International Symposium on Mathematical Foundations of Computer Science最新文献

FPT Approximation and Subexponential Algorithms for Covering Few or Many Edges 覆盖少边或多边的FPT逼近和亚指数算法

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-08-29 DOI: 10.4230/LIPIcs.MFCS.2023.46

F. Fomin, P. Golovach, Tanmay Inamdar, Tomohiro Koana

{"title":"FPT Approximation and Subexponential Algorithms for Covering Few or Many Edges","authors":"F. Fomin, P. Golovach, Tanmay Inamdar, Tomohiro Koana","doi":"10.4230/LIPIcs.MFCS.2023.46","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2023.46","url":null,"abstract":"We study the textsc{$alpha$-Fixed Cardinality Graph Partitioning ($alpha$-FCGP)} problem, the generic local graph partitioning problem introduced by Bonnet et al. [Algorithmica 2015]. In this problem, we are given a graph $G$, two numbers $k,p$ and $0leqalphaleq 1$, the question is whether there is a set $Ssubseteq V$ of size $k$ with a specified coverage function $cov_{alpha}(S)$ at least $p$ (or at most $p$ for the minimization version). The coverage function $cov_{alpha}(cdot)$ counts edges with exactly one endpoint in $S$ with weight $alpha$ and edges with both endpoints in $S$ with weight $1 - alpha$. $alpha$-FCGP generalizes a number of fundamental graph problems such as textsc{Densest $k$-Subgraph}, textsc{Max $k$-Vertex Cover}, and textsc{Max $(k,n-k)$-Cut}. A natural question in the study of $alpha$-FCGP is whether the algorithmic results known for its special cases, like textsc{Max $k$-Vertex Cover}, could be extended to more general settings. One of the simple but powerful methods for obtaining parameterized approximation [Manurangsi, SOSA 2019] and subexponential algorithms [Fomin et al. IPL 2011] for textsc{Max $k$-Vertex Cover} is based on the greedy vertex degree orderings. The main insight of our work is that the idea of greed vertex degree ordering could be used to design fixed-parameter approximation schemes (FPT-AS) for $alpha>0$ and the subexponential-time algorithms for the problem on apex-minor free graphs for maximization with $alpha>1/3$ and minimization with $alpha<1/3$.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133686875","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

Dynamic constant time parallel graph algorithms with sub-linear work 具有次线性功的动态常数时间并行图算法

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-07-19 DOI: 10.48550/arXiv.2307.10107

Jonas Schmidt, T. Schwentick

引用次数: 0

On the Expressive Power of Regular Expressions with Backreferences 带反向引用的正则表达式的表达能力

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-07-13 DOI: 10.48550/arXiv.2307.08531

Taisei Nogami, Tachio Terauchi

{"title":"On the Expressive Power of Regular Expressions with Backreferences","authors":"Taisei Nogami, Tachio Terauchi","doi":"10.48550/arXiv.2307.08531","DOIUrl":"https://doi.org/10.48550/arXiv.2307.08531","url":null,"abstract":"A rewb is a regular expression extended with a feature called backreference. It is broadly known that backreference is a practical extension of regular expressions, and is supported by most modern regular expression engines, such as those in the standard libraries of Java, Python, and more. Meanwhile, indexed languages are the languages generated by indexed grammars, a formal grammar class proposed by A.V.Aho. We show that these two models' expressive powers are related in the following way: every language described by a rewb is an indexed language. As the smallest formal grammar class previously known to contain rewbs is the class of context sensitive languages, our result strictly improves the known upper-bound. Moreover, we prove the following two claims: there exists a rewb whose language does not belong to the class of stack languages, which is a proper subclass of indexed languages, and the language described by a rewb without a captured reference is in the class of nonerasing stack languages, which is a proper subclass of stack languages. Finally, we show that the hierarchy investigated in a prior study, which separates the expressive power of rewbs by the notion of nested levels, is within the class of nonerasing stack languages.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133518133","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

Entropic Risk for Turn-Based Stochastic Games 回合制随机博弈的熵风险

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-07-13 DOI: 10.48550/arXiv.2307.06611

