5 Search Results for "Yang, Fan"

Document
DOI: 10.4230/LIPIcs.ITCS.2023.35
Black-Box Constructive Proofs Are Unavoidable

Authors: Lijie Chen, Ryan Williams, and Tianqi Yang

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

Abstract
Following Razborov and Rudich, a "natural property" for proving a circuit lower bound satisfies three axioms: constructivity, largeness, and usefulness. In 2013, Williams proved that for any reasonable circuit class C, NEXP ⊂ C is equivalent to the existence of a constructive property useful against C. Here, a property is constructive if it can be decided in poly(N) time, where N = 2ⁿ is the length of the truth-table of the given n-input function. Recently, Fan, Li, and Yang initiated the study of black-box natural properties, which require a much stronger notion of constructivity, called black-box constructivity: the property should be decidable in randomized polylog(N) time, given oracle access to the n-input function. They showed that most proofs based on random restrictions yield black-box natural properties, and demonstrated limitations on what black-box natural properties can prove. In this paper, perhaps surprisingly, we prove that the equivalence of Williams holds even with this stronger notion of black-box constructivity: for any reasonable circuit class C, NEXP ⊂ C is equivalent to the existence of a black-box constructive property useful against C. The main technical ingredient in proving this equivalence is a smooth, strong, and locally-decodable probabilistically checkable proof (PCP), which we construct based on a recent work by Paradise. As a by-product, we show that average-case witness lower bounds for PCP verifiers follow from NEXP lower bounds. We also show that randomness is essential in the definition of black-box constructivity: we unconditionally prove that there is no deterministic polylog(N)-time constructive property that is useful against even polynomial-size AC⁰ circuits.
Cite as

Lijie Chen, Ryan Williams, and Tianqi Yang. Black-Box Constructive Proofs Are Unavoidable. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 35:1-35:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2023.35,
  author =	{Chen, Lijie and Williams, Ryan and Yang, Tianqi},
  title =	{{Black-Box Constructive Proofs Are Unavoidable}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{35:1--35:24},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.35},
  URN =		{urn:nbn:de:0030-drops-175380},
  doi =		{10.4230/LIPIcs.ITCS.2023.35},
  annote =	{Keywords: Circuit lower bounds, natural proofs, probabilistic checkable proofs}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.23
Extremely Efficient Constructions of Hash Functions, with Applications to Hardness Magnification and PRFs

Authors: Lijie Chen, Jiatu Li, and Tianqi Yang

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

Abstract
In a recent work, Fan, Li, and Yang (STOC 2022) constructed a family of almost-universal hash functions such that each function in the family is computable by (2n + o(n))-gate circuits of fan-in 2 over the B₂ basis. Applying this family, they established the existence of pseudorandom functions computable by circuits of the same complexity, under the standard assumption that OWFs exist. However, a major disadvantage of the hash family construction by Fan, Li, and Yang (STOC 2022) is that it requires a seed length of poly(n), which limits its potential applications. We address this issue by giving an improved construction of almost-universal hash functions with seed length polylog(n), such that each function in the family is computable with POLYLOGTIME-uniform (2n + o(n))-gate circuits. Our new construction has the following applications in both complexity theory and cryptography. - (Hardness magnification). Let α : ℕ → ℕ be any function such that α(n) ≤ log n / log log n. We show that if there is an n^{α(n)}-sparse NP language that does not have probabilistic circuits of 2n + O(n/log log n) gates, then we have (1) NTIME[2ⁿ] ⊈ SIZE[2^{n^{1/5}}] and (2) NP ⊈ SIZE[n^k] for every constant k. Complementing this magnification phenomenon, we present an O(n)-sparse language in P which requires probabilistic circuits of size at least 2n - 2. This is the first result in hardness magnification showing that even a sub-linear additive improvement on known circuit size lower bounds would imply NEXP ⊄ P_{/poly}. Following Chen, Jin, and Williams (STOC 2020), we also establish a sharp threshold for explicit obstructions: we give an explict obstruction against (2n-2)-size circuits, and prove that a sub-linear additive improvement on the circuit size would imply (1) DTIME[2ⁿ] ⊈ SIZE[2^{n^{1/5}}] and (2) P ⊈ SIZE[n^k] for every constant k. - (Extremely efficient construction of pseudorandom functions). Assuming that one of integer factoring, decisional Diffie-Hellman, or ring learning-with-errors is sub-exponentially hard, we show the existence of pseudorandom functions computable by POLYLOGTIME-uniform AC⁰[2] circuits with 2n + o(n) wires, with key length polylog(n). We also show that PRFs computable by POLYLOGTIME-uniform B₂ circuits of 2n + o(n) gates follows from the existence of sub-exponentially secure one-way functions.
Cite as

Lijie Chen, Jiatu Li, and Tianqi Yang. Extremely Efficient Constructions of Hash Functions, with Applications to Hardness Magnification and PRFs. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 23:1-23:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chen_et_al:LIPIcs.CCC.2022.23,
  author =	{Chen, Lijie and Li, Jiatu and Yang, Tianqi},
  title =	{{Extremely Efficient Constructions of Hash Functions, with Applications to Hardness Magnification and PRFs}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{23:1--23:37},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.23},
  URN =		{urn:nbn:de:0030-drops-165852},
  doi =		{10.4230/LIPIcs.CCC.2022.23},
  annote =	{Keywords: Almost universal hash functions, hardness magnification, pseudorandom functions}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2021.52
Linear-Time Temporal Logic with Team Semantics: Expressivity and Complexity

