Learning automata by queries is a long-studied area initiated by Angluin in 1987 with the introduction of the $L^*$ algorithm to learn regular languages, with a large body of work afterwards on many different variations and generalizations of DFAs. Recently, Chase and Freitag introduced a novel approach to proving query learning bounds by computing combinatorial complexity measures for the classes in question, which they applied to the setting of DFAs to obtain qualitatively different results compared to the $L^*$ algorithm. Using this approach, we prove new query learning bounds for two generalizations of DFAs. The first setting is that of advice DFAs, which are DFAs augmented with an advice string that informs the DFA's transition behavior at each step. For advice DFAs, we give the first known upper bounds for query complexity. The second setting is that of nominal DFAs, which generalize DFAs to infinite alphabets which admit some structure via symmetries. For nominal DFAs, we make qualitative improvements over prior results.
{"title":"Query Learning of Advice and Nominal Automata","authors":"Kevin Zhou","doi":"arxiv-2409.10822","DOIUrl":"https://doi.org/arxiv-2409.10822","url":null,"abstract":"Learning automata by queries is a long-studied area initiated by Angluin in\u00001987 with the introduction of the $L^*$ algorithm to learn regular languages,\u0000with a large body of work afterwards on many different variations and\u0000generalizations of DFAs. Recently, Chase and Freitag introduced a novel\u0000approach to proving query learning bounds by computing combinatorial complexity\u0000measures for the classes in question, which they applied to the setting of DFAs\u0000to obtain qualitatively different results compared to the $L^*$ algorithm.\u0000Using this approach, we prove new query learning bounds for two generalizations\u0000of DFAs. The first setting is that of advice DFAs, which are DFAs augmented\u0000with an advice string that informs the DFA's transition behavior at each step.\u0000For advice DFAs, we give the first known upper bounds for query complexity. The\u0000second setting is that of nominal DFAs, which generalize DFAs to infinite\u0000alphabets which admit some structure via symmetries. For nominal DFAs, we make\u0000qualitative improvements over prior results.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249545","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}
Regular expressions are commonly understood in terms of their denotational semantics, that is, through formal languages -- the regular languages. This view is inductive in nature: two primitives are equivalent if they are constructed in the same way. Alternatively, regular expressions can be understood in terms of their operational semantics, that is, through deterministic finite automata. This view is coinductive in nature: two primitives are equivalent if they are deconstructed in the same way. It is implied by Kleene's famous theorem that both views are equivalent: regular languages are precisely the formal languages accepted by deterministic finite automata. In this paper, we use Dafny, a verification-aware programming language, to formally verify, for the first time, what has been previously established only through proofs-by-hand: the two semantics of regular expressions are well-behaved, in the sense that they are in fact one and the same, up to pointwise bisimilarity. At each step of our formalisation, we propose an interpretation in the language of Coalgebra. We found that Dafny is particularly well suited for the task due to its inductive and coinductive features and hope our approach serves as a blueprint for future generalisations to other theories.
{"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}
We consider weighted automata over words and over trees where the weight algebras are strong bimonoids, i.e., semirings which may lack distributivity. It is well known that, for each such weighted automaton, its run semantics and its initial algebra semantics can be different, due to the presence of nondeterminism and the absence of distributivity. Here we investigate the question under which conditions on the strong bimonoid the support of the run semantics equals the support of the initial algebra semantics. We prove a characterization of this equality in terms of strongly zero-sum-free strong bimonoids (for weighted automata over words) and in terms of bi-strongly zero-sum-free strong bimonoids (for weighted automata over trees). We also consider shortly the images of the two semantics functions.
{"title":"Run supports and initial algebra supports of weighted automata","authors":"Manfred Droste, Heiko Vogler","doi":"arxiv-2409.08727","DOIUrl":"https://doi.org/arxiv-2409.08727","url":null,"abstract":"We consider weighted automata over words and over trees where the weight\u0000algebras are strong bimonoids, i.e., semirings which may lack distributivity.\u0000It is well known that, for each such weighted automaton, its run semantics and\u0000its initial algebra semantics can be different, due to the presence of\u0000nondeterminism and the absence of distributivity. Here we investigate the\u0000question under which conditions on the strong bimonoid the support of the run\u0000semantics equals the support of the initial algebra semantics. We prove a\u0000characterization of this equality in terms of strongly zero-sum-free strong\u0000bimonoids (for weighted automata over words) and in terms of bi-strongly\u0000zero-sum-free strong bimonoids (for weighted automata over trees). We also\u0000consider shortly the images of the two semantics functions.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249547","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}
A fundamental construction in formal language theory is the Myhill-Nerode congruence on words, whose finitedness characterizes regular language. This construction was generalized to functions from $Sigma^*$ to $mathbb{Z}$ by Colcombet, Dou'eneau-Tabot, and Lopez to characterize the class of so-called $mathbb{Z}$-polyregular functions. In this paper, we relax the notion of equivalence relation to quasi-ordering in order to study the class of $mathbb{N}$-polyregular functions, that plays the role of $mathbb{Z}$-polyregular functions among functions from $Sigma^*$ to $mathbb{N}$. The analogue of having a finite index is then being a well-quasi-ordering. This provides a canonical object to describe $mathbb{N}$-polyregular functions, together with a powerful new characterization of this class.
