arXiv - CS - Formal Languages and Automata Theory最新文献_第8页

Verifying Unboundedness via Amalgamation 通过合并验证无界性

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-16 DOI: arxiv-2405.10296

Ashwani Anand, Sylvain Schmitz, Lia Schütze, Georg Zetzsche

{"title":"Verifying Unboundedness via Amalgamation","authors":"Ashwani Anand, Sylvain Schmitz, Lia Schütze, Georg Zetzsche","doi":"arxiv-2405.10296","DOIUrl":"https://doi.org/arxiv-2405.10296","url":null,"abstract":"Well-structured transition systems (WSTS) are an abstract family of systems\u0000that encompasses a vast landscape of infinite-state systems. By requiring a\u0000well-quasi-ordering (wqo) on the set of states, a WSTS enables generic\u0000algorithms for classic verification tasks such as coverability and termination.\u0000However, even for systems that are WSTS like vector addition systems (VAS), the\u0000framework is notoriously ill-equipped to analyse reachability (as opposed to\u0000coverability). Moreover, some important types of infinite-state systems fall\u0000out of WSTS' scope entirely, such as pushdown systems (PDS). Inspired by recent algorithmic techniques on VAS, we propose an abstract\u0000notion of systems where the set of runs is equipped with a wqo and supports\u0000amalgamation of runs. We show that it subsumes a large class of infinite-state\u0000systems, including (reachability languages of) VAS and PDS, and even all\u0000systems from the abstract framework of valence systems, except for those\u0000already known to be Turing-complete. Moreover, this abstract setting enables simple and general algorithmic\u0000solutions to unboundedness problems, which have received much attention in\u0000recent years. We present algorithms for the (i) simultaneous unboundedness\u0000problem (which implies computability of downward closures and decidability of\u0000separability by piecewise testable languages), (ii) computing priority downward\u0000closures, (iii) deciding whether a language is bounded, meaning included in\u0000$w_1^*cdots w_k^*$ for some words $w_1,ldots,w_k$, and (iv)~effective\u0000regularity of unary languages. This leads to either drastically simpler proofs\u0000or new decidability results for a rich variety of systems.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061016","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

Extended time Petri nets 扩展时间 Petri 网

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-15 DOI: arxiv-2405.09208

Marcin Radom, Piotr Formanowicz

引用次数: 0

A Formal Approach for Tuning Stochastic Oscillators 调整随机振荡器的正式方法

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-15 DOI: arxiv-2405.09183

Paolo BallariniMICS, Mahmoud Bentriou, Paul-Henry Cournède

{"title":"A Formal Approach for Tuning Stochastic Oscillators","authors":"Paolo BallariniMICS, Mahmoud Bentriou, Paul-Henry Cournède","doi":"arxiv-2405.09183","DOIUrl":"https://doi.org/arxiv-2405.09183","url":null,"abstract":"Periodic recurrence is a prominent behavioural of many biological phenomena,\u0000including cell cycle and circadian rhythms. Although deterministic models are\u0000commonly used to represent the dynamics of periodic phenomena, it is known that\u0000they are little appropriate in the case of systems in which stochastic noise\u0000induced by small population numbers is actually responsible for periodicity.\u0000Within the stochastic modelling settings automata-based model checking\u0000approaches have proven an effective means for the analysis of oscillatory\u0000dynamics, the main idea being that of coupling a period detector automaton with\u0000a continuous-time Markov chain model of an alleged oscillator. In this paper we\u0000address a complementary aspect, i.e. that of assessing the dependency of\u0000oscillation related measure (period and amplitude) against the parameters of a\u0000stochastic oscillator. To this aim we introduce a framework which, by combining\u0000an Approximate Bayesian Computation scheme with a hybrid automata capable of\u0000quantifying how distant an instance of a stochastic oscillator is from matching\u0000a desired (average) period, leads us to identify regions of the parameter space\u0000in which oscillation with given period are highly likely. The method is\u0000demonstrated through a couple of case studies, including a model of the popular\u0000Repressilator circuit.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061001","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

Containment Problem for Deterministic Multicounter Machine Models 确定性多计数器机器模型的包含问题

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-14 DOI: arxiv-2405.08988

Oscar H. Ibarra, Ian McQuillan

{"title":"Containment Problem for Deterministic Multicounter Machine Models","authors":"Oscar H. Ibarra, Ian McQuillan","doi":"arxiv-2405.08988","DOIUrl":"https://doi.org/arxiv-2405.08988","url":null,"abstract":"There are many types of automata and grammar models that have been studied in\u0000the literature, and for these models, it is common to determine whether certain\u0000problems are decidable. One problem that has been difficult to answer\u0000throughout the history of automata and formal language theory is to decide\u0000whether a given system $M$ accepts a bounded language (whether there exist\u0000words $w_1, ldots,w_k$ such that $L(M) subseteq w_1^* cdots w_k^*$?).\u0000Boundedness was only known to be decidable for regular and context-free\u0000languages until recently when it was shown to also be decidable for finite\u0000automata and pushdown automata augmented with reversal-bounded counters, and\u0000for vector addition systems with states. However, decidability of this problem\u0000has still gone unanswered for the majority of automata/grammar models with a\u0000decidable emptiness problem that have been studied in the literature. In this paper, we develop new techniques to show that the boundedness problem\u0000is decidable for larger classes of one-way nondeterministic automata and\u0000grammar models by reducing the problem to the decidability of boundedness for\u0000simpler classes of automata. One technique involves characterizing the models\u0000in terms of multi-tape automata. We give new characterizations of finite-turn\u0000Turing machines, finite-turn Turing machines augmented with various storage\u0000structures (like a pushdown, multiple reversal-bounded counters,\u0000partially-blind counters, etc.), and simple matrix grammars. The\u0000characterizations are then used to show that the boundedness problem for these\u0000models is decidable. Another technique uses the concept of the store language\u0000of an automaton. This is used to show that the boundedness problem is decidable\u0000for pushdown automata that can \"flip\" their pushdown a bounded number of times.\u0000Boundedness remains decidable even if we augment this device with additional\u0000stores.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061061","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

