37 Search Results for "Hirahara, Shuichi"

Document
DOI: 10.4230/LIPIcs.CCC.2024.29
Exact Search-To-Decision Reductions for Time-Bounded Kolmogorov Complexity

Authors: Shuichi Hirahara, Valentine Kabanets, Zhenjian Lu, and Igor C. Oliveira

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

Abstract
A search-to-decision reduction is a procedure that allows one to find a solution to a problem from the mere ability to decide when a solution exists. The existence of a search-to-decision reduction for time-bounded Kolmogorov complexity, i.e., the problem of checking if a string x can be generated by a t-time bounded program of description length s, is a long-standing open problem that dates back to the 1960s. In this work, we obtain new average-case and worst-case search-to-decision reductions for the complexity measure 𝖪^t and its randomized analogue rK^t: 1) (Conditional Errorless and Error-Prone Reductions for 𝖪^t) Under the assumption that 𝖤 requires exponential size circuits, we design polynomial-time average-case search-to-decision reductions for 𝖪^t in both errorless and error-prone settings. In fact, under the easiness of deciding 𝖪^t under the uniform distribution, we obtain a search algorithm for any given polynomial-time samplable distribution. In the error-prone reduction, the search algorithm works in the more general setting of conditional 𝖪^t complexity, i.e., it finds a minimum length t-time bound program for generating x given a string y. 2) (Unconditional Errorless Reduction for rK^t) We obtain an unconditional polynomial-time average-case search-to-decision reduction for rK^t in the errorless setting. Similarly to the results described above, we obtain a search algorithm for each polynomial-time samplable distribution, assuming the existence of a decision algorithm under the uniform distribution. To our knowledge, this is the first unconditional sub-exponential time search-to-decision reduction among the measures 𝖪^t and rK^t that works with respect to any given polynomial-time samplable distribution. 3) (Worst-Case to Average-Case Reductions) Under the errorless average-case easiness of deciding rK^t, we design a worst-case search algorithm running in time 2^O(n/log n) that produces a minimum length randomized t-time program for every input string x ∈ {0,1}ⁿ, with the caveat that it only succeeds on some explicitly computed sub-exponential time bound t ≤ 2^{n^ε} that depends on x. A similar result holds for 𝖪^t, under the assumption that 𝖤 requires exponential size circuits. In these results, the corresponding search problem is solved exactly, i.e., a successful run of the search algorithm outputs a t-time bounded program for x of minimum length, as opposed to an approximately optimal program of slightly larger description length or running time.
Cite as

Shuichi Hirahara, Valentine Kabanets, Zhenjian Lu, and Igor C. Oliveira. Exact Search-To-Decision Reductions for Time-Bounded Kolmogorov Complexity. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 29:1-29:56, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hirahara_et_al:LIPIcs.CCC.2024.29,
  author =	{Hirahara, Shuichi and Kabanets, Valentine and Lu, Zhenjian and Oliveira, Igor C.},
  title =	{{Exact Search-To-Decision Reductions for Time-Bounded Kolmogorov Complexity}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{29:1--29:56},
  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.2024.29},
  URN =		{urn:nbn:de:0030-drops-204256},
  doi =		{10.4230/LIPIcs.CCC.2024.29},
  annote =	{Keywords: average-case complexity, Kolmogorov complexity, search-to-decision reductions}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.34
Search-To-Decision Reductions for Kolmogorov Complexity

Authors: Noam Mazor and Rafael Pass

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

Abstract
A long-standing open problem dating back to the 1960s is whether there exists a search-to-decision reduction for the time-bounded Kolmogorov complexity problem - that is, the problem of determining whether the length of the shortest time-t program generating a given string x is at most s. In this work, we consider the more "robust" version of the time-bounded Kolmogorov complexity problem, referred to as the GapMINKT problem, where given a size bound s and a running time bound t, the goal is to determine whether there exists a poly(t,|x|)-time program of length s+O(log |x|) that generates x. We present the first non-trivial search-to-decision reduction R for the GapMINKT problem; R has a running-time bound of 2^{ε n} for any ε > 0 and additionally only queries its oracle on "thresholds" s of size s+O(log |x|). As such, we get that any algorithm with running-time (resp. circuit size) 2^{α s} poly(|x|,t,s) for solving GapMINKT (given an instance (x,t,s), yields an algorithm for finding a witness with running-time (resp. circuit size) 2^{(α+ε) s} poly(|x|,t,s). Our second result is a polynomial-time search-to-decision reduction for the time-bounded Kolmogorov complexity problem in the average-case regime. Such a reduction was recently shown by Liu and Pass (FOCS'20), heavily relying on cryptographic techniques. Our reduction is more direct and additionally has the advantage of being length-preserving, and as such also applies in the exponential time/size regime. A central component in both of these results is the use of Kolmogorov and Levin’s Symmetry of Information Theorem.
Cite as

