Related papers: On the Intersection of Context-Free and Regular La…
This paper investigates acceptance conditions for finite automata recognizing omega-regular languages. As a first result, we show that, under any acceptance condition that can be defined in the MSO logic, a finite automaton can recognize at…
In this work we construct an automaton for the commutative closure of a given regular group language. The number of states of the resulting automaton is bounded by the number of states of the original automaton, raised to the power of the…
It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of…
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event…
Automata over infinite objects are a well-established model with applications in logic and formal verification. Traditionally, acceptance in such automata is defined based on the set of states visited infinitely often during a run. However,…
The operator precedence languages (OPLs) represent the largest known subclass of the context-free languages which enjoys all desirable closure and decidability properties. This includes the decidability of language inclusion, which is the…
A new family of categorial grammars is proposed, defined by enriching basic categorial grammars with a conjunction operation. It is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that…
Requirements are informal and semi-formal descriptions of the expected behavior of a complex system from the viewpoints of its stakeholders (customers, users, operators, designers, and engineers). However, for the purpose of design,…
We observe that pre-trained large language models (LLMs) are capable of autoregressively completing complex token sequences -- from arbitrary ones procedurally generated by probabilistic context-free grammars (PCFG), to more rich spatial…
The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation…
While automata theory often concerns itself with regular predicates, relations corresponding to acceptance by a finite state automaton, in this article we study the regular functions, such relations which are also functions in the…
We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted by deterministic multipass automata is exactly the Boolean…
We give another proof of a theorem of Fife - understood broadly as providing a finite automaton that gives a complete description of all infinite binary overlap-free words. Our proof is significantly simpler than those in the literature. As…
We study the structure of the language of binary cube-free words. Namely, we are interested in the cube-free words that cannot be infinitely extended preserving cube-freeness. We show the existence of such words with arbitrarily long finite…
We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such…
In this work we use a framework of finite-state automata constructions based on equivalences over words to provide new insights on the relation between well-known methods for computing the minimal deterministic automaton of a language.
The Random Language Model, proposed as a simple model of human languages, is defined by the averaged model of a probabilistic context-free grammar. This grammar expresses the process of sentence generation as a tree graph with nodes having…
Given a regular language L, we effectively construct a unary semigroup that recognizes the topological closure of L in the free unary semigroup relative to the variety of unary semigroups generated by the pseudovariety R of all finite…
In this paper we consider the class of lambda-nondeterministic linear automata as a model of the class of linear languages. As usual in other automata models, lambda-moves do not increase the acceptance power. The main contribution of this…