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Extending finite-memory determinacy by Boolean combination of winning conditions 利用获胜条件的布尔组合扩展有限记忆确定性
Foundations of Software Technology and Theoretical Computer Science Pub Date : 2018-08-17 DOI: 10.4230/LIPIcs.FSTTCS.2018.38
Stéphane Le Roux, A. Pauly, Mickael Randour
{"title":"Extending finite-memory determinacy by Boolean combination of winning conditions","authors":"Stéphane Le Roux, A. Pauly, Mickael Randour","doi":"10.4230/LIPIcs.FSTTCS.2018.38","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.38","url":null,"abstract":"We study finite-memory (FM) determinacy in games on finite graphs, a central question for applications in controller synthesis, as FM strategies correspond to implementable controllers. We establish general conditions under which FM strategies suffice to play optimally, even in a broad multi-objective setting. We show that our framework encompasses important classes of games from the literature, and permits to go further, using a unified approach. While such an approach cannot match ad-hoc proofs with regard to tightness of memory bounds, it has two advantages: first, it gives a widely-applicable criterion for FM determinacy; second, it helps to understand the cornerstones of FM determinacy, which are often hidden but common in proofs for specific (combinations of) winning conditions.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"2 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122645893","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: 16
The Delta-framework 的Delta-framework
Foundations of Software Technology and Theoretical Computer Science Pub Date : 2018-08-13 DOI: 10.4230/LIPIcs.FSTTCS.2018.37
F. Honsell, L. Liquori, C. Stolze, Ivan Scagnetto
{"title":"The Delta-framework","authors":"F. Honsell, L. Liquori, C. Stolze, Ivan Scagnetto","doi":"10.4230/LIPIcs.FSTTCS.2018.37","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.37","url":null,"abstract":"We introduce the Delta-framework, LF-Delta, a dependent type theory based on the Edinburgh Logical Framework LF, extended with the strong proof-functional connectives, i.e. strong intersection, minimal relevant implication and strong union. Strong proof-functional connectives take into account the shape of logical proofs, thus reflecting polymorphic features of proofs in formulae. This is in contrast to classical or intuitionistic connectives where the meaning of a compound formula depends only on the truth value or the provability of its subformulae. Our framework encompasses a wide range of type disciplines. Moreover, since relevant implication permits to express subtyping, LF-Delta subsumes also Pfenning's refinement types. We discuss the design decisions which have led us to the formulation of LF-Delta, study its metatheory, and provide various examples of applications. Our strong proof-functional type theory can be plugged in existing common proof assistants.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134471397","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
Reducing Transducer Equivalence to Register Automata Problems Solved by "Hilbert Method" “希尔伯特法”解决的换能器等价化登记自动机问题
Foundations of Software Technology and Theoretical Computer Science Pub Date : 2018-06-12 DOI: 10.4230/LIPIcs.FSTTCS.2018.48
Adrien Boiret, Radoslaw Piórkowski, J. Schmude
{"title":"Reducing Transducer Equivalence to Register Automata Problems Solved by \"Hilbert Method\"","authors":"Adrien Boiret, Radoslaw Piórkowski, J. Schmude","doi":"10.4230/LIPIcs.FSTTCS.2018.48","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.48","url":null,"abstract":"In the past decades, classical results from algebra, including Hilbert's Basis Theorem, had various applications in formal languages, including a proof of the Ehrenfeucht Conjecture, decidability of HDT0L sequence equivalence, and decidability of the equivalence problem for functional tree-to-string transducers. In this paper, we study the scope of the algebraic methods mentioned above, particularily as applied to the equivalence problem for register automata. We provide two results, one positive, one negative. The positive result is that equivalence is decidable for MSO transformations on unordered forests. The negative result comes from a try to extend this method to decide equivalence on macro tree transducers. We reduce macro tree transducers equivalence to an equivalence problem for some class of register automata naturally relevant to our method. We then prove this latter problem to be undecidable.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"283 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132053912","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: 6
Equivalence of Hidden Markov Models with Continuous Observations 具有连续观测值的隐马尔可夫模型的等价性
Foundations of Software Technology and Theoretical Computer Science Pub Date : 2018-06-11 DOI: 10.4230/LIPIcs.CVIT.2016.23
O. Darwin, S. Kiefer
{"title":"Equivalence of Hidden Markov Models with Continuous Observations","authors":"O. Darwin, S. Kiefer","doi":"10.4230/LIPIcs.CVIT.2016.23","DOIUrl":"https://doi.org/10.4230/LIPIcs.CVIT.2016.23","url":null,"abstract":"We describe a procedure to derive equality tests and their correctness proofs from inductive type declarations. Programs and proofs are derived compositionally, reusing code and proofs derived previously. The key steps are two. First, we design appropriate induction principles for data types defined using parametric containers. Second, we develop a technique to work around the modularity limitations imposed by the purely syntactic termination check Coq performs on recursive proofs. The unary parametricity translation of inductive data types turns out to be the key to both steps. Last but not least, we provide an implementation of the procedure for the Coq proof assistant based on the Elpi [3] extension language.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114754688","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: 12