Noam Mazor and Rafael Pass. Search-To-Decision Reductions for Kolmogorov Complexity. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mazor_et_al:LIPIcs.CCC.2024.34,
  author =	{Mazor, Noam and Pass, Rafael},
  title =	{{Search-To-Decision Reductions for Kolmogorov Complexity}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{34:1--34:20},
  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.2024.34},
  URN =		{urn:nbn:de:0030-drops-204308},
  doi =		{10.4230/LIPIcs.CCC.2024.34},
  annote =	{Keywords: Kolmogorov complexity, search to decision}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.36
Gap MCSP Is Not (Levin) NP-Complete in Obfustopia

Authors: Noam Mazor and Rafael Pass

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

Abstract
We demonstrate that under believable cryptographic hardness assumptions, Gap versions of standard meta-complexity problems, such as the Minimum Circuit Size Problem (MCSP) and the Minimum Time-Bounded Kolmogorov Complexity problem (MKTP) are not NP-complete w.r.t. Levin (i.e., witness-preserving many-to-one) reductions. In more detail: - Assuming the existence of indistinguishability obfuscation, and subexponentially-secure one-way functions, an appropriate Gap version of MCSP is not NP-complete under randomized Levin-reductions. - Assuming the existence of subexponentially-secure indistinguishability obfuscation, subexponentially-secure one-way functions and injective PRGs, an appropriate Gap version of MKTP is not NP-complete under randomized Levin-reductions.
Cite as

Noam Mazor and Rafael Pass. Gap MCSP Is Not (Levin) NP-Complete in Obfustopia. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mazor_et_al:LIPIcs.CCC.2024.36,
  author =	{Mazor, Noam and Pass, Rafael},
  title =	{{Gap MCSP Is Not (Levin) NP-Complete in Obfustopia}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{36:1--36:21},
  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.2024.36},
  URN =		{urn:nbn:de:0030-drops-204322},
  doi =		{10.4230/LIPIcs.CCC.2024.36},
  annote =	{Keywords: Kolmogorov complexity, MCSP, Levin Reduction}
}
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 A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.85
Optimal PSPACE-Hardness of Approximating Set Cover Reconfiguration

Authors: Shuichi Hirahara and Naoto Ohsaka

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

Abstract
In the Minmax Set Cover Reconfiguration problem, given a set system ℱ over a universe 𝒰 and its two covers 𝒞^start and 𝒞^goal of size k, we wish to transform 𝒞^start into 𝒞^goal by repeatedly adding or removing a single set of ℱ while covering the universe 𝒰 in any intermediate state. Then, the objective is to minimize the maximum size of any intermediate cover during transformation. We prove that Minmax Set Cover Reconfiguration and Minmax Dominating Set Reconfiguration are PSPACE-hard to approximate within a factor of 2-(1/polyloglog N), where N is the size of the universe and the number of vertices in a graph, respectively, improving upon Ohsaka (SODA 2024) [Ohsaka, 2024] and Karthik C. S. and Manurangsi (2023) [Karthik C. S. and Manurangsi, 2023]. This is the first result that exhibits a sharp threshold for the approximation factor of any reconfiguration problem because both problems admit a 2-factor approximation algorithm as per Ito, Demaine, Harvey, Papadimitriou, Sideri, Uehara, and Uno (Theor. Comput. Sci., 2011) [Takehiro Ito et al., 2011]. Our proof is based on a reconfiguration analogue of the FGLSS reduction [Feige et al., 1996] from Probabilistically Checkable Reconfiguration Proofs of Hirahara and Ohsaka (STOC 2024) [Hirahara and Ohsaka, 2024]. We also prove that for any constant ε ∈ (0,1), Minmax Hypergraph Vertex Cover Reconfiguration on poly(ε^-1)-uniform hypergraphs is PSPACE-hard to approximate within a factor of 2-ε.
Cite as

