Foundations of Software Technology and Theoretical Computer Science最新文献

{"title":"Büchi Good-for-Games Automata Are Efficiently Recognizable","authors":"Marc Bagnol, Denis Kuperberg","doi":"10.4230/LIPIcs.FSTTCS.2018.16","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.16","url":null,"abstract":"Good-for-Games (GFG) automata offer a compromise between deterministic and nondetermin-istic automata. They can resolve nondeterministic choices in a step-by-step fashion, without needing any information about the remaining suffix of the word. These automata can be used to solve games with ω-regular conditions, and in particular were introduced as a tool to solve Church's synthesis problem. We focus here on the problem of recognizing Buchi GFG automata, that we call Buchi GFGness problem: given a nondeterministic Buchi automaton, is it GFG? We show that this problem can be decided in P, and more precisely in O(n^4 m^2 |Σ|^2) , where n is the number of states, m the number of transitions and |Σ| is the size of the alphabet. We conjecture that a very similar algorithm solves the problem in polynomial time for any fixed parity acceptance condition.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"311 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132760516","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}

{"title":"On the Parameterized Complexity of [1, j]-Domination Problems","authors":"M. A. Meybodi, F. Fomin, A. E. Mouawad, Fahad Panolan","doi":"10.4230/LIPIcs.FSTTCS.2018.34","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.34","url":null,"abstract":"Abstract For a graph G, a set D ⊆ V ( G ) is called a [ 1 , j ] -dominating set if every vertex in V ( G ) ∖ D has at least one and at most j neighbors in D. A set D ⊆ V ( G ) is called a [ 1 , j ] -total dominating set if every vertex in V ( G ) has at least one and at most j neighbors in D. In the [ 1 , j ] -(Total) Dominating Set problem we are given a graph G and a positive integer k. The objective is to test whether there exists a [ 1 , j ] -(total) dominating set of size at most k. The [ 1 , j ] -Dominating Set problem is known to be NP-complete, even for restricted classes of graphs such as chordal and planar graphs, but polynomial-time solvable on split graphs. The [ 1 , 2 ] -Total Dominating Set problem is known to be NP-complete, even for bipartite graphs. As both problems generalize the Dominating Set problem, both are W[1]-hard when parameterized by solution size. In this work, we study the aforementioned problems on various graph classes from the perspective of parameterized complexity and prove the following results: • [ 1 , j ] -Dominating Set parameterized by solution size is W[1]-hard on d-degenerate graphs for d = j + 1 . • [ 1 , j ] -Dominating Set parameterized by solution size is FPT on nowhere dense graphs. • The known algorithm for [ 1 , j ] -Dominating Set on split graphs is optimal under the Strong Exponential Time Hypothesis (SETH). • Assuming SETH, we provide a lower bound for the running time of any algorithm solving the [ 1 , 2 ] -Total Dominating Set problem parameterized by pathwidth. • Finally, we study another variant of Dominating Set , called Restrained Dominating Set , that asks if there is a dominating set D of G of size at most k such that no vertex outside of D has all of its neighbors in D. We prove this variant is W[1]-hard even on 3-degenerate graphs.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126620355","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}

{"title":"Safe and Optimal Scheduling for Hard and Soft Tasks","authors":"G. Geeraerts, Shibashis Guha, Jean-François Raskin","doi":"10.4230/LIPIcs.FSTTCS.2018.36","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.36","url":null,"abstract":"We consider a stochastic scheduling problem with both hard and soft tasks on a single machine. Each task is described by a discrete probability distribution over possible execution times, and possible inter-arrival times of the job, and a fixed deadline. Soft tasks also carry a penalty cost to be paid when they miss a deadline. We ask to compute an online and non-clairvoyant scheduler (i.e. one that must take decisions without knowing the future evolution of the system) that is safe and efficient. Safety imposes that deadline of hard tasks are never violated while efficient means that we want to minimise the mean cost of missing deadlines by soft tasks. First, we show that the dynamics of such a system can be modelled as a finite Markov Decision Process (MDP). Second, we show that our scheduling problem is PP-hard and in EXPTime. Third, we report on a prototype tool that solves our scheduling problem by relying on the Storm tool to analyse the corresponding MDP. We show how antichain techniques can be used as a potential heuristic. 2012 ACM Subject Classification Theory of computation → Probabilistic computation, Computer systems organization→ Real-time system specification, Computer systems organization→ Embedded systems","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127776603","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}

