Foundations of Software Technology and Theoretical Computer Science最新文献

Hardness of Learning Boolean Functions from Label Proportions 从标签比例学习布尔函数的难易程度

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2024-03-28 DOI: 10.4230/LIPIcs.FSTTCS.2023.37

V. Guruswami, Rishi Saket

{"title":"Hardness of Learning Boolean Functions from Label Proportions","authors":"V. Guruswami, Rishi Saket","doi":"10.4230/LIPIcs.FSTTCS.2023.37","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2023.37","url":null,"abstract":"In recent years the framework of learning from label proportions (LLP) has been gaining importance in machine learning. In this setting, the training examples are aggregated into subsets or bags and only the average label per bag is available for learning an example-level predictor. This generalizes traditional PAC learning which is the special case of unit-sized bags. The computational learning aspects of LLP were studied in recent works (Saket, NeurIPS'21; Saket, NeurIPS'22) which showed algorithms and hardness for learning halfspaces in the LLP setting. In this work we focus on the intractability of LLP learning Boolean functions. Our first result shows that given a collection of bags of size at most $2$ which are consistent with an OR function, it is NP-hard to find a CNF of constantly many clauses which satisfies any constant-fraction of the bags. This is in contrast with the work of (Saket, NeurIPS'21) which gave a $(2/5)$-approximation for learning ORs using a halfspace. Thus, our result provides a separation between constant clause CNFs and halfspaces as hypotheses for LLP learning ORs. Next, we prove the hardness of satisfying more than $1/2 + o(1)$ fraction of such bags using a $t$-DNF (i.e. DNF where each term has $leq t$ literals) for any constant $t$. In usual PAC learning such a hardness was known (Khot-Saket, FOCS'08) only for learning noisy ORs. We also study the learnability of parities and show that it is NP-hard to satisfy more than $(q/2^{q-1} + o(1))$-fraction of $q$-sized bags which are consistent with a parity using a parity, while a random parity based algorithm achieves a $(1/2^{q-2})$-approximation.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"10 5","pages":"37:1-37:15"},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140369359","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

Synchronized CTL over One-Counter Automata 单计数器自动机上的同步 CTL

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2023-08-07 DOI: 10.4230/LIPIcs.FSTTCS.2023.19

Shaull Almagor, Daniel Assa, Udi Boker

{"title":"Synchronized CTL over One-Counter Automata","authors":"Shaull Almagor, Daniel Assa, Udi Boker","doi":"10.4230/LIPIcs.FSTTCS.2023.19","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2023.19","url":null,"abstract":"We consider the model-checking problem of Synchronized Computation-Tree Logic (CTL+Sync) over One-Counter Automata (OCAs). CTL+Sync augments CTL with temporal operators that require several paths to satisfy properties in a synchronous manner, e.g., the property\"all paths should eventually see $p$ at the same time\". The model-checking problem for CTL+Sync over finite-state Kripke structures was shown to be in $mathsf{P}^{mathsf{NP}^{mathsf{NP}}}$. OCAs are labelled transition systems equipped with a non-negative counter that can be zero-tested. Thus, they induce infinite-state systems whose computation trees are not regular. The model-checking problem for CTL over OCAs was shown to be $mathsf{PSPACE}$-complete. We show that the model-checking problem for CTL+Sync over OCAs is decidable. However, the upper bound we give is non-elementary. We therefore proceed to study the problem for a central fragment of CTL+Sync, extending CTL with operators that require all paths to satisfy properties in a synchronous manner, and show that it is in $mathsf{EXP}^mathsf{NEXP}$ (and in particular in $mathsf{EXPSPACE}$), by exhibiting a certain\"segmented periodicity\"in the computation trees of OCAs.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"21 1","pages":"19:1-19:22"},"PeriodicalIF":0.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139351436","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

Randomized and Quantum Query Complexities of Finding a King in a Tournament 在锦标赛中寻找国王的随机和量子查询复杂性

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2023-07-25 DOI: 10.4230/LIPIcs.FSTTCS.2023.30

Nikhil S. Mande, Manaswi Paraashar, Nitin Saurabh

{"title":"Randomized and Quantum Query Complexities of Finding a King in a Tournament","authors":"Nikhil S. Mande, Manaswi Paraashar, Nitin Saurabh","doi":"10.4230/LIPIcs.FSTTCS.2023.30","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2023.30","url":null,"abstract":"This paper discusses the problem of efficiently solving parity games where player Odd has to obey an additional 'strong transition fairness constraint' on its vertices -- given that a player Odd vertex $v$ is visited infinitely often, a particular subset of the outgoing edges (called live edges) of $v$ has to be taken infinitely often. Such games, which we call 'Odd-fair parity games', naturally arise from abstractions of cyber-physical systems for planning and control. In this paper, we present a new Zielonka-type algorithm for solving Odd-fair parity games. This algorithm not only shares 'the same worst-case time complexity' as Zielonka's algorithm for (normal) parity games but also preserves the algorithmic advantage Zielonka's algorithm possesses over other parity solvers with exponential time complexity. We additionally introduce a formalization of Odd player winning strategies in such games, which were unexplored previous to this work. This formalization serves dual purposes: firstly, it enables us to prove our Zielonka-type algorithm; secondly, it stands as a noteworthy contribution in its own right, augmenting our understanding of additional fairness assumptions in two-player games.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"54 1","pages":"30:1-30:19"},"PeriodicalIF":0.0,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139355322","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