Shuichi Hirahara and Naoto Ohsaka. Optimal PSPACE-Hardness of Approximating Set Cover Reconfiguration. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 85:1-85:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hirahara_et_al:LIPIcs.ICALP.2024.85,
  author =	{Hirahara, Shuichi and Ohsaka, Naoto},
  title =	{{Optimal PSPACE-Hardness of Approximating Set Cover Reconfiguration}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{85:1--85:18},
  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.2024.85},
  URN =		{urn:nbn:de:0030-drops-202283},
  doi =		{10.4230/LIPIcs.ICALP.2024.85},
  annote =	{Keywords: reconfiguration problems, hardness of approximation, probabilistic proof systems, FGLSS reduction}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.110
Impagliazzo’s Worlds Through the Lens of Conditional Kolmogorov Complexity

Authors: Zhenjian Lu and Rahul Santhanam

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

Abstract
We develop new characterizations of Impagliazzo’s worlds Algorithmica, Heuristica and Pessiland by the intractability of conditional Kolmogorov complexity 𝖪 and conditional probabilistic time-bounded Kolmogorov complexity pK^t. In our first set of results, we show that NP ⊆ BPP iff pK^t(x ∣ y) can be computed efficiently in the worst case when t is sublinear in |x| + |y|; DistNP ⊆ HeurBPP iff pK^t(x ∣ y) can be computed efficiently over all polynomial-time samplable distributions when t is sublinear in |x| + |y|; and infinitely-often one-way functions fail to exist iff pK^t(x ∣ y) can be computed efficiently over all polynomial-time samplable distributions for t a sufficiently large polynomial in |x| + |y|. These results characterize Impagliazzo’s worlds Algorithmica, Heuristica and Pessiland purely in terms of the tractability of conditional pK^t. Notably, the results imply that Pessiland fails to exist iff the average-case intractability of conditional pK^t is insensitive to the difference between sublinear and polynomially bounded t. As a corollary, while we prove conditional pK^t to be NP-hard for sublinear t, showing NP-hardness for large enough polynomially bounded t would eliminate Pessiland as a possible world of average-case complexity. In our second set of results, we characterize Impagliazzo’s worlds Algorithmica, Heuristica and Pessiland by the distributional tractability of a natural problem, i.e., approximating the conditional Kolmogorov complexity, that is provably intractable in the worst case. We show that NP ⊆ BPP iff conditional Kolmogorov complexity can be approximated in the semi-worst case; and DistNP ⊆ HeurBPP iff conditional Kolmogorov complexity can be approximated on average over all independent polynomial-time samplable distributions. It follows from a result by Ilango, Ren, and Santhanam (STOC 2022) that infinitely-often one-way functions fail to exist iff conditional Kolmogorov complexity can be approximated on average over all polynomial-time samplable distributions. Together, these results yield the claimed characterizations. Our techniques, combined with previous work, also yield a characterization of auxiliary-input one-way functions and equivalences between different average-case tractability assumptions for conditional Kolmogorov complexity and its variants. Our results suggest that novel average-case tractability assumptions such as tractability in the semi-worst case and over independent polynomial-time samplable distributions might be worthy of further study.
Cite as

Zhenjian Lu and Rahul Santhanam. Impagliazzo’s Worlds Through the Lens of Conditional Kolmogorov Complexity. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 110:1-110:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lu_et_al:LIPIcs.ICALP.2024.110,
  author =	{Lu, Zhenjian and Santhanam, Rahul},
  title =	{{Impagliazzo’s Worlds Through the Lens of Conditional Kolmogorov Complexity}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{110:1--110:17},
  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.2024.110},
  URN =		{urn:nbn:de:0030-drops-202538},
  doi =		{10.4230/LIPIcs.ICALP.2024.110},
  annote =	{Keywords: meta-complexity, Kolmogorov complexity, one-way functions, average-case complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.113
Alphabet Reduction for Reconfiguration Problems