Constructing a BPE Tokenization DFA 构建 BPE 标记化 DFA

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-13 DOI: arxiv-2405.07671

Martin Berglund, Willeke Martens, Brink van der Merwe

引用次数: 0

Gödel Number based Clustering Algorithm with Decimal First Degree Cellular Automata 基于哥德尔数的十进制一级细胞自动机聚类算法

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-08 DOI: arxiv-2405.04881

Vicky Vikrant, Narodia Parth P, Kamalika Bhattacharjee

引用次数: 0

Probabilistic Finite Automaton Emptiness is undecidable 概率有限自动机的空性是不可判定的

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-05 DOI: arxiv-2405.03035

Günter Rote

引用次数: 0

A Direct Translation from LTL with Past to Deterministic Rabin Automata 从带过去时的 LTL 到确定性拉宾自动机的直接转换

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-02 DOI: arxiv-2405.01178

Shaun Azzopardi, David Lidell, Nir Piterman

引用次数: 0

FSM Builder: A Tool for Writing Autograded Finite Automata Questions FSM 生成器：编写自分级有限自动机问题的工具

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-05-02 DOI: arxiv-2405.01717

Eliot Wong Robson, Sam Ruggerio, Jeff Erickson

{"title":"FSM Builder: A Tool for Writing Autograded Finite Automata Questions","authors":"Eliot Wong Robson, Sam Ruggerio, Jeff Erickson","doi":"arxiv-2405.01717","DOIUrl":"https://doi.org/arxiv-2405.01717","url":null,"abstract":"Deterministic and nondeterministic finite automata (DFAs and NFAs) are\u0000abstract models of computation commonly taught in introductory computing theory\u0000courses. These models have important applications (such as fast regular\u0000expression matching), and are used to introduce formal language theory.\u0000Undergraduate students often struggle with understanding these models at first,\u0000due to the level of abstraction. As a result, various pedagogical tools have\u0000been developed to allow students to practice with these models. We introduce\u0000the FSM Builder, a new pedagogical tool enabling students to practice\u0000constructing DFAs and NFAs with a graphical editor, giving personalized\u0000feedback and partial credit. The algorithms used for generating these are\u0000heavily inspired by previous works. The key advantages to its competitors are\u0000greater flexibility and scalability. This is because the FSM Builder is\u0000implemented using efficient algorithms from an open source package, allowing\u0000for easy extension and question creation. We discuss the implementation of the\u0000tool, how it stands out from previous tools, and takeaways from experiences of\u0000using the tool in multiple large courses. Survey results indicate the interface\u0000and feedback provided by the tool were useful to students.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881775","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

Finding Diverse Strings and Longest Common Subsequences in a Graph 查找图形中的不同字符串和最长公共后序

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-04-30 DOI: arxiv-2405.00131

Yuto Shida, Giulia Punzi, Yasuaki Kobayashi, Takeaki Uno, Hiroki Arimura

{"title":"Finding Diverse Strings and Longest Common Subsequences in a Graph","authors":"Yuto Shida, Giulia Punzi, Yasuaki Kobayashi, Takeaki Uno, Hiroki Arimura","doi":"arxiv-2405.00131","DOIUrl":"https://doi.org/arxiv-2405.00131","url":null,"abstract":"In this paper, we study for the first time the Diverse Longest Common\u0000Subsequences (LCSs) problem under Hamming distance. Given a set of a constant\u0000number of input strings, the problem asks to decide if there exists some subset\u0000$mathcal X$ of $K$ longest common subsequences whose diversity is no less than\u0000a specified threshold $Delta$, where we consider two types of diversities of a\u0000set $mathcal X$ of strings of equal length: the Sum diversity and the Min\u0000diversity defined as the sum and the minimum of the pairwise Hamming distance\u0000between any two strings in $mathcal X$, respectively. We analyze the\u0000computational complexity of the respective problems with Sum- and Min-diversity\u0000measures, called the Max-Sum and Max-Min Diverse LCSs, respectively,\u0000considering both approximation algorithms and parameterized complexity. Our\u0000results are summarized as follows. When $K$ is bounded, both problems are\u0000polynomial time solvable. In contrast, when $K$ is unbounded, both problems\u0000become NP-hard, while Max-Sum Diverse LCSs problem admits a PTAS. Furthermore,\u0000we analyze the parameterized complexity of both problems with combinations of\u0000parameters $K$ and $r$, where $r$ is the length of the candidate strings to be\u0000selected. Importantly, all positive results above are proven in a more general\u0000setting, where an input is an edge-labeled directed acyclic graph (DAG) that\u0000succinctly represents a set of strings of the same length. Negative results are\u0000proven in the setting where an input is explicitly given as a set of strings.\u0000The latter results are equipped with an encoding such a set as the longest\u0000common subsequences of a specific input string set.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839542","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