{"title":"On the Boundedness Problem for Higher-Order Pushdown Vector Addition Systems","authors":"Vincent Penelle, Sylvain Salvati, G. Sutre","doi":"10.4230/LIPIcs.FSTTCS.2018.44","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.44","url":null,"abstract":"Karp and Miller's algorithm is a well-known decision procedure that solves the termination and boundedness problems for vector addition systems with states (VASS), or equivalently Petri nets. This procedure was later extended to a general class of models, well-structured transition systems, and, more recently, to pushdown VASS. In this paper, we extend pushdown VASS to higher-order pushdown VASS (called HOPVASS), and we investigate whether an approach a la Karp and Miller can still be used to solve termination and boundedness. \u0000 \u0000We provide a decidable characterisation of runs that can be iterated arbitrarily many times, which is the main ingredient of Karp and Miller's approach. However, the resulting Karp and Miller procedure only gives a semi-algorithm for HOPVASS. In fact, we show that coverability, termination and boundedness are all undecidable for HOPVASS, even in the restricted subcase of one counter and an order 2 stack. On the bright side, we prove that this semi-algorithm is in fact an algorithm for higher-order pushdown automata.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129572468","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}

{"title":"On Canonical Models for Rational Functions over Infinite Words","authors":"E. Filiot, Olivier Gauwin, N. Lhote, A. Muscholl","doi":"10.4230/LIPIcs.FSTTCS.2018.30","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.30","url":null,"abstract":"This paper investigates canonical transducers for rational functions over infinite words, i.e., functions of infinite words defined by finite transducers. We first consider sequential functions, defined by finite transducers with a deterministic underlying automaton. We provide a Myhill-Nerode-like characterization, in the vein of Choffrut's result over finite words, from which we derive an algorithm that computes a transducer realizing the function which is minimal and unique (up to the automaton for the domain). The main contribution of the paper is the notion of a canonical transducer for rational functions over infinite words, extending the notion of canonical bimachine due to Reutenauer and Schutzenberger from finite to infinite words. As an application, we show that the canonical transducer is aperiodic whenever the function is definable by some aperiodic transducer, or equivalently, by a first-order transduction. This allows to decide whether a rational function of infinite words is first-order definable.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131712002","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}

{"title":"The Preemptive Resource Allocation Problem","authors":"Kanthi Kiran Sarpatwar, B. Schieber, H. Shachnai","doi":"10.4230/LIPIcs.FSTTCS.2019.26","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2019.26","url":null,"abstract":"We revisit a classical scheduling model to incorporate modern trends in data center networks and cloud services. Addressing some key challenges in the allocation of shared resources to user requests (jobs) in such settings, we consider the following variants of the classic {em resource allocation problem} (textsf{RAP}). The input to our problems is a set $J$ of jobs and a set $M$ of homogeneous hosts, each has an available amount of some resource. A job is associated with a release time, a due date, a weight, and a given length, as well as its resource requirement. A emph{feasible} schedule is an allocation of the resource to a subset of the jobs, satisfying the job release times/due dates as well as the resource constraints. A crucial distinction between classic {textsf{RAP}} and our problems is that we allow preemption and migration of jobs, motivated by virtualization techniques. \u0000We consider two natural objectives: {em throughput maximization} (textsf{MaxT}), which seeks a maximum weight subset of the jobs that can be feasibly scheduled on the hosts in $M$, and {em resource minimization} (textsf{MinR}), that is finding the minimum number of (homogeneous) hosts needed to feasibly schedule all jobs. Both problems are known to be NP-hard. \u0000We first present a $Omega(1)$-approximation algorithm for textsf{MaxT} instances where time-windows form a laminar family of intervals. We then extend the algorithm to handle instances with arbitrary time-windows, assuming there is sufficient slack for each job to be completed. \u0000For textsf{MinR} we study a more general setting with $d$ resources and derive an $O(log d)$-approximation for any fixed $d geq 1$, under the assumption that time-windows are not too small. This assumption can be removed leading to a slightly worse ratio of $O(log dlog^* T)$, where $T$ is the maximum due date of any job.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114056239","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}

{"title":"The complexity of separation for levels in concatenation hierarchies","authors":"Thomas Place, M. Zeitoun","doi":"10.4230/LIPIcs.FSTTCS.2018.47","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.47","url":null,"abstract":"We investigate the complexity of the separation problem associated to classes of regular languages. For a class C, C-separation takes two regular languages as input and asks whether there exists a third language in C which includes the first and is disjoint from the second. First, in contrast with the situation for the classical membership problem, we prove that for most classes C, the complexity of C-separation does not depend on how the input languages are represented: it is the same for nondeterministic finite automata and monoid morphisms. Then, we investigate specific classes belonging to finitely based concatenation hierarchies. It was recently proved that the problem is always decidable for levels 1/2 and 1 of any such hierarchy (with inefficient algorithms). Here, we build on these results to show that when the alphabet is fixed, there are polynomial time algorithms for both levels. Finally, we investigate levels 3/2 and 2 of the famous Straubing-Th'erien hierarchy. We show that separation is PSPACE-complete for level 3/2 and between PSPACE-hard and EXPTIME for level 2.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"97 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128828558","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}