Authors: Naoto Ohsaka

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

Abstract
We present a reconfiguration analogue of alphabet reduction à la Dinur (J. ACM, 2007) and its applications. Given a binary constraint graph G and its two satisfying assignments ψ^ini and ψ^tar, the Maxmin 2-CSP Reconfiguration problem requests to transform ψ^ini into ψ^tar by repeatedly changing the value of a single vertex so that the minimum fraction of satisfied edges is maximized. We demonstrate a polynomial-time reduction from Maxmin 2-CSP Reconfiguration with arbitrarily large alphabet size W ∈ ℕ to itself with universal alphabet size W₀ ∈ ℕ such that 1) the perfect completeness is preserved, and 2) if any reconfiguration for the former violates ε-fraction of edges, then Ω(ε)-fraction of edges must be unsatisfied during any reconfiguration for the latter. The crux of its construction is the reconfigurability of Hadamard codes, which enables to reconfigure between a pair of codewords, while avoiding getting too close to the other codewords. Combining this alphabet reduction with gap amplification due to Ohsaka (SODA 2024), we are able to amplify the 1 vs. 1-ε gap for arbitrarily small ε ∈ (0,1) up to the 1 vs. 1-ε₀ for some universal ε₀ ∈ (0,1) without blowing up the alphabet size. In particular, a 1 vs. 1-ε₀ gap version of Maxmin 2-CSP Reconfiguration with alphabet size W₀ is PSPACE-hard given a probabilistically checkable reconfiguration proof system having any soundness error 1-ε due to Hirahara and Ohsaka (STOC 2024) and Karthik C. S. and Manurangsi (2023). As an immediate corollary, we show that there exists a universal constant ε₀ ∈ (0,1) such that many popular reconfiguration problems are PSPACE-hard to approximate within a factor of 1-ε₀, including those of 3-SAT, Independent Set, Vertex Cover, Clique, Dominating Set, and Set Cover. This may not be achieved only by gap amplification of Ohsaka, which makes the alphabet size gigantic depending on ε^-1.
Cite as

Naoto Ohsaka. Alphabet Reduction for Reconfiguration Problems. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 113:1-113:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ohsaka:LIPIcs.ICALP.2024.113,
  author =	{Ohsaka, Naoto},
  title =	{{Alphabet Reduction for Reconfiguration Problems}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{113:1--113:17},
  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.2024.113},
  URN =		{urn:nbn:de:0030-drops-202560},
  doi =		{10.4230/LIPIcs.ICALP.2024.113},
  annote =	{Keywords: reconfiguration problems, hardness of approximation, Hadamard codes, alphabet reduction}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.75
Total NP Search Problems with Abundant Solutions

Authors: Jiawei Li

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
We define a new complexity class TFAP to capture TFNP problems that possess abundant solutions for each input. We identify several problems across diverse fields that belong to TFAP, including WeakPigeon (finding a collision in a mapping from [2n] pigeons to [n] holes), Yamakawa-Zhandry’s problem [Takashi Yamakawa and Mark Zhandry, 2022], and all problems in TFZPP. Conversely, we introduce the notion of "semi-gluability" to characterize TFNP problems that could have a unique or a very limited number of solutions for certain inputs. We prove that there is no black-box reduction from any "semi-gluable" problems to any TFAP problems. Furthermore, it can be extended to rule out randomized black-box reduction in most cases. We identify that the majority of common TFNP subclasses, including PPA, PPAD, PPADS, PPP, PLS, CLS, SOPL, and UEOPL, are "semi-gluable". This leads to a broad array of oracle separation results within TFNP regime. As a corollary, UEOPL^O ⊈ PWPP^O relative to an oracle O.
Cite as

Jiawei Li. Total NP Search Problems with Abundant Solutions. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 75:1-75:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{li:LIPIcs.ITCS.2024.75,
  author =	{Li, Jiawei},
  title =	{{Total NP Search Problems with Abundant Solutions}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{75:1--75:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.75},
  URN =		{urn:nbn:de:0030-drops-196031},
  doi =		{10.4230/LIPIcs.ITCS.2024.75},
  annote =	{Keywords: TFNP, Pigeonhole Principle}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.39
Regularization of Low Error PCPs and an Application to MCSP