Authors: Jonni Virtema, Jana Hofmann, Bernd Finkbeiner, Juha Kontinen, and Fan Yang

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
We study the expressivity and complexity of model checking of linear temporal logic with team semantics (TeamLTL). TeamLTL, despite being a purely modal logic, is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. TeamLTL has been introduced quite recently and only few results are known regarding its expressivity and its model checking problem. We relate the expressivity of TeamLTL to logics for hyperproperties obtained by extending LTL with trace and propositional quantifiers (HyperLTL and HyperQPTL). By doing so, we obtain a number of model checking results for TeamLTL and identify its undecidability frontier. In particular, we show decidability of model checking of the so-called left-flat fragment of any downward closed TeamLTL -extension. Moreover, we establish that the model checking problem of TeamLTL with Boolean disjunction and inclusion atoms is undecidable.
Cite as

Jonni Virtema, Jana Hofmann, Bernd Finkbeiner, Juha Kontinen, and Fan Yang. Linear-Time Temporal Logic with Team Semantics: Expressivity and Complexity. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 52:1-52:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{virtema_et_al:LIPIcs.FSTTCS.2021.52,
  author =	{Virtema, Jonni and Hofmann, Jana and Finkbeiner, Bernd and Kontinen, Juha and Yang, Fan},
  title =	{{Linear-Time Temporal Logic with Team Semantics: Expressivity and Complexity}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{52:1--52:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.52},
  URN =		{urn:nbn:de:0030-drops-155634},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.52},
  annote =	{Keywords: Linear temporal logic, Hyperproperties, Model Checking, Expressivity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.19
Counting of Teams in First-Order Team Logics

Authors: Anselm Haak, Juha Kontinen, Fabian Müller, Heribert Vollmer, and Fan Yang

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We study descriptive complexity of counting complexity classes in the range from #P to #*NP. A corollary of Fagin’s characterization of NP by existential second-order logic is that #P can be logically described as the class of functions counting satisfying assignments to free relation variables in first-order formulae. In this paper we extend this study to classes beyond #P and extensions of first-order logic with team semantics. These team-based logics are closely related to existential second-order logic and its fragments, hence our results also shed light on the complexity of counting for extensions of first-order logic in Tarski’s semantics. Our results show that the class #*NP can be logically characterized by independence logic and existential second-order logic, whereas dependence logic and inclusion logic give rise to subclasses of #*NP and #P, respectively. We also study the function class generated by inclusion logic and relate it to the complexity class TotP, which is a subclass of #P. Our main technical result shows that the problem of counting satisfying assignments for monotone Boolean Sigma_1-formulae is #*NP-complete with respect to Turing reductions as well as complete for the function class generated by dependence logic with respect to first-order reductions.
Cite as

Anselm Haak, Juha Kontinen, Fabian Müller, Heribert Vollmer, and Fan Yang. Counting of Teams in First-Order Team Logics. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{haak_et_al:LIPIcs.MFCS.2019.19,
  author =	{Haak, Anselm and Kontinen, Juha and M\"{u}ller, Fabian and Vollmer, Heribert and Yang, Fan},
  title =	{{Counting of Teams in First-Order Team Logics}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.19},
  URN =		{urn:nbn:de:0030-drops-109634},
  doi =		{10.4230/LIPIcs.MFCS.2019.19},
  annote =	{Keywords: team-based logics, counting classes, finite model theory, descriptive complexity}
}
Document
DOI: 10.4230/LIPIcs.CPM.2016.15
Genomic Scaffold Filling Revisited

Authors: Haitao Jiang, Chenglin Fan, Boting Yang, Farong Zhong, Daming Zhu, and Binhai Zhu

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

Abstract
The genomic scaffold filling problem has attracted a lot of attention recently. The problem is on filling an incomplete sequence (scaffold) I into I', with respect to a complete reference genome G, such that the number of adjacencies between G and I' is maximized. The problem is NP-complete and APX-hard, and admits a 1.2-approximation. However, the sequence input I is not quite practical and does not fit most of the real datasets (where a scaffold is more often given as a list of contigs). In this paper, we revisit the genomic scaffold filling problem by considering this important case when, (1) a scaffold S is given, the missing genes X = c(G) - c(S) can only be inserted in between the contigs, and the objective is to maximize the number of adjacencies between G and the filled S' and (2) a scaffold S is given, a subset of the missing genes X' subset X = c(G) - c(S) can only be inserted in between the contigs, and the objective is still to maximize the number of adjacencies between G and the filled S''. For problem (1), we present a simple NP-completeness proof, we then present a factor-2 greedy approximation algorithm, and finally we show that the problem is FPT when each gene appears at most d times in G. For problem (2), we prove that the problem is W[1]-hard and then we present a factor-2 FPT-approximation for the case when each gene appears at most d times in G.
Cite as

Haitao Jiang, Chenglin Fan, Boting Yang, Farong Zhong, Daming Zhu, and Binhai Zhu. Genomic Scaffold Filling Revisited. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 15:1-15:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{jiang_et_al:LIPIcs.CPM.2016.15,
  author =	{Jiang, Haitao and Fan, Chenglin and Yang, Boting and Zhong, Farong and Zhu, Daming and Zhu, Binhai},
  title =	{{Genomic Scaffold Filling Revisited}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{15:1--15:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.15},
  URN =		{urn:nbn:de:0030-drops-60791},
  doi =		{10.4230/LIPIcs.CPM.2016.15},
  annote =	{Keywords: Computational biology, Approximation algorithms, FPT algorithms, NP- completeness}
}
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