International Symposium on Mathematical Foundations of Computer Science最新文献_第6页

Gaps, Ambiguity, and Establishing Complexity-Class Containments via Iterative Constant-Setting 间隙、模糊性和通过迭代常数设置建立复杂性类包含

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-09-29 DOI: 10.4230/LIPIcs.MFCS.2022.57

L. Hemaspaandra, Mandar Juvekar, A. Nadjimzadah, Patrick Phillips

{"title":"Gaps, Ambiguity, and Establishing Complexity-Class Containments via Iterative Constant-Setting","authors":"L. Hemaspaandra, Mandar Juvekar, A. Nadjimzadah, Patrick Phillips","doi":"10.4230/LIPIcs.MFCS.2022.57","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2022.57","url":null,"abstract":"Cai and Hemachandra used iterative constant-setting to prove that Few ⊆ ⊕ P (and thus that FewP ⊆ ⊕ P). In this paper, we note that there is a tension between the nondeterministic ambiguity of the class one is seeking to capture, and the density (or, to be more precise, the needed “nongappy”-ness) of the easy-to-ﬁnd “targets” used in iterative constant-setting. In particular, we show that even less restrictive gap-size upper bounds regarding the targets allow one to capture ambiguity-limited classes. Through a ﬂexible, metatheorem-based approach, we do so for a wide range of classes including the logarithmic-ambiguity version of Valiant’s unambiguous nondeterminism class UP. Our work lowers the bar for what advances regarding the existence of inﬁnite, P-printable sets of primes would suﬃce to show that restricted counting classes based on the primes have the power to accept superconstant-ambiguity analogues of UP. As an application of our work, we prove that the Lenstra–Pomerance–Wagstaﬀ Conjecture implies that all O (log log n )-ambiguity NP sets are in the restricted counting class RC PRIMES .","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128757128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Kernels for d-Path Vertex Cover 关于d路径顶点覆盖的核

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-07-26 DOI: 10.4230/LIPIcs.MFCS.2022.29

Radovan Cervený, Pratibha Choudhary, O. Suchý

引用次数: 5

Griddings of permutations and hardness of pattern matching 排列网格和模式匹配的硬度

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-07-22 DOI: 10.4230/LIPIcs.MFCS.2021.65

V'it Jel'inek, Michal Opler, J. Pek'arek

{"title":"Griddings of permutations and hardness of pattern matching","authors":"V'it Jel'inek, Michal Opler, J. Pek'arek","doi":"10.4230/LIPIcs.MFCS.2021.65","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.65","url":null,"abstract":"We study the complexity of the decision problem known as Permutation Pattern Matching, or PPM. The input of PPM consists of a pair of permutations $tau$ (the `text') and $pi$ (the `pattern'), and the goal is to decide whether $tau$ contains $pi$ as a subpermutation. On general inputs, PPM is known to be NP-complete by a result of Bose, Buss and Lubiw. In this paper, we focus on restricted instances of PPM where the text is assumed to avoid a fixed (small) pattern $sigma$; this restriction is known as Av($sigma$)-PPM. It has been previously shown that Av($sigma$)-PPM is polynomial for any $sigma$ of size at most 3, while it is NP-hard for any $sigma$ containing a monotone subsequence of length four. In this paper, we present a new hardness reduction which allows us to show, in a uniform way, that Av($sigma$)-PPM is hard for every $sigma$ of size at least 6, for every $sigma$ of size 5 except the symmetry class of $41352$, as well as for every $sigma$ symmetric to one of the three permutations $4321$, $4312$ and $4231$. Moreover, assuming the exponential time hypothesis, none of these hard cases of Av($sigma$)-PPM can be solved in time $2^{o(n/log n)}$. Previously, such conditional lower bound was not known even for the unconstrained PPM problem. On the tractability side, we combine the CSP approach of Guillemot and Marx with the structural results of Huczynska and Vatter to show that for any monotone-griddable permutation class C, PPM is polynomial when the text is restricted to a permutation from C.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127186574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Fractional homomorphism, Weisfeiler-Leman invariance, and the Sherali-Adams hierarchy for the Constraint Satisfaction Problem 约束满足问题的分数同态、Weisfeiler-Leman不变性和Sherali-Adams层次