C. Baier, K. Chatterjee, Tobias Meggendorfer, Jakob Piribauer

{"title":"Entropic Risk for Turn-Based Stochastic Games","authors":"C. Baier, K. Chatterjee, Tobias Meggendorfer, Jakob Piribauer","doi":"10.48550/arXiv.2307.06611","DOIUrl":"https://doi.org/10.48550/arXiv.2307.06611","url":null,"abstract":"Entropic risk (ERisk) is an established risk measure in finance, quantifying risk by an exponential re-weighting of rewards. We study ERisk for the first time in the context of turn-based stochastic games with the total reward objective. This gives rise to an objective function that demands the control of systems in a risk-averse manner. We show that the resulting games are determined and, in particular, admit optimal memoryless deterministic strategies. This contrasts risk measures that previously have been considered in the special case of Markov decision processes and that require randomization and/or memory. We provide several results on the decidability and the computational complexity of the threshold problem, i.e. whether the optimal value of ERisk exceeds a given threshold. In the most general case, the problem is decidable subject to Shanuel's conjecture. If all inputs are rational, the resulting threshold problem can be solved using algebraic numbers, leading to decidability via a polynomial-time reduction to the existential theory of the reals. Further restrictions on the encoding of the input allow the solution of the threshold problem in NP$cap$coNP. Finally, an approximation algorithm for the optimal value of ERisk is provided.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132289986","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 the Finite Variable-Occurrence Fragment of the Calculus of Relations with Bounded Dot-Dagger Alternation 有界点-匕首交替关系演算的有限变现片段

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-07-11 DOI: 10.48550/arXiv.2307.05046

Yoshiki Nakamura

引用次数: 0

Deciding Predicate Logical Theories of Real-Valued Functions 确定实值函数的谓词逻辑理论

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-06-28 DOI: 10.48550/arXiv.2306.16505

Stefan Ratschan

引用次数: 0

Separating Automatic Relations 分离自动关系

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-05-15 DOI: 10.48550/arXiv.2305.08727

Pablo Barcel'o, Diego Figueira, Rémi Morvan

引用次数: 0

Solving irreducible stochastic mean-payoff games and entropy games by relative Krasnoselskii-Mann iteration 用相对Krasnoselskii-Mann迭代求解不可约随机均值-收益对策和熵对策

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-05-03 DOI: 10.48550/arXiv.2305.02458

M. Akian, S. Gaubert, Ulysse Naepels, Basile Terver

{"title":"Solving irreducible stochastic mean-payoff games and entropy games by relative Krasnoselskii-Mann iteration","authors":"M. Akian, S. Gaubert, Ulysse Naepels, Basile Terver","doi":"10.48550/arXiv.2305.02458","DOIUrl":"https://doi.org/10.48550/arXiv.2305.02458","url":null,"abstract":"We analyse an algorithm solving stochastic mean-payoff games, combining the ideas of relative value iteration and of Krasnoselskii-Mann damping. We derive parameterized complexity bounds for several classes of games satisfying irreducibility conditions. We show in particular that an $epsilon$-approximation of the value of an irreducible concurrent stochastic game can be computed in a number of iterations in $O(|logepsilon|)$ where the constant in the $O(cdot)$ is explicit, depending on the smallest non-zero transition probabilities. This should be compared with a bound in $O(|epsilon|^{-1}|log(epsilon)|)$ obtained by Chatterjee and Ibsen-Jensen (ICALP 2014) for the same class of games, and to a $O(|epsilon|^{-1})$ bound by Allamigeon, Gaubert, Katz and Skomra (ICALP 2022) for turn-based games. We also establish parameterized complexity bounds for entropy games, a class of matrix multiplication games introduced by Asarin, Cervelle, Degorre, Dima, Horn and Kozyakin. We derive these results by methods of variational analysis, establishing contraction properties of the relative Krasnoselskii-Mann iteration with respect to Hilbert's semi-norm.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115312836","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

Speed Me up if You Can: Conditional Lower Bounds on Opacity Verification 如果可以，请加快速度:不透明度验证的条件下界

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-04-19 DOI: 10.48550/arXiv.2304.09920

Jivr'i Balun, Tomas Masopust, Petr Osivcka

引用次数: 0

Locality Theorems in Semiring Semantics 半环语义中的局部性定理

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2023-03-22 DOI: 10.48550/arXiv.2303.12627

Clotilde Biziere, E. Grädel, Matthias Naaf

引用次数: 1