arXiv - CS - Formal Languages and Automata Theory最新文献

Query Learning of Advice and Nominal Automata 建议和名义自动机的查询学习

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-09-17 DOI: arxiv-2409.10822

Kevin Zhou

引用次数: 0

Well-Behaved (Co)algebraic Semantics of Regular Expressions in Dafny Dafny 中正则表达式的完备（共）代数语义学

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-09-15 DOI: arxiv-2409.09889

Stefan Zetzsche, Wojciech Rozowski

{"title":"Well-Behaved (Co)algebraic Semantics of Regular Expressions in Dafny","authors":"Stefan Zetzsche, Wojciech Rozowski","doi":"arxiv-2409.09889","DOIUrl":"https://doi.org/arxiv-2409.09889","url":null,"abstract":"Regular expressions are commonly understood in terms of their denotational\u0000semantics, that is, through formal languages -- the regular languages. This\u0000view is inductive in nature: two primitives are equivalent if they are\u0000constructed in the same way. Alternatively, regular expressions can be\u0000understood in terms of their operational semantics, that is, through\u0000deterministic finite automata. This view is coinductive in nature: two\u0000primitives are equivalent if they are deconstructed in the same way. It is\u0000implied by Kleene's famous theorem that both views are equivalent: regular\u0000languages are precisely the formal languages accepted by deterministic finite\u0000automata. In this paper, we use Dafny, a verification-aware programming\u0000language, to formally verify, for the first time, what has been previously\u0000established only through proofs-by-hand: the two semantics of regular\u0000expressions are well-behaved, in the sense that they are in fact one and the\u0000same, up to pointwise bisimilarity. At each step of our formalisation, we\u0000propose an interpretation in the language of Coalgebra. We found that Dafny is\u0000particularly well suited for the task due to its inductive and coinductive\u0000features and hope our approach serves as a blueprint for future generalisations\u0000to other theories.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"195 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249546","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

Run supports and initial algebra supports of weighted automata 加权自动机的运行支持和初始代数支持

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08727

Manfred Droste, Heiko Vogler

引用次数: 0

$mathbb{N}$-polyregular functions arise from well-quasi-orderings $mathbb{N}$多不规则函数产生于良好准有序性

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-09-12 DOI: arxiv-2409.07882

Aliaume Lopez

引用次数: 0

Alternating hierarchy of sushifts defined by nondeterministic plane-walking automata 由非确定性平面行走自动机定义的交替分层苏轼

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-09-12 DOI: arxiv-2409.08024

Benjamin Hellouin de Menibus, Pacôme Perrotin

引用次数: 0

Winning Strategies for the Synchronization Game on Subclasses of Finite Automata 有限自动机子类上同步博弈的制胜策略

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-09-11 DOI: arxiv-2409.06971

Henning FernauUniversität Trier, Fachbereich IV, Informatikwissenschaften, Trier, Germany, Carolina HaaseUniversität Trier, Fachbereich IV, Informatikwissenschaften, Trier, Germany, Stefan HoffmannInstitute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia, Mikhail VolkovInstitute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia

引用次数: 0

Determinism in Multi-Soliton Automata 多孑子自动机中的决定论

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-09-11 DOI: arxiv-2409.06969

Henning BordihnUniversity of Potsdam, Institute of Computer Science, Helena Schulz

引用次数: 0

Large Language Models and the Extended Church-Turing Thesis 大型语言模型和扩展的丘奇-图灵理论

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-09-11 DOI: arxiv-2409.06978

Jiří Wiedermann, Jan van Leeuwen

{"title":"Large Language Models and the Extended Church-Turing Thesis","authors":"Jiří Wiedermann, Jan van Leeuwen","doi":"arxiv-2409.06978","DOIUrl":"https://doi.org/arxiv-2409.06978","url":null,"abstract":"The Extended Church-Turing Thesis (ECTT) posits that all effective\u0000information processing, including unbounded and non-uniform interactive\u0000computations, can be described in terms of interactive Turing machines with\u0000advice. Does this assertion also apply to the abilities of contemporary large\u0000language models (LLMs)? From a broader perspective, this question calls for an\u0000investigation of the computational power of LLMs by the classical means of\u0000computability and computational complexity theory, especially the theory of\u0000automata. Along these lines, we establish a number of fundamental results.\u0000Firstly, we argue that any fixed (non-adaptive) LLM is computationally\u0000equivalent to a, possibly very large, deterministic finite-state transducer.\u0000This characterizes the base level of LLMs. We extend this to a key result\u0000concerning the simulation of space-bounded Turing machines by LLMs. Secondly,\u0000we show that lineages of evolving LLMs are computationally equivalent to\u0000interactive Turing machines with advice. The latter finding confirms the\u0000validity of the ECTT for lineages of LLMs. From a computability viewpoint, it\u0000also suggests that lineages of LLMs possess super-Turing computational power.\u0000Consequently, in our computational model knowledge generation is in general a\u0000non-algorithmic process realized by lineages of LLMs. Finally, we discuss the\u0000merits of our findings in the broader context of several related disciplines\u0000and philosophies.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197181","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

How to Demonstrate Metalinearness and Regularity by Tree-Restricted General Grammars 如何通过树状限制的通用语法证明金属线性和规则性

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-09-11 DOI: arxiv-2409.06972

Martin HavelBrno University of Technology, Faculty of Information Technology, Zbyněk KřivkaBrno University of Technology, Faculty of Information Technology, Alexander MedunaBrno University of Technology, Faculty of Information Technology

{"title":"How to Demonstrate Metalinearness and Regularity by Tree-Restricted General Grammars","authors":"Martin HavelBrno University of Technology, Faculty of Information Technology, Zbyněk KřivkaBrno University of Technology, Faculty of Information Technology, Alexander MedunaBrno University of Technology, Faculty of Information Technology","doi":"arxiv-2409.06972","DOIUrl":"https://doi.org/arxiv-2409.06972","url":null,"abstract":"This paper introduces derivation trees for general grammars. Within these\u0000trees, it defines context-dependent pairs of nodes, corresponding to rewriting\u0000two neighboring symbols using a non context-free rule. It proves that the\u0000language generated by a linear core general grammar with a slow-branching\u0000derivation tree is k-linear if there is a constant u such that every sentence w\u0000in the generated language is the frontier of a derivation tree in which any\u0000pair of neighboring paths contains u or fewer context-dependent pairs of nodes.\u0000Next, it proves that the language generated by a general grammar with a regular\u0000core is regular if there is a constant u such that every sentence w in the\u0000generated language is the frontier of a derivation tree in which any pair of\u0000neighboring paths contains u or fewer context-dependent pairs of nodes. The\u0000paper explains that this result is a powerful tool for showing that certain\u0000languages are k-linear or regular.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"s1-8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197186","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

Various Types of Comet Languages and their Application in External Contextual Grammars 各种类型的彗星语言及其在外部语境语法中的应用

arXiv - CS - Formal Languages and Automata Theory Pub Date : 2024-09-11 DOI: arxiv-2409.06974

Marvin Ködding, Bianca Truthe

引用次数: 0