels of the hierarchy. More recently, sum-of-squares SDPs have been applied extensively towards designing algorithms for average case problems. These include planted problems, random constraint satisfaction problems, and computational problems arising in statistics. From the standpoint of complexity theory, sum-of-squares SDPs can be applied towards measuring the average-case hardness of a problem. Most natural optimization problems can often be shown to be solvable by degree n sum-of-squares SDP, which corresponds to an exponential time algorithm. The smallest degree of the sum-of-squares relaxation needed to solve a problem can be used as a measure of the computational complexity of the problem. This approach seems especially useful for understanding average-case complexity under natural distributions. For example, the sum-of-squares degree has been used to nearly characterize the computational complexity of refuting random CSPs as a function of the number of constraints. Using the sum-of-squares degree as a proxy measure for average case complexity opens the door to formalizing certain computational phase transitions that have been conjectured for average case problems such as recovery in stochastic block models. In this talk, we discuss applications of this approach to average-case complexity and present some open problems.

Cite as

Prasad Raghavendra. On Measuring Average Case Complexity via Sum-Of-Squares Degree (Invited Talk). In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{raghavendra:LIPIcs.FSTTCS.2023.2,
  author =	{Raghavendra, Prasad},
  title =	{{On Measuring Average Case Complexity via Sum-Of-Squares Degree}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{2:1--2:1},
  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.2023.2},
  URN =		{urn:nbn:de:0030-drops-193750},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.2},
  annote =	{Keywords: semidefinite programming, sum-of-squares SDP, average case complexity, random SAT, stochastic block models}
}

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Invited Talk

DOI: 10.4230/LIPIcs.FSTTCS.2023.3

Computational and Information-Theoretic Questions from Causal Inference (Invited Talk)

Authors: Leonard J. Schulman

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

Abstract

Data, for the most part, is used in order to inform potential interventions: whether by individuals (decisions about education or employment), government (public health, environmental regulation, infrastructure investment) or business. The most common data analysis tools are those which identify correlations among variables - think of regression or of clustering. However, some famous paradoxes illustrate the futility of relying on correlations alone without a model for the causal relationships between variables. Historically, causality has been teased apart from correlation through controlled experiments. But for a variety of reasons - cost, ethical constraints, or uniqueness of the system - we must often make do with passive observation alone. A theory based upon directed graphical models has been developed over the past three decades, which in some situations, enables statistically defensible causal inference even in the absence of controlled experiments. Yet "some situations" is rather fewer than one would like. This limitation spurs a range of research questions. In this talk I will describe a couple of causality paradoxes along with how they are captured within the graphical model framework; this will lead naturally toward some of the computational and information-theoretic questions which arise in the theory.

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Leonard J. Schulman. Computational and Information-Theoretic Questions from Causal Inference (Invited Talk). In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{schulman:LIPIcs.FSTTCS.2023.3,
  author =	{Schulman, Leonard J.},
  title =	{{Computational and Information-Theoretic Questions from Causal Inference}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{3:1--3:1},
  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.2023.3},
  URN =		{urn:nbn:de:0030-drops-193769},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.3},
  annote =	{Keywords: Causal Inference, Bayesian Networks}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.FSTTCS.2023.4

From Concept Learning to SAT-Based Invariant Inference (Invited Talk)

Authors: Sharon Shoham

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

Abstract

In recent years SAT-based invariant inference algorithms such as interpolation-based model checking and PDR/IC3 have proven to be extremely successful in practice. However, the essence of their practical success and their performance guarantees are far less understood. This talk surveys results that establish formal connections and distinctions between SAT-based invariant inference and exact concept learning with queries, showing that learning techniques and algorithms can clarify foundational questions, illuminate existing algorithms, and suggest new directions for efficient invariant inference.

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Sharon Shoham. From Concept Learning to SAT-Based Invariant Inference (Invited Talk). In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{shoham:LIPIcs.FSTTCS.2023.4,
  author =	{Shoham, Sharon},
  title =	{{From Concept Learning to SAT-Based Invariant Inference}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{4:1--4:1},
  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.2023.4},
  URN =		{urn:nbn:de:0030-drops-193771},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.4},
  annote =	{Keywords: invariant inference, complexity, exact learning, interpolation, IC3}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.FSTTCS.2023.5

Algorithms in the Presence of Biased Inputs (Invited Talk)

Authors: Nisheeth K. Vishnoi

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

Abstract

Algorithms for optimization problems such as selection, ranking, and classification typically assume that the inputs are what they are promised to be. However, in several real-world applications of these problems, the input may contain systematic biases along socially salient attributes associated with inputs such as race, gender, or political opinion. Such biases can not only lead the outputs of the current algorithms to output sub-optimal solutions with respect to true inputs but may also adversely affect opportunities for individuals in disadvantaged socially salient groups. This talk will consider the question of using optimization to solve the aforementioned problems in the presence of biased inputs. It will start with models of biases in inputs and discuss alternate ways to design algorithms for the underlying problem that can mitigate the effects of biases by taking into account knowledge about biases. This talk is based on several joint works with a number of co-authors.

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Nisheeth K. Vishnoi. Algorithms in the Presence of Biased Inputs (Invited Talk). 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. 5:1-5:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vishnoi:LIPIcs.FSTTCS.2023.5,
  author =	{Vishnoi, Nisheeth K.},
  title =	{{Algorithms in the Presence of Biased Inputs}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{5:1--5:2},
  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.2023.5},
  URN =		{urn:nbn:de:0030-drops-193788},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.5},
  annote =	{Keywords: Algorithmic Bias}
}

Document

DOI: 10.4230/LIPIcs.FSTTCS.2023.6

Online Facility Location with Weights and Congestion

Authors: Arghya Chakraborty and Rahul Vaze

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

Abstract

The classic online facility location problem deals with finding the optimal set of facilities in an online fashion when demand requests arrive one at a time and facilities need to be opened to service these requests. In this work, we study two variants of the online facility location problem; (1) weighted requests and (2) congestion. Both of these variants are motivated by their applications to real life scenarios and the previously known results on online facility location cannot be directly adapted to analyse them. - Weighted requests: In this variant, each demand request is a pair (x,w) where x is the standard location of the demand while w is the corresponding weight of the request. The cost of servicing request (x,w) at facility F is w⋅ d(x,F). For this variant, given n requests, we present an online algorithm attaining a competitive ratio of 𝒪(log n) in the secretarial model for the weighted requests and show that it is optimal. -Congestion: The congestion variant considers the case when there is a congestion cost that grows with the number of requests served by each facility. For this variant, when the congestion cost is a monomial, we show that there exists an algorithm attaining a constant competitive ratio. This constant is a function of the exponent of the monomial and the facility opening cost but independent of the number of requests.

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Arghya Chakraborty and Rahul Vaze. Online Facility Location with Weights and Congestion. 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. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chakraborty_et_al:LIPIcs.FSTTCS.2023.6,
  author =	{Chakraborty, Arghya and Vaze, Rahul},
  title =	{{Online Facility Location with Weights and Congestion}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{6:1--6:22},
  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.2023.6},
  URN =		{urn:nbn:de:0030-drops-193797},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.6},
  annote =	{Keywords: online algorithms, online facility location, probabilistic method, weighted-requests, congestion}
}

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