International Symposium on Mathematical Foundations of Computer Science最新文献_第3页

An Iterative Approach for Counting Reduced Ordered Binary Decision Diagrams 一种计数约简有序二元决策图的迭代方法

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-11-09 DOI: 10.4230/LIPIcs.MFCS.2023.36

Julien Cl'ement, Antoine Genitrini

{"title":"An Iterative Approach for Counting Reduced Ordered Binary Decision Diagrams","authors":"Julien Cl'ement, Antoine Genitrini","doi":"10.4230/LIPIcs.MFCS.2023.36","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2023.36","url":null,"abstract":"For three decades binary decision diagrams, a data structure efficiently representing Boolean functions, have been widely used in many distinct contexts like model verification, machine learning, cryptography and also resolution of combinatorial problems. The most famous variant, called reduced ordered binary decision diagram (ROBDD for short), can be viewed as the result of a compaction procedure on the full decision tree. A useful property is that once an order over the Boolean variables is fixed, each Boolean function is represented by exactly one ROBDD. In this paper we aim at computing the exact distribution of the Boolean functions in $k$ variables according to the ROBDD size}, where the ROBDD size is equal to the number of decision nodes of the underlying directed acyclic graph (DAG for short) structure. Recall the number of Boolean functions with $k$ variables is equal to $2^{2^k}$, which is of double exponential growth with respect to the number of variables. The maximal size of a ROBDD with $k$ variables is $M_k approx 2^k / k$. Apart from the natural combinatorial explosion observed, another difficulty for computing the distribution according to size is to take into account dependencies within the DAG structure of ROBDDs. In this paper, we develop the first polynomial algorithm to derive the distribution of Boolean functions over $k$ variables with respect to ROBDD size denoted by $n$. The algorithm computes the (enumerative) generating function of ROBDDs with $k$ variables up to size $n$. It performs $O(k n^4)$ arithmetical operations on integers and necessitates storing $O((k+n) n^2)$ integers with bit length $O(nlog n)$. Our new approach relies on a decomposition of ROBDDs layer by layer and on an inclusion-exclusion argument.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134188593","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

Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications 量子态的分布式梅林-阿瑟合成及其应用

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-10-04 DOI: 10.48550/arXiv.2210.01389

Franccois Le Gall, Masayuki Miyamoto, H. Nishimura

{"title":"Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications","authors":"Franccois Le Gall, Masayuki Miyamoto, H. Nishimura","doi":"10.48550/arXiv.2210.01389","DOIUrl":"https://doi.org/10.48550/arXiv.2210.01389","url":null,"abstract":"The generation and verification of quantum states are fundamental tasks for quantum information processing that have recently been investigated by Irani, Natarajan, Nirkhe, Rao and Yuen [CCC 2022], Rosenthal and Yuen [ITCS 2022], Metger and Yuen [FOCS 2023] under the term emph{state synthesis}. This paper studies this concept from the viewpoint of quantum distributed computing, and especially distributed quantum Merlin-Arthur (dQMA) protocols. We first introduce a novel task, on a line, called state generation with distributed inputs (SGDI). In this task, the goal is to generate the quantum state $Uket{psi}$ at the rightmost node of the line, where $ket{psi}$ is a quantum state given at the leftmost node and $U$ is a unitary matrix whose description is distributed over the nodes of the line. We give a dQMA protocol for SGDI and utilize this protocol to construct a dQMA protocol for the Set Equality problem studied by Naor, Parter and Yogev [SODA 2020], and complement our protocol by showing classical lower bounds for this problem. Our second contribution is a dQMA protocol, based on a recent work by Zhu and Hayashi [Physical Review A, 2019], to create EPR-pairs between adjacent nodes of a network without quantum communication. As an application of this dQMA protocol, we prove a general result showing how to convert any dQMA protocol on an arbitrary network into another dQMA protocol where the verification stage does not require any quantum communication.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114168223","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

A robust class of languages of 2-nested words 一类鲁棒的双嵌套词语言

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-08-22 DOI: 10.48550/arXiv.2208.10347

Séverine Fratani, Guillaume Maurras, P. Reynier

引用次数: 0

Approximation algorithms for covering vertices by long paths 用长路径覆盖顶点的近似算法

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-08-05 DOI: 10.48550/arXiv.2208.03294

Mingyang Gong, Brett Edgar, Jing Fan, Guohui Lin, Eiji Miyano

引用次数: 1

Deepening the (Parameterized) Complexity Analysis of Incremental Stable Matching Problems 增量稳定匹配问题的(参数化)复杂度分析深化

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-08-02 DOI: 10.48550/arXiv.2208.01563