{"title":"$mathbb{N}$-polyregular functions arise from well-quasi-orderings","authors":"Aliaume Lopez","doi":"arxiv-2409.07882","DOIUrl":"https://doi.org/arxiv-2409.07882","url":null,"abstract":"A fundamental construction in formal language theory is the Myhill-Nerode\u0000congruence on words, whose finitedness characterizes regular language. This\u0000construction was generalized to functions from $Sigma^*$ to $mathbb{Z}$ by\u0000Colcombet, Dou'eneau-Tabot, and Lopez to characterize the class of so-called\u0000$mathbb{Z}$-polyregular functions. In this paper, we relax the notion of\u0000equivalence relation to quasi-ordering in order to study the class of\u0000$mathbb{N}$-polyregular functions, that plays the role of\u0000$mathbb{Z}$-polyregular functions among functions from $Sigma^*$ to\u0000$mathbb{N}$. The analogue of having a finite index is then being a\u0000well-quasi-ordering. This provides a canonical object to describe\u0000$mathbb{N}$-polyregular functions, together with a powerful new\u0000characterization of this class.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197180","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}
Plane-walking automata were introduced by Salo & T"orma to recognise languages of two-dimensional infinite words (subshifts), the counterpart of $4$-way finite automata for two-dimensional finite words. We extend the model to allow for nondeterminism and alternation of quantifiers. We prove that the recognised subshifts form a strict subclass of sofic subshifts, and that the classes corresponding to existential and universal nondeterminism are incomparable and both larger that the deterministic class. We define a hierarchy of subshifts recognised by plane-walking automata with alternating quantifiers, which we conjecture to be strict.
{"title":"Alternating hierarchy of sushifts defined by nondeterministic plane-walking automata","authors":"Benjamin Hellouin de Menibus, Pacôme Perrotin","doi":"arxiv-2409.08024","DOIUrl":"https://doi.org/arxiv-2409.08024","url":null,"abstract":"Plane-walking automata were introduced by Salo & T\"orma to recognise\u0000languages of two-dimensional infinite words (subshifts), the counterpart of\u0000$4$-way finite automata for two-dimensional finite words. We extend the model\u0000to allow for nondeterminism and alternation of quantifiers. We prove that the\u0000recognised subshifts form a strict subclass of sofic subshifts, and that the\u0000classes corresponding to existential and universal nondeterminism are\u0000incomparable and both larger that the deterministic class. We define a\u0000hierarchy of subshifts recognised by plane-walking automata with alternating\u0000quantifiers, which we conjecture to be strict.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"93 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197179","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}
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
We exhibit a winning strategy for Synchronizer in the synchronization game on every synchronizing automaton in whose transition monoid the regular D-classes form subsemigroups
我们展示了同步器在同步博弈中的制胜策略，即在每一个同步自动机中，其过渡单元中的正则 D 类都构成子组
{"title":"Winning Strategies for the Synchronization Game on Subclasses of Finite Automata","authors":"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","doi":"arxiv-2409.06971","DOIUrl":"https://doi.org/arxiv-2409.06971","url":null,"abstract":"We exhibit a winning strategy for Synchronizer in the synchronization game on\u0000every synchronizing automaton in whose transition monoid the regular D-classes\u0000form subsemigroups","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197187","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}
Henning BordihnUniversity of Potsdam, Institute of Computer Science, Helena Schulz
Soliton automata are mathematical models of soliton switching in chemical molecules. Several concepts of determinism for soliton automata have been defined. The concept of strong determinism has been investigated for the case in which only a single soliton can be present in a molecule. In the present paper, several different concepts of determinism are explored for the multi-soliton case. It is shown that the degree of non-determinism is a connected measure of descriptional complexity for multi-soliton automata. A characterization of the class of strongly deterministic multi-soliton automata is presented. Finally, the concept of perfect determinism, forming a natural extension of strong determinism, is introduced and considered for multi-soliton automata.