Romeo and Juliet Meeting in Forest Like Regions 罗密欧与朱丽叶在森林般的地区相遇

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2022-10-05 DOI: 10.48550/arXiv.2210.02582

Neeldhara Misra, M. Mulpuri, P. Tale, Gaurav Viramgami

{"title":"Romeo and Juliet Meeting in Forest Like Regions","authors":"Neeldhara Misra, M. Mulpuri, P. Tale, Gaurav Viramgami","doi":"10.48550/arXiv.2210.02582","DOIUrl":"https://doi.org/10.48550/arXiv.2210.02582","url":null,"abstract":"The game of rendezvous with adversaries is a game on a graph played by two players: Facilitator and Divider. Facilitator has two agents and Divider has a team of $k ge 1$ agents. While the initial positions of Facilitator's agents are fixed, Divider gets to select the initial positions of his agents. Then, they take turns to move their agents to adjacent vertices (or stay put) with Facilitator's goal to bring both her agents at same vertex and Divider's goal to prevent it. The computational question of interest is to determine if Facilitator has a winning strategy against Divider with $k$ agents. Fomin, Golovach, and Thilikos [WG, 2021] introduced this game and proved that it is PSPACE-hard and co-W[2]-hard parameterized by the number of agents. This hardness naturally motivates the structural parameterization of the problem. The authors proved that it admits an FPT algorithm when parameterized by the modular width and the number of allowed rounds. However, they left open the complexity of the problem from the perspective of other structural parameters. In particular, they explicitly asked whether the problem admits an FPT or XP-algorithm with respect to the treewidth of the input graph. We answer this question in the negative and show that Rendezvous is co-NP-hard even for graphs of constant treewidth. Further, we show that the problem is co-W[1]-hard when parameterized by the feedback vertex set number and the number of agents, and is unlikely to admit a polynomial kernel when parameterized by the vertex cover number and the number of agents. Complementing these hardness results, we show that the Rendezvous is FPT when parameterized by both the vertex cover number and the solution size. Finally, for graphs of treewidth at most two and girds, we show that the problem can be solved in polynomial time.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121100958","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

The DAG Visit approach for Pebbling and I/O Lower Bounds 卵石和I/O下界的DAG访问方法

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2022-10-04 DOI: 10.48550/arXiv.2210.01897

G. Bilardi, L. Stefani

{"title":"The DAG Visit approach for Pebbling and I/O Lower Bounds","authors":"G. Bilardi, L. Stefani","doi":"10.48550/arXiv.2210.01897","DOIUrl":"https://doi.org/10.48550/arXiv.2210.01897","url":null,"abstract":"We introduce the notion of an $r$-visit of a Directed Acyclic Graph DAG $G=(V,E)$, a sequence of the vertices of the DAG complying with a given rule $r$. A rule $r$ specifies for each vertex $vin V$ a family of $r$-enabling sets of (immediate) predecessors: before visiting $v$, at least one of its enabling sets must have been visited. Special cases are the $r^{(top)}$-rule (or, topological rule), for which the only enabling set is the set of all predecessors and the $r^{(sin)}$-rule (or, singleton rule), for which the enabling sets are the singletons containing exactly one predecessor. The $r$-boundary complexity of a DAG $G$, $b_{r}left(Gright)$, is the minimum integer $b$ such that there is an $r$-visit where, at each stage, for at most $b$ of the vertices yet to be visited an enabling set has already been visited. By a reformulation of known results, it is shown that the boundary complexity of a DAG $G$ is a lower bound to the pebbling number of the reverse DAG, $G^R$. Several known pebbling lower bounds can be cast in terms of the $r^{(sin)}$-boundary complexity. A visit partition technique for I/O lower bounds, which generalizes the $S$-partition I/O technique introduced by Hong and Kung in their classic paper\"I/O complexity: The Red-Blue pebble game\". The visit partition approach yields tight I/O bounds for some DAGs for which the $S$-partition technique can only yield an $Omega(1)$ lower bound.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"NS20 12 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":"123423023","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

When you come at the kings you best not miss 当你攻击国王时，最好不要失手

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2022-09-24 DOI: 10.48550/arXiv.2209.12082