On Fair Division for Indivisible Items 论不可分割物品的公平划分
Foundations of Software Technology and Theoretical Computer Science Pub Date : 2018-05-16 DOI: 10.4230/LIPIcs.FSTTCS.2018.25
Yun Kuen Cheung, Bhaskar Chaudhuri, J. Garg, Naveen Garg, M. Hoefer, K. Mehlhorn
{"title":"On Fair Division for Indivisible Items","authors":"Yun Kuen Cheung, Bhaskar Chaudhuri, J. Garg, Naveen Garg, M. Hoefer, K. Mehlhorn","doi":"10.4230/LIPIcs.FSTTCS.2018.25","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.25","url":null,"abstract":"We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in multiple items or copies, and the utility of an agent diminishes as it receives more items of the same good. The utility of a bundle of items for an agent is the sum of the utilities of the items in the bundle. Each agent has a utility cap beyond which he does not value additional items. We give a polynomial time approximation algorithm that maximizes Nash social welfare up to a factor of e^{1/{e}} ~~ 1.445. The computed allocation is Pareto-optimal and approximates envy-freeness up to one item up to a factor of 2 + epsilon.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129145679","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: 60
A Structural and Algorithmic Study of Stable Matching Lattices of "Nearby" Instances, with Applications “邻近”实例稳定匹配格的结构与算法研究及其应用
Foundations of Software Technology and Theoretical Computer Science Pub Date : 2018-04-16 DOI: 10.4230/LIPIcs.FSTTCS.2022.19
Rohith Reddy Gangam, Tung Mai, Nitya Raju, V. Vazirani
{"title":"A Structural and Algorithmic Study of Stable Matching Lattices of \"Nearby\" Instances, with Applications","authors":"Rohith Reddy Gangam, Tung Mai, Nitya Raju, V. Vazirani","doi":"10.4230/LIPIcs.FSTTCS.2022.19","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2022.19","url":null,"abstract":"Recently MV18 identified and initiated work on the new problem of understanding structural relationships between the lattices of solutions of two\"nearby\"instances of stable matching. They also gave an application of their work to finding a robust stable matching. However, the types of changes they allowed in going from instance $A$ to $B$ were very restricted, namely any one agent executes an upward shift. In this paper, we allow any one agent to permute its preference list arbitrarily. Let $M_A$ and $M_B$ be the sets of stable matchings of the resulting pair of instances $A$ and $B$, and let $mathcal{L}_A$ and $mathcal{L}_B$ be the corresponding lattices of stable matchings. We prove that the matchings in $M_A cap M_B$ form a sublattice of both $mathcal{L}_A$ and $mathcal{L}_B$ and those in $M_A setminus M_B$ form a join semi-sublattice of $mathcal{L}_A$. These properties enable us to obtain a polynomial time algorithm for not only finding a stable matching in $M_A cap M_B$, but also for obtaining the partial order, as promised by Birkhoff's Representation Theorem, thereby enabling us to generate all matchings in this sublattice. Our algorithm also helps solve a version of the robust stable matching problem. We discuss another potential application, namely obtaining new insights into the incentive compatibility properties of the Gale-Shapley Deferred Acceptance Algorithm.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115020881","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
Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network (定参数)浅-轻斯坦纳网络需求图的刻画
Foundations of Software Technology and Theoretical Computer Science Pub Date : 2018-02-01 DOI: 10.4230/LIPIcs.FSTTCS.2018.33
Amy Babay, M. Dinitz, Zeyu Zhang
{"title":"Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network","authors":"Amy Babay, M. Dinitz, Zeyu Zhang","doi":"10.4230/LIPIcs.FSTTCS.2018.33","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.33","url":null,"abstract":"We consider the Shallow-Light Steiner Network problem from a fixed-parameter perspective. Given a graph $G$, a distance bound $L$, and $p$ pairs of vertices $(s_1,t_1),cdots,(s_p,t_p)$, the objective is to find a minimum-cost subgraph $G'$ such that $s_i$ and $t_i$ have distance at most $L$ in $G'$ (for every $i in [p]$). Our main result is on the fixed-parameter tractability of this problem with parameter $p$. We exactly characterize the demand structures that make the problem \"easy\", and give FPT algorithms for those cases. In all other cases, we show that the problem is W$[1]$-hard. We also extend our results to handle general edge lengths and costs, precisely characterizing which demands allow for good FPT approximation algorithms and which demands remain W$[1]$-hard even to approximate.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116510050","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
Shortest k-Disjoint Paths via Determinants 通过行列式的最短k-不相交路径
Foundations of Software Technology and Theoretical Computer Science Pub Date : 2018-02-01 DOI: 10.4230/LIPIcs.FSTTCS.2018.19
Samir Datta, Siddharth Iyer, R. Kulkarni, A. Mukherjee