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-07-07 DOI: 10.4230/LIPIcs.MFCS.2021.27

Silvia Butti, V. Dalmau

{"title":"Fractional homomorphism, Weisfeiler-Leman invariance, and the Sherali-Adams hierarchy for the Constraint Satisfaction Problem","authors":"Silvia Butti, V. Dalmau","doi":"10.4230/LIPIcs.MFCS.2021.27","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.27","url":null,"abstract":"Given a pair of graphs $textbf{A}$ and $textbf{B}$, the problems of deciding whether there exists either a homomorphism or an isomorphism from $textbf{A}$ to $textbf{B}$ have received a lot of attention. While graph homomorphism is known to be NP-complete, the complexity of the graph isomorphism problem is not fully understood. A well-known combinatorial heuristic for graph isomorphism is the Weisfeiler-Leman test together with its higher order variants. On the other hand, both problems can be reformulated as integer programs and various LP methods can be applied to obtain high-quality relaxations that can still be solved efficiently. We study so-called fractional relaxations of these programs in the more general context where $textbf{A}$ and $textbf{B}$ are not graphs but arbitrary relational structures. We give a combinatorial characterization of the Sherali-Adams hierarchy applied to the homomorphism problem in terms of fractional isomorphism. Collaterally, we also extend a number of known results from graph theory to give a characterization of the notion of fractional isomorphism for relational structures in terms of the Weisfeiler-Leman test, equitable partitions, and counting homomorphisms from trees. As a result, we obtain a description of the families of CSPs that are closed under Weisfeiler-Leman invariance in terms of their polymorphisms as well as decidability by the first level of the Sherali-Adams hierarchy.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128383799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 10

Syntactic Minimization of Nondeterministic Finite Automata 不确定有限自动机的句法最小化

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-07-07 DOI: 10.4230/LIPIcs.MFCS.2021.78

R. Myers, Henning Urbat

{"title":"Syntactic Minimization of Nondeterministic Finite Automata","authors":"R. Myers, Henning Urbat","doi":"10.4230/LIPIcs.MFCS.2021.78","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.78","url":null,"abstract":"Nondeterministic automata may be viewed as succinct programs implementing deterministic automata, i.e. complete specifications. Converting a given deterministic automaton into a small nondeterministic one is known to be computationally very hard; in fact, the ensuing decision problem is PSPACE-complete. This paper stands in stark contrast to the status quo. We restrict attention to subatomic nondeterministic automata, whose individual states accept unions of syntactic congruence classes. They are general enough to cover almost all structural results concerning nondeterministic state-minimality. We prove that converting a monoid recognizing a regular language into a small subatomic acceptor corresponds to an NP-complete problem. The NP certificates are solutions of simple equations involving relations over the syntactic monoid. We also consider the subclass of atomic nondeterministic automata introduced by Brzozowski and Tamm. Given a deterministic automaton and another one for the reversed language, computing small atomic acceptors is shown to be NP-complete with analogous certificates. Our complexity results emerge from an algebraic characterization of (sub)atomic acceptors in terms of deterministic automata with semilattice structure, combined with an equivalence of categories leading to succinct representations.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124596913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

On Search Complexity of Discrete Logarithm 关于离散对数的搜索复杂度

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-07-06 DOI: 10.4230/LIPIcs.MFCS.2021.60