Oded Lachish, F. Reidl, Chhaya Trehan

{"title":"When you come at the kings you best not miss","authors":"Oded Lachish, F. Reidl, Chhaya Trehan","doi":"10.48550/arXiv.2209.12082","DOIUrl":"https://doi.org/10.48550/arXiv.2209.12082","url":null,"abstract":"A tournament is an orientation of a complete graph. We say that a vertex $x$ in a tournament $vec T$ controls another vertex $y$ if there exists a directed path of length at most two from $x$ to $y$. A vertex is called a king if it controls every vertex of the tournament. It is well known that every tournament has a king. We follow Shen, Sheng, and Wu (SIAM J. Comput., 2003) in investigating the query complexity of finding a king, that is, the number of arcs in $vec T$ one has to know in order to surely identify at least one vertex as a king. The aforementioned authors showed that one always has to query at least $Omega(n^{4/3})$ arcs and provided a strategy that queries at most $O(n^{3/2})$. While this upper bound has not yet been improved for the original problem, Biswas et al. (Frontiers in Algorithmics, 2017) proved that with $O(n^{4/3})$ queries one can identify a semi-king, meaning a vertex which controls at least half of all vertices. Our contribution is a novel strategy which improves upon the number of controlled vertices: using $O(n^{4/3} operatorname{polylog} n)$ queries, we can identify a $(frac{1}{2}+frac{2}{17})$-king. To achieve this goal we use a novel structural result for tournaments.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128170730","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

Parikh Automata over Infinite Words Parikh Automata over Infinite Words

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2022-07-15 DOI: 10.48550/arXiv.2207.07694

Shibashis Guha, Ismaël Jecker, K. Lehtinen, Martin Zimmermann

引用次数: 4

Degree-restricted strength decompositions and algebraic branching programs 受限度强度分解与代数分支规划

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2022-05-04 DOI: 10.4230/LIPIcs.FSTTCS.2022.20

Purnata Ghosal, Fulvio Gesmundo, Christian Ikenmeyer, Vladimir Lysikov

引用次数: 2

New Characterizations of Core Imputations of Matching and b-Matching Games 匹配与b-匹配博弈核心归算的新特征

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2022-02-01 DOI: 10.4230/LIPIcs.FSTTCS.2022.28

V. Vazirani

{"title":"New Characterizations of Core Imputations of Matching and b-Matching Games","authors":"V. Vazirani","doi":"10.4230/LIPIcs.FSTTCS.2022.28","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.28","url":null,"abstract":"We give new characterizations of core imputations for the following games: * The assignment game. * Concurrent games, i.e., general graph matching games having non-empty core. * The unconstrained bipartite $b$-matching game (edges can be matched multiple times). * The constrained bipartite $b$-matching game (edges can be matched at most once). The classic paper of Shapley and Shubik cite{Shapley1971assignment} showed that core imputations of the assignment game are precisely optimal solutions to the dual of the LP-relaxation of the game. Building on this, Deng et al. cite{Deng1999algorithms} gave a general framework which yields analogous characterizations for several fundamental combinatorial games. Interestingly enough, their framework does not apply to the last two games stated above. In turn, we show that some of the core imputations of these games correspond to optimal dual solutions and others do not. This leads to the tantalizing question of understanding the origins of the latter. We also present new characterizations of the profits accrued by agents and teams in core imputations of the first two games. Our characterization for the first game is stronger than that for the second; the underlying reason is that the characterization of vertices of the Birkhoff polytope is stronger than that of the Balinski polytope.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115708607","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: 3

History Determinism vs. Good for Gameness in Quantitative Automata 定量自动机中的历史决定论与博弈优势

Foundations of Software Technology and Theoretical Computer Science Pub Date : 2021-10-27 DOI: 10.4230/LIPIcs.FSTTCS.2021.38

Udi Boker, K. Lehtinen

{"title":"History Determinism vs. Good for Gameness in Quantitative Automata","authors":"Udi Boker, K. Lehtinen","doi":"10.4230/LIPIcs.FSTTCS.2021.38","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2021.38","url":null,"abstract":"Automata models between determinism and nondeterminism/alternations can retain some of the algorithmic properties of deterministic automata while enjoying some of the expressiveness and succinctness of nondeterminism. We study three closely related such models -- history determinism, good for gameness and determinisability by pruning -- on quantitative automata. While in the Boolean setting, history determinism and good for gameness coincide, we show that this is no longer the case in the quantitative setting: good for gameness is broader than history determinism, and coincides with a relaxed version of it, defined with respect to thresholds. We further identify criteria in which history determinism, which is generally broader than determinisability by pruning, coincides with it, which we then apply to typical quantitative automata types. As a key application of good for games and history deterministic automata is synthesis, we clarify the relationship between the two notions and various quantitative synthesis problems. We show that good-for-games automata are central for\"global\"(classical) synthesis, while\"local\"(good-enough) synthesis reduces to deciding whether a nondeterministic automaton is history deterministic.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"727 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121422848","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: 14