{"title":"Determinism in Multi-Soliton Automata","authors":"Henning BordihnUniversity of Potsdam, Institute of Computer Science, Helena Schulz","doi":"arxiv-2409.06969","DOIUrl":"https://doi.org/arxiv-2409.06969","url":null,"abstract":"Soliton automata are mathematical models of soliton switching in chemical\u0000molecules. Several concepts of determinism for soliton automata have been\u0000defined. The concept of strong determinism has been investigated for the case\u0000in which only a single soliton can be present in a molecule. In the present\u0000paper, several different concepts of determinism are explored for the\u0000multi-soliton case. It is shown that the degree of non-determinism is a\u0000connected measure of descriptional complexity for multi-soliton automata. A\u0000characterization of the class of strongly deterministic multi-soliton automata\u0000is presented. Finally, the concept of perfect determinism, forming a natural\u0000extension of strong determinism, is introduced and considered for multi-soliton\u0000automata.","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":"142197189","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}
The Extended Church-Turing Thesis (ECTT) posits that all effective information processing, including unbounded and non-uniform interactive computations, can be described in terms of interactive Turing machines with advice. Does this assertion also apply to the abilities of contemporary large language models (LLMs)? From a broader perspective, this question calls for an investigation of the computational power of LLMs by the classical means of computability and computational complexity theory, especially the theory of automata. Along these lines, we establish a number of fundamental results. Firstly, we argue that any fixed (non-adaptive) LLM is computationally equivalent to a, possibly very large, deterministic finite-state transducer. This characterizes the base level of LLMs. We extend this to a key result concerning the simulation of space-bounded Turing machines by LLMs. Secondly, we show that lineages of evolving LLMs are computationally equivalent to interactive Turing machines with advice. The latter finding confirms the validity of the ECTT for lineages of LLMs. From a computability viewpoint, it also suggests that lineages of LLMs possess super-Turing computational power. Consequently, in our computational model knowledge generation is in general a non-algorithmic process realized by lineages of LLMs. Finally, we discuss the merits of our findings in the broader context of several related disciplines and philosophies.
{"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}
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
This paper introduces derivation trees for general grammars. Within these trees, it defines context-dependent pairs of nodes, corresponding to rewriting two neighboring symbols using a non context-free rule. It proves that the language generated by a linear core general grammar with a slow-branching derivation tree is k-linear if there is a constant u such that every sentence w in the generated language is the frontier of a derivation tree in which any pair of neighboring paths contains u or fewer context-dependent pairs of nodes. Next, it proves that the language generated by a general grammar with a regular core is regular if there is a constant u such that every sentence w in the generated language is the frontier of a derivation tree in which any pair of neighboring paths contains u or fewer context-dependent pairs of nodes. The paper explains that this result is a powerful tool for showing that certain languages are k-linear or regular.
本文介绍了一般语法的推导树。在推导树中，它定义了与上下文相关的节点对，对应于使用非无上下文规则重写两个相邻符号。如果存在一个常数 u，使得生成语言中的每个句子都是派生树的前沿，在派生树中，任何一对相邻路径都包含 u 或更少的上下文相关节点对，那么它就证明了具有慢分支派生树的线性核心通用语法生成的语言是 k 线性的。接下来，论文证明，如果存在一个常数 u，使得生成语言中的每个句子 w 都是一棵派生树的前沿，在这棵派生树中，任何一对相邻路径都包含 u 或更少的上下文相关节点对，那么由具有正则核的一般语法生成的语言就是正则语言。论文解释说，这一结果是证明某些语言是 k 线性或正则性语言的有力工具。
{"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}
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate various comet-like types of languages and compare such language families to some other subregular families of languages (finite, monoidal, nilpotent, combinational, (symmetric) definite, ordered, non-counting, power-separating, suffix-closed, commutative, circular, or union-free languages). Further, we compare the language families defined by these types for the selection with each other and with the families of the hierarchy obtained for external contextual grammars. In this way, we extend the existing hierarchy by new language families.
{"title":"Various Types of Comet Languages and their Application in External Contextual Grammars","authors":"Marvin Ködding, Bianca Truthe","doi":"arxiv-2409.06974","DOIUrl":"https://doi.org/arxiv-2409.06974","url":null,"abstract":"In this paper, we continue the research on the power of contextual grammars\u0000with selection languages from subfamilies of the family of regular languages.\u0000We investigate various comet-like types of languages and compare such language\u0000families to some other subregular families of languages (finite, monoidal,\u0000nilpotent, combinational, (symmetric) definite, ordered, non-counting,\u0000power-separating, suffix-closed, commutative, circular, or union-free\u0000languages). Further, we compare the language families defined by these types\u0000for the selection with each other and with the families of the hierarchy\u0000obtained for external contextual grammars. In this way, we extend the existing\u0000hierarchy by new language families.","PeriodicalId":501124,"journal":{"name":"arXiv - CS - Formal Languages and Automata Theory","volume":"93 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197184","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}
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