{"title":"Shortest k-Disjoint Paths via Determinants","authors":"Samir Datta, Siddharth Iyer, R. Kulkarni, A. Mukherjee","doi":"10.4230/LIPIcs.FSTTCS.2018.19","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.19","url":null,"abstract":"The well-known $k$-disjoint path problem ($k$-DPP) asks for pairwise vertex-disjoint paths between $k$ specified pairs of vertices $(s_i, t_i)$ in a given graph, if they exist. The decision version of the shortest $k$-DPP asks for the length of the shortest (in terms of total length) such paths. Similarly the search and counting versions ask for one such and the number of such shortest set of paths, respectively. \u0000We restrict attention to the shortest $k$-DPP instances on undirected planar graphs where all sources and sinks lie on a single face or on a pair of faces. We provide efficient sequential and parallel algorithms for the search versions of the problem answering one of the main open questions raised by Colin de Verdiere and Schrijver for the general one-face problem. We do so by providing a randomised $NC^2$ algorithm along with an $O(n^{omega})$ time randomised sequential algorithm. We also obtain deterministic algorithms with similar resource bounds for the counting and search versions. \u0000In contrast, previously, only the sequential complexity of decision and search versions of the \"well-ordered\" case has been studied. For the one-face case, sequential versions of our routines have better running times for constantly many terminals. In addition, the earlier best known sequential algorithms (e.g. Borradaile et al.) were randomised while ours are also deterministic. \u0000The algorithms are based on a bijection between a shortest $k$-tuple of disjoint paths in the given graph and cycle covers in a related digraph. This allows us to non-trivially modify established techniques relating counting cycle covers to the determinant. We further need to do a controlled inclusion-exclusion to produce a polynomial sum of determinants such that all \"bad\" cycle covers cancel out in the sum allowing us to count \"good\" cycle covers.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127554045","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: 8
Improved Pseudo-Polynomial-Time Approximation for Strip Packing 条形填料的改进伪多项式时间逼近
Foundations of Software Technology and Theoretical Computer Science Pub Date : 2018-01-23 DOI: 10.4230/LIPIcs.FSTTCS.2016.9
Waldo Gálvez, F. Grandoni, Salvatore Ingala, A. Khan
{"title":"Improved Pseudo-Polynomial-Time Approximation for Strip Packing","authors":"Waldo Gálvez, F. Grandoni, Salvatore Ingala, A. Khan","doi":"10.4230/LIPIcs.FSTTCS.2016.9","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2016.9","url":null,"abstract":"We study the strip packing problem, a classical packing problem which generalizes both bin packing and makespan minimization. Here we are given a set of axis-parallel rectangles in the two-dimensional plane and the goal is to pack them in a vertical strip of a fixed width such that the height of the obtained packing is minimized. The packing must be non-overlapping and the rectangles cannot be rotated. A reduction from the partition problem shows that no approximation better than 3/2 is possible for strip packing in polynomial time (assuming P$neq$NP). Nadiradze and Wiese [SODA16] overcame this barrier by presenting a $(frac{7}{5}+epsilon)$-approximation algorithm in pseudo-polynomial-time (PPT). As the problem is strongly NP-hard, it does not admit an exact PPT algorithm. In this paper, we make further progress on the PPT approximability of strip packing, by presenting a $(frac43+epsilon)$-approximation algorithm. Our result is based on a non-trivial repacking of some rectangles in the emph{empty space} left by the construction by Nadiradze and Wiese, and in some sense pushes their approach to its limit. Our PPT algorithm can be adapted to the case where we are allowed to rotate the rectangles by $90^circ$, achieving the same approximation factor and breaking the polynomial-time approximation barrier of 3/2 for the case with rotations as well.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130320993","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: 20
On Symbolic Heaps Modulo Permission Theories 论符号堆模许可理论
Foundations of Software Technology and Theoretical Computer Science Pub Date : 2017-12-15 DOI: 10.4230/LIPIcs.FSTTCS.2017.25
Stephane Demri, É. Lozes, D. Lugiez
{"title":"On Symbolic Heaps Modulo Permission Theories","authors":"Stephane Demri, É. Lozes, D. Lugiez","doi":"10.4230/LIPIcs.FSTTCS.2017.25","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2017.25","url":null,"abstract":"We address the entailment problem for separation logic with symbolic heaps admitting list pred- icates and permissions for memory cells that are essential to express ownership of a heap region. In the permission-free case, the entailment problem is known to be in P. Herein, we design new decision procedures for solving the satisfiability and entailment problems that are parameterised by the permission theories. This permits the use of solvers dealing with the permission theory at hand, independently of the shape analysis. We also show that the entailment problem without list predicates is coNP-complete for several permission models, such as counting permissions and binary tree shares but the problem is in P for fractional permissions. Furthermore, when list predicates are added, we prove that the entailment problem is coNP-complete when the entail- ment problem for permission formulae is in coNP, assuming the write permission can be split into as many read permissions as desired. Finally, we show that the entailment problem for any Boolean permission model with infinite width is coNP-complete.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134028354","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
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