Authors: Shuichi Hirahara and Dana Moshkovitz

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
In a regular PCP the verifier queries each proof symbol in the same number of tests. This number is called the degree of the proof, and it is at least 1/(sq) where s is the soundness error and q is the number of queries. It is incredibly useful to have regularity and reduced degree in PCP. There is an expander-based transformation by Papadimitriou and Yannakakis that transforms any PCP with a constant number of queries and constant soundness error to a regular PCP with constant degree. There are also transformations for low error projection and unique PCPs. Other PCPs are constructed especially to be regular. In this work we show how to regularize and reduce degree of PCPs with a possibly large number of queries and low soundness error. As an application, we prove NP-hardness of an unweighted variant of the collective minimum monotone satisfying assignment problem, which was introduced by Hirahara (FOCS'22) to prove NP-hardness of MCSP^* (the partial function variant of the Minimum Circuit Size Problem) under randomized reductions. We present a simplified proof and sufficient conditions under which MCSP^* is NP-hard under the standard notion of reduction: MCSP^* is NP-hard under deterministic polynomial-time many-one reductions if there exists a function in E that satisfies certain direct sum properties.
Cite as

Shuichi Hirahara and Dana Moshkovitz. Regularization of Low Error PCPs and an Application to MCSP. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 39:1-39:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hirahara_et_al:LIPIcs.ISAAC.2023.39,
  author =	{Hirahara, Shuichi and Moshkovitz, Dana},
  title =	{{Regularization of Low Error PCPs and an Application to MCSP}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{39:1--39:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.39},
  URN =		{urn:nbn:de:0030-drops-193411},
  doi =		{10.4230/LIPIcs.ISAAC.2023.39},
  annote =	{Keywords: PCP theorem, regularization, Minimum Circuit Size Problem}
}
Document
DOI: 10.4230/LIPIcs.CCC.2023.6
Bounded Relativization

Authors: Shuichi Hirahara, Zhenjian Lu, and Hanlin Ren

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract
Relativization is one of the most fundamental concepts in complexity theory, which explains the difficulty of resolving major open problems. In this paper, we propose a weaker notion of relativization called bounded relativization. For a complexity class ℭ, we say that a statement is ℭ-relativizing if the statement holds relative to every oracle 𝒪 ∈ ℭ. It is easy to see that every result that relativizes also ℭ-relativizes for every complexity class ℭ. On the other hand, we observe that many non-relativizing results, such as IP = PSPACE, are in fact PSPACE-relativizing. First, we use the idea of bounded relativization to obtain new lower bound results, including the following nearly maximum circuit lower bound: for every constant ε > 0, BPE^{MCSP}/2^{εn} ⊈ SIZE[2ⁿ/n]. We prove this by PSPACE-relativizing the recent pseudodeterministic pseudorandom generator by Lu, Oliveira, and Santhanam (STOC 2021). Next, we study the limitations of PSPACE-relativizing proof techniques, and show that a seemingly minor improvement over the known results using PSPACE-relativizing techniques would imply a breakthrough separation NP ≠ L. For example: - Impagliazzo and Wigderson (JCSS 2001) proved that if EXP ≠ BPP, then BPP admits infinitely-often subexponential-time heuristic derandomization. We show that their result is PSPACE-relativizing, and that improving it to worst-case derandomization using PSPACE-relativizing techniques implies NP ≠ L. - Oliveira and Santhanam (STOC 2017) recently proved that every dense subset in P admits an infinitely-often subexponential-time pseudodeterministic construction, which we observe is PSPACE-relativizing. Improving this to almost-everywhere (pseudodeterministic) or (infinitely-often) deterministic constructions by PSPACE-relativizing techniques implies NP ≠ L. - Santhanam (SICOMP 2009) proved that pr-MA does not have fixed polynomial-size circuits. This lower bound can be shown PSPACE-relativizing, and we show that improving it to an almost-everywhere lower bound using PSPACE-relativizing techniques implies NP ≠ L. In fact, we show that if we can use PSPACE-relativizing techniques to obtain the above-mentioned improvements, then PSPACE ≠ EXPH. We obtain our barrier results by constructing suitable oracles computable in EXPH relative to which these improvements are impossible.
Cite as

Shuichi Hirahara, Zhenjian Lu, and Hanlin Ren. Bounded Relativization. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 6:1-6:45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hirahara_et_al:LIPIcs.CCC.2023.6,
  author =	{Hirahara, Shuichi and Lu, Zhenjian and Ren, Hanlin},
  title =	{{Bounded Relativization}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{6:1--6:45},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.6},
  URN =		{urn:nbn:de:0030-drops-182764},
  doi =		{10.4230/LIPIcs.CCC.2023.6},
  annote =	{Keywords: relativization, circuit lower bound, derandomization, explicit construction, pseudodeterministic algorithms, interactive proofs}
}
Document
DOI: 10.4230/LIPIcs.CCC.2023.12
Improved Learning from Kolmogorov Complexity