{"title":"Approximate Online Pattern Matching in Sub-linear Time","authors":"Diptarka Chakraborty, Debarati Das, M. Koucký","doi":"10.4230/LIPIcs.FSTTCS.2019.10","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2019.10","url":null,"abstract":"We consider the approximate pattern matching problem under edit distance. In this problem we are given a pattern $P$ of length $w$ and a text $T$ of length $n$ over some alphabet $Sigma$, and a positive integer $k$. The goal is to find all the positions $j$ in $T$ such that there is a substring of $T$ ending at $j$ which has edit distance at most $k$ from the pattern $P$. Recall, the edit distance between two strings is the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. For a position $t$ in ${1,...,n}$, let $k_t$ be the smallest edit distance between $P$ and any substring of $T$ ending at $t$. In this paper we give a constant factor approximation to the sequence $k_1,k_2,...,k_{n}$. We consider both offline and online settings. \u0000In the offline setting, where both $P$ and $T$ are available, we present an algorithm that for all $t$ in ${1,...,n}$, computes the value of $k_t$ approximately within a constant factor. The worst case running time of our algorithm is $O(n w^{3/4})$. As a consequence we break the $O(nw)$-time barrier for this problem. \u0000In the online setting, we are given $P$ and then $T$ arrives one symbol at a time. We design an algorithm that upon arrival of the $t$-th symbol of $T$ computes $k_t$ approximately within $O(1)$-multiplicative factor and $w^{8/9}$-additive error. Our algorithm takes $O(w^{1-(7/54)})$ amortized time per symbol arrival and takes $O(w^{1-(1/54)})$ additional space apart from storing the pattern $P$. \u0000Both of our algorithms are randomized and produce correct answer with high probability. To the best of our knowledge this is the first worst-case sub-linear (in the length of the pattern) time and sub-linear succinct space algorithm for online approximate pattern matching problem.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126208337","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}

{"title":"Combinatorial Algorithms for General Linear Arrow-Debreu Markets","authors":"B. Chaudhury, K. Mehlhorn","doi":"10.4230/LIPIcs.FSTTCS.2018.26","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.26","url":null,"abstract":"We present a combinatorial algorithm for determining the market clearing prices of a general linear Arrow-Debreu market, where every agent can own multiple goods. The existing combinatorial algorithms for linear Arrow-Debreu markets consider the case where each agent can own all of one good only. We present an $tilde{mathcal{O}}((n+m)^7 log^3(UW))$ algorithm where $n$, $m$, $U$ and $W$ refer to the number of agents, the number of goods, the maximal integral utility and the maximum quantity of any good in the market respectively. The algorithm refines the iterative algorithm of Duan, Garg and Mehlhorn using several new ideas. We also identify the hard instances for existing combinatorial algorithms for linear Arrow-Debreu markets. In particular we find instances where the ratio of the maximum to the minimum equilibrium price of a good is $U^{Omega(n)}$ and the number of iterations required by the existing iterative combinatorial algorithms of Duan, and Mehlhorn and Duan, Garg, and Mehlhorn are high. Our instances also separate the two algorithms.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"27 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116309979","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}

{"title":"Graph Pattern Polynomials","authors":"M. Bläser, Balagopal Komarath, Karteek Sreenivasaiah","doi":"10.4230/LIPIcs.FSTTCS.2018.18","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSTTCS.2018.18","url":null,"abstract":"Given a host graph G and a pattern graph H, the induced subgraph isomorphism problem is to decide whether G contains an induced subgraph that is isomorphic to H. We study the time complexity of induced subgraph isomorphism problems when the pattern graph is fixed. Nesetril and Poljak gave an O(n^{k omega}) time algorithm that decides the induced subgraph isomorphism problem for any 3k vertex pattern graph (the universal algorithm), where omega is the matrix multiplication exponent. Improvements are not known for any infinite pattern family.\u0000Algorithms faster than the universal algorithm are known only for a finite number of pattern graphs. In this paper, we show that there exists infinitely many pattern graphs for which the induced subgraph isomorphism problem has algorithms faster than the universal algorithm.\u0000Our algorithm works by reducing the pattern detection problem into a multilinear term detection problem on special classes of polynomials called graph pattern polynomials. We show that many of the existing algorithms including the universal algorithm can also be described in terms of such a reduction. We formalize this class of algorithms by defining graph pattern polynomial families and defining a notion of reduction between these polynomial families. The reduction also allows us to argue about relative hardness of various graph pattern detection problems within this framework. We show that solving the induced subgraph isomorphism for any pattern graph that contains a k-clique is at least as hard detecting k-cliques. An equivalent theorem is not known in the general case.\u0000In the full version of this paper, we obtain new algorithms for P_5 and C_5 that are optimal under reasonable hardness assumptions. We also use this method to derive new combinatorial algorithms - algorithms that do not use fast matrix multiplication - for paths and cycles. We also show why graph homomorphisms play a major role in algorithms for subgraph isomorphism problems. Using this, we show that the arithmetic circuit complexity of the graph homomorphism polynomial for K_k - e (The k-clique with an edge removed) is related to the complexity of many subgraph isomorphism problems. This generalizes and unifies many existing results.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126058828","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}