Niclas Boehmer, Klaus Heeger, R. Niedermeier

{"title":"Deepening the (Parameterized) Complexity Analysis of Incremental Stable Matching Problems","authors":"Niclas Boehmer, Klaus Heeger, R. Niedermeier","doi":"10.48550/arXiv.2208.01563","DOIUrl":"https://doi.org/10.48550/arXiv.2208.01563","url":null,"abstract":"When computing stable matchings, it is usually assumed that the preferences of the agents in the matching market are fixed. However, in many realistic scenarios, preferences change over time. Consequently, an initially stable matching may become unstable. Then, a natural goal is to find a matching which is stable with respect to the modified preferences and as close as possible to the initial one. For Stable Marriage/Roommates , this problem was formally defined as Incremental Stable Marriage/Roommates by Bredereck et al. [AAAI ’20]. As they showed that Incremental Stable Roommates and Incremental Stable Marriage with Ties are NP-hard, we focus on the parameterized complexity of these problems. We answer two open questions of Bredereck et al. [AAAI ’20]: We show that Incremental Stable Roommates is W[1]-hard parameterized by the number of changes in the preferences, yet admits an intricate XP-algorithm, and we show that Incremental Stable Marriage with Ties is W[1]-hard parameterized by the number of ties. Furthermore, we analyze the influence of the degree of “similarity” between the agents’ preference lists, identifying several polynomial-time solvable and fixed-parameter tractable cases, but also proving that Incremental Stable Roommates and Incremental Stable Marriage with Ties parameterized by the number of different preference lists are W[1]-hard.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125964637","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

Countdown μ-calculus 倒计时μ微积分

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-07-31 DOI: 10.48550/arXiv.2208.00536

J. Kolodziejski, Bartek Klin

引用次数: 0

Bounding the Escape Time of a Linear Dynamical System over a Compact Semialgebraic Set 紧半代数集上线性动力系统逃逸时间的定界

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-07-04 DOI: 10.48550/arXiv.2207.01550

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

引用次数: 0

Probabilistic Model Checking for Strategic Equilibria-based Decision Making: Advances and Challenges 基于战略均衡决策的概率模型检验:进展与挑战

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-06-30 DOI: 10.48550/arXiv.2206.15148

M. Kwiatkowska, G. Norman, Gabriel Santos, Rui Yan

{"title":"Probabilistic Model Checking for Strategic Equilibria-based Decision Making: Advances and Challenges","authors":"M. Kwiatkowska, G. Norman, Gabriel Santos, Rui Yan","doi":"10.48550/arXiv.2206.15148","DOIUrl":"https://doi.org/10.48550/arXiv.2206.15148","url":null,"abstract":"Game-theoretic concepts have been extensively studied in economics to provide insight into competitive behaviour and strategic decision making. As computing systems increasingly involve concurrently acting autonomous agents, game-theoretic approaches are becoming widespread in computer science as a faithful modelling abstraction. These techniques can be used to reason about the competitive or collaborative behaviour of multiple rational agents with distinct goals or objectives. This paper provides an overview of recent advances in developing a modelling, verification and strategy synthesis framework for concurrent stochastic games implemented in the probabilistic model checker PRISM-games. This is based on a temporal logic that supports finite- and infinite-horizon temporal properties in both a zero-sum and nonzero-sum setting, the latter using Nash and correlated equilibria with respect to two optimality criteria, social welfare and social fairness. We summarise the key concepts, logics and algorithms and the currently available tool support. Future challenges and recent progress in adapting the framework and algorithmic solutions to continuous environments and neural networks are also outlined.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128759590","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: 4

Space-Bounded Unitary Quantum Computation with Postselection 具有后选择的空间有界幺正量子计算

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-06-30 DOI: 10.4230/LIPIcs.MFCS.2022.81

S. Tani

{"title":"Space-Bounded Unitary Quantum Computation with Postselection","authors":"S. Tani","doi":"10.4230/LIPIcs.MFCS.2022.81","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2022.81","url":null,"abstract":"Space-bounded computation has been a central topic in classical and quantum complexity theory. In the quantum case, every elementary gate must be unitary. This restriction makes it unclear whether the power of space-bounded computation changes by allowing intermediate measurement. In the bounded error case, Fefferman and Remscrim [STOC 2021, pp.1343–1356] and Girish, Raz and Zhan [ICALP 2021, pp.73:1–73:20] recently provided the break-through results that the power does not change. This paper shows that a similar result holds for space-bounded quantum computation with postselection . Namely, it is proved possible to eliminate intermediate postselections and measurements in the space-bounded quantum computation in the bounded-error setting. Our result strengthens the recent result by Le Gall, Nishimura and Yakaryilmaz [TQC 2021, pp.10:1– 10:17] that logarithmic-space bounded-error quantum computation with intermediate postselections and measurements is equivalent in computational power to logarithmic-space unbounded-error probabilistic computation. As an application, it is shown that bounded-error space-bounded one-clean qubit computation (DQC1) with postselection is equivalent in computational power to unbounded-error space-bounded probabilistic computation, and the computational supremacy of the bounded-error space-bounded DQC1 is interpreted in complexity-theoretic terms.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129189689","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

RAC Drawings of Graphs with Low Degree 低度图的RAC绘图

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2022-06-29 DOI: 10.48550/arXiv.2206.14909

Patrizio Angelini, M. Bekos, Julia Katheder, Michael Kaufmann, Maximilian Pfister

引用次数: 3