Authors: Halley Goldberg and Valentine Kabanets

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract
Carmosino, Impagliazzo, Kabanets, and Kolokolova (CCC, 2016) showed that the existence of natural properties in the sense of Razborov and Rudich (JCSS, 1997) implies PAC learning algorithms in the sense of Valiant (Comm. ACM, 1984), for boolean functions in P/poly, under the uniform distribution and with membership queries. It is still an open problem to get from natural properties learning algorithms that do not rely on membership queries but rather use randomly drawn labeled examples. Natural properties may be understood as an average-case version of MCSP, the problem of deciding the minimum size of a circuit computing a given truth-table. Problems related to MCSP include those concerning time-bounded Kolmogorov complexity. MKTP, for example, asks for the KT-complexity of a given string. KT-complexity is a relaxation of circuit size, as it does away with the requirement that a short description of a string be interpreted as a boolean circuit. In this work, under assumptions of MKTP and the related problem MK^tP being easy on average, we get learning algorithms for boolean functions in P/poly that - work over any distribution D samplable by a family of polynomial-size circuits (given explicitly in the case of MKTP), - only use randomly drawn labeled examples from D, and - are agnostic (do not require the target function to belong to the hypothesis class). Our results build upon the recent work of Hirahara and Nanashima (FOCS, 2021) who showed similar learning consequences but under a stronger assumption that NP is easy on average.
Cite as

Halley Goldberg and Valentine Kabanets. Improved Learning from Kolmogorov Complexity. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 12:1-12:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{goldberg_et_al:LIPIcs.CCC.2023.12,
  author =	{Goldberg, Halley and Kabanets, Valentine},
  title =	{{Improved Learning from Kolmogorov Complexity}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{12:1--12:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.12},
  URN =		{urn:nbn:de:0030-drops-182825},
  doi =		{10.4230/LIPIcs.CCC.2023.12},
  annote =	{Keywords: learning, Kolmogorov complexity, meta-complexity, average-case complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.3
Kolmogorov Complexity Characterizes Statistical Zero Knowledge

Authors: Eric Allender, Shuichi Hirahara, and Harsha Tirumala

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We show that a decidable promise problem has a non-interactive statistical zero-knowledge proof system if and only if it is randomly reducible via an honest polynomial-time reduction to a promise problem for Kolmogorov-random strings, with a superlogarithmic additive approximation term. This extends recent work by Saks and Santhanam (CCC 2022). We build on this to give new characterizations of Statistical Zero Knowledge SZK, as well as the related classes NISZK_L and SZK_L.
Cite as

Eric Allender, Shuichi Hirahara, and Harsha Tirumala. Kolmogorov Complexity Characterizes Statistical Zero Knowledge. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{allender_et_al:LIPIcs.ITCS.2023.3,
  author =	{Allender, Eric and Hirahara, Shuichi and Tirumala, Harsha},
  title =	{{Kolmogorov Complexity Characterizes Statistical Zero Knowledge}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{3:1--3:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.3},
  URN =		{urn:nbn:de:0030-drops-175063},
  doi =		{10.4230/LIPIcs.ITCS.2023.3},
  annote =	{Keywords: Kolmogorov Complexity, Interactive Proofs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.70
Learning Versus Pseudorandom Generators in Constant Parallel Time