Pavel Hubácek, Jan Václavek

{"title":"On Search Complexity of Discrete Logarithm","authors":"Pavel Hubácek, Jan Václavek","doi":"10.4230/LIPIcs.MFCS.2021.60","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.60","url":null,"abstract":"In this work, we study the discrete logarithm problem in the context of TFNP – the complexity class of search problems with a syntactically guaranteed existence of a solution for all instances. Our main results establish that suitable variants of the discrete logarithm problem are complete for the complexity class PPP, respectively PWPP, i.e., the subclasses of TFNP capturing total search problems with a solution guaranteed by the pigeonhole principle, respectively the weak pigeonhole principle. Besides answering an open problem from the recent work of Sotiraki, Zampetakis, and Zirdelis (FOCS’18), our completeness results for PPP and PWPP have implications for the recent line of work proving conditional lower bounds for problems in TFNP under cryptographic assumptions. In particular, they highlight that any attempt at basing average-case hardness in subclasses of TFNP (other than PWPP and PPP) on the average-case hardness of the discrete logarithm problem must exploit its structural properties beyond what is necessary for constructions of collision-resistant hash functions. Additionally, our reductions provide new structural insights into the class PWPP by establishing two new PWPP-complete problems. First, the problem Dove, a relaxation of the PPP-complete problem Pigeon. Dove is the first PWPP-complete problem not defined in terms of an explicitly shrinking function. Second, the problem Claw, a total search problem capturing the computational complexity of breaking claw-free permutations. In the context of TFNP, the PWPP-completeness of Claw matches the known intrinsic relationship between collision-resistant hash functions and claw-free permutations established in the cryptographic literature. A preliminary version of this work appeared in the 46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021 [HV21]. Research was supported by the Grant Agency of the Czech Republic under the grant agreement no. 19-27871X and by the Charles University projects PRIMUS/17/SCI/9 and UNCE/SCI/004.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116733221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

On the Complexity of the Escape Problem for Linear Dynamical Systems over Compact Semialgebraic Sets 紧半代数集上线性动力系统逃逸问题的复杂性

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-07-05 DOI: 10.4230/LIPIcs.MFCS.2021.33

Julian D'Costa, Engel Lefaucheux, E. Neumann, J. Ouaknine, J. Worrell

引用次数: 6

Stabilization Bounds for Influence Propagation from a Random Initial State 随机初始状态影响传播的镇定界

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-07-05 DOI: 10.4230/LIPIcs.MFCS.2021.83

P. Papp, Roger Wattenhofer

引用次数: 0

Exponential Lower Bounds for Threshold Circuits of Sub-Linear Depth and Energy 次线性深度和能量阈值电路的指数下界

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-07-01 DOI: 10.4230/LIPIcs.MFCS.2023.85

Kei Uchizawa, Haruki Abe

{"title":"Exponential Lower Bounds for Threshold Circuits of Sub-Linear Depth and Energy","authors":"Kei Uchizawa, Haruki Abe","doi":"10.4230/LIPIcs.MFCS.2023.85","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2023.85","url":null,"abstract":"In this paper, we investigate computational power of threshold circuits and other theoretical models of neural networks in terms of the following four complexity measures: size (the number of gates), depth, weight and energy. Here the energy complexity of a circuit measures sparsity of their computation, and is defined as the maximum number of gates outputting non-zero values taken over all the input assignments. As our main result, we prove that any threshold circuit $C$ of size $s$, depth $d$, energy $e$ and weight $w$ satisfies $log (rk(M_C)) le ed (log s + log w + log n)$, where $rk(M_C)$ is the rank of the communication matrix $M_C$ of a $2n$-variable Boolean function that $C$ computes. Thus, such a threshold circuit $C$ is able to compute only a Boolean function of which communication matrix has rank bounded by a product of logarithmic factors of $s,w$ and linear factors of $d,e$. This implies an exponential lower bound on the size of even sublinear-depth threshold circuit if energy and weight are sufficiently small. For other models of neural networks such as a discretized ReLE circuits and decretized sigmoid circuits, we prove that a similar inequality also holds for a discretized circuit $C$: $rk(M_C) = O(ed(log s + log w + log n)^3)$.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134491619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Parallel Polynomial Permanent Mod Powers of 2 and Shortest Disjoint Cycles 2的永久模幂与最短不相交环的平行多项式

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-06-01 DOI: 10.4230/LIPIcs.MFCS.2021.36

Samir Datta, Kishlaya Jaiswal

引用次数: 2