Authors: Shuichi Hirahara and Mikito Nanashima

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
A polynomial-stretch pseudorandom generator (PPRG) in NC⁰ (i.e., constant parallel time) is one of the most important cryptographic primitives, especially for constructing highly efficient cryptography and indistinguishability obfuscation. The celebrated work (Applebaum, Ishai, and Kushilevitz, SIAM Journal on Computing, 2006) on randomized encodings yields the characterization of sublinear-stretch pseudorandom generators in NC⁰ by the existence of logspace-computable one-way functions, but characterizing PPRGs in NC⁰ seems out of reach at present. Therefore, it is natural to ask which sort of hardness notion is essential for constructing PPRGs in NC⁰. Particularly, to the best of our knowledge, all the previously known candidates for PPRGs in NC⁰ follow only one framework based on Goldreich’s one-way function. In this paper, we present a new learning-theoretic characterization for PPRGs in NC⁰ and related classes. Specifically, we consider the average-case hardness of learning for well-studied classes in parameterized settings, where the number of samples is restricted to fixed-parameter tractable (FPT), and show that the following are equivalent: - The existence of (a collection of) PPRGs in NC⁰. - The average-case hardness of learning sparse 𝔽₂-polynomials on a sparse example distribution and an NC⁰-samplable target distribution (i.e., a distribution on target functions). - The average-case hardness of learning Fourier-sparse functions on a sparse example distribution and an NC⁰-samplable target distribution. - The average-case hardness of learning constant-depth parity decision trees on a sparse example distribution and an NC⁰-samplable target distribution. Furthermore, we characterize a (single) PPRG in parity-NC⁰ by the average-case hardness of learning constant-degree 𝔽₂-polynomials on a uniform example distribution with FPT samples. Based on our results, we propose new candidates for PPRGs in NC⁰ and related classes under a hardness assumption on a natural learning problem. An important property of PPRGs in NC⁰ constructed in our framework is that the output bits are computed by various predicates; thus, it seems to resist an attack that depends on a specific property of one fixed predicate. Conceptually, the main contribution of this study is to formalize a theory of FPT dualization of concept classes, which yields a meta-theorem for the first result. For the second result on PPRGs in parity-NC⁰, we use a different technique of pseudorandom 𝔽₂-polynomials.
Cite as

Shuichi Hirahara and Mikito Nanashima. Learning Versus Pseudorandom Generators in Constant Parallel Time. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 70:1-70:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hirahara_et_al:LIPIcs.ITCS.2023.70,
  author =	{Hirahara, Shuichi and Nanashima, Mikito},
  title =	{{Learning Versus Pseudorandom Generators in Constant Parallel Time}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{70:1--70:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.70},
  URN =		{urn:nbn:de:0030-drops-175736},
  doi =		{10.4230/LIPIcs.ITCS.2023.70},
  annote =	{Keywords: Parallel cryptography, polynomial-stretch pseudorandom generators in NC⁰, PAC learning, average-case complexity, fixed-parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.16
Probabilistic Kolmogorov Complexity with Applications to Average-Case Complexity

Authors: Halley Goldberg, Valentine Kabanets, Zhenjian Lu, and Igor C. Oliveira

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
Understanding the relationship between the worst-case and average-case complexities of NP and of other subclasses of PH is a long-standing problem in complexity theory. Over the last few years, much progress has been achieved in this front through the investigation of meta-complexity: the complexity of problems that refer to the complexity of the input string x (e.g., given a string x, estimate its time-bounded Kolmogorov complexity). In particular, [Shuichi Hirahara, 2021] employed techniques from meta-complexity to show that if DistNP ⊆ AvgP then UP ⊆ DTIME[2^{O(n/log n)}]. While this and related results [Shuichi Hirahara and Mikito Nanashima, 2021; Lijie Chen et al., 2022] offer exciting progress after a long gap, they do not survive in the setting of randomized computations: roughly speaking, "randomness" is the opposite of "structure", and upper bounding the amount of structure (time-bounded Kolmogorov complexity) of different objects is crucial in recent applications of meta-complexity. This limitation is significant, since randomized computations are ubiquitous in algorithm design and give rise to a more robust theory of average-case complexity [Russell Impagliazzo and Leonid A. Levin, 1990]. In this work, we develop a probabilistic theory of meta-complexity, by incorporating randomness into the notion of complexity of a string x. This is achieved through a new probabilistic variant of time-bounded Kolmogorov complexity that we call pK^t complexity. Informally, pK^t(x) measures the complexity of x when shared randomness is available to all parties involved in a computation. By porting key results from meta-complexity to the probabilistic domain of pK^t complexity and its variants, we are able to establish new connections between worst-case and average-case complexity in the important setting of probabilistic computations: - If DistNP ⊆ AvgBPP, then UP ⊆ RTIME[2^O(n/log n)]. - If DistΣ^P_2 ⊆ AvgBPP, then AM ⊆ BPTIME[2^O(n/log n)]. - In the fine-grained setting [Lijie Chen et al., 2022], we get UTIME[2^O(√{nlog n})] ⊆ RTIME[2^O(√{nlog n})] and AMTIME[2^O(√{nlog n})] ⊆ BPTIME[2^O(√{nlog n})] from stronger average-case assumptions. - If DistPH ⊆ AvgBPP, then PH ⊆ BPTIME[2^O(n/log n)]. Specifically, for any 𝓁 ≥ 0, if DistΣ_{𝓁+2}^P ⊆ AvgBPP then Σ_𝓁^{P} ⊆ BPTIME[2^O(n/log n)]. - Strengthening a result from [Shuichi Hirahara and Mikito Nanashima, 2021], we show that if DistNP ⊆ AvgBPP then polynomial size Boolean circuits can be agnostically PAC learned under any unknown 𝖯/poly-samplable distribution in polynomial time. In some cases, our framework allows us to significantly simplify existing proofs, or to extend results to the more challenging probabilistic setting with little to no extra effort.
Cite as

Halley Goldberg, Valentine Kabanets, Zhenjian Lu, and Igor C. Oliveira. Probabilistic Kolmogorov Complexity with Applications to Average-Case Complexity. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 16:1-16:60, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{goldberg_et_al:LIPIcs.CCC.2022.16,
  author =	{Goldberg, Halley and Kabanets, Valentine and Lu, Zhenjian and Oliveira, Igor C.},
  title =	{{Probabilistic Kolmogorov Complexity with Applications to Average-Case Complexity}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{16:1--16:60},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.16},
  URN =		{urn:nbn:de:0030-drops-165785},
  doi =		{10.4230/LIPIcs.CCC.2022.16},
  annote =	{Keywords: average-case complexity, Kolmogorov complexity, meta-complexity, worst-case to average-case reductions, learning}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.25
Finding Errorless Pessiland in Error-Prone Heuristica

Authors: Shuichi Hirahara and Mikito Nanashima

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
Average-case complexity has two standard formulations, i.e., errorless complexity and error-prone complexity. In average-case complexity, a critical topic of research is to show the equivalence between these formulations, especially on the average-case complexity of NP. In this study, we present a relativization barrier for such an equivalence. Specifically, we construct an oracle relative to which NP is easy on average in the error-prone setting (i.e., DistNP ⊆ HeurP) but hard on average in the errorless setting even by 2^o(n/log n)-size circuits (i.e., DistNP ⊈ AvgSIZE[2^o(n/log n)]), which provides an answer to the open question posed by Impagliazzo (CCC 2011). Additionally, we show the following in the same relativized world: - Lower bound of meta-complexity: GapMINKT^𝒪 ∉ prSIZE^𝒪[2^o(n/log n)] and GapMCSP^𝒪 ∉ prSIZE^𝒪[2^(n^ε)] for some ε > 0. - Worst-case hardness of learning on uniform distributions: P/poly is not weakly PAC learnable with membership queries on the uniform distribution by nonuniform 2ⁿ/n^ω(1)-time algorithms. - Average-case hardness of distribution-free learning: P/poly is not weakly PAC learnable on average by nonuniform 2^o(n/log n)-time algorithms. - Weak cryptographic primitives: There exist a hitting set generator, an auxiliary-input one-way function, an auxiliary-input pseudorandom generator, and an auxiliary-input pseudorandom function against SIZE^𝒪[2^o(n/log n)]. This provides considerable insights into Pessiland (i.e., the world in which no one-way function exists, and NP is hard on average), such as the relativized separation of the error-prone average-case hardness of NP and auxiliary-input cryptography. At the core of our oracle construction is a new notion of random restriction with masks.
Cite as

Shuichi Hirahara and Mikito Nanashima. Finding Errorless Pessiland in Error-Prone Heuristica. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 25:1-25:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hirahara_et_al:LIPIcs.CCC.2022.25,
  author =	{Hirahara, Shuichi and Nanashima, Mikito},
  title =	{{Finding Errorless Pessiland in Error-Prone Heuristica}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{25:1--25:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.25},
  URN =		{urn:nbn:de:0030-drops-165875},
  doi =		{10.4230/LIPIcs.CCC.2022.25},
  annote =	{Keywords: average-case complexity, oracle separation, relativization barrier, meta-complexity, learning, auxiliary-input cryptography}
}
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