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The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on…
This paper is devoted to finite state automata, regular expression matching, pattern recognition, and the exponential blow-up problem, which is the growing complexity of automata exponentially depending on regular expression length. This…
The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved…
In this paper we introduce a new type of approximate state reductions where the behaviors of the reduced and the original automaton do not have to be identical, but they must match on all words of length less than or equal to some given…
Most Formal Languages and Automata Theory courses explore the duality between computation models to recognize words in a language and computation models to generate words in a language. For students unaccustomed to formal statements, these…
In this work, we present multiple new optimizations and heuristics for the determinization of B\"uchi automata that exploit a number of semantic and structural properties, most of which may be applied together with any determinization…
A synchronizing word of a deterministic finite complete automaton is a word whose action maps every state to a single one. Finding a shortest or a short synchronizing word is a central computational problem in the theory of synchronizing…
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.
Regular languages are closed under a wealth of formal language operators. Incorporating such operators in regular expressions leads to concise language specifications, but the transformation of such enhanced regular expressions to finite…
To deal with system uncertainty, finite automata have been generalized into fuzzy automata. Stamenkovic and Ciric proposed an approach using the position automata for the construction of fuzzy automata from fuzzy regular expressions. There…
State reduction of finite automata plays a significant role in improving efficiency in formal verification, pattern recognition, and machine learning, where automata-based models are widely used. While deterministic automata have…
This paper introduces a new algorithm for the induction if complex finite state automata from samples of behavior. The algorithm is based on information theoretic principles. The algorithm reduces the search space by many orders of…
Several methods are discussed that construct a finite automaton given a context-free grammar, including both methods that lead to subsets and those that lead to supersets of the original context-free language. Some of these methods of…
Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from $n$ states to $2^n$ states.…
We introduce a new technique for constructing a finite state deterministic automaton from a regular expression, based on the idea of marking a suitable set of positions inside the expression, intuitively representing the possible points…
We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…
We present counting reward automata-a finite state machine variant capable of modelling any reward function expressible as a formal language. Unlike previous approaches, which are limited to the expression of tasks as regular languages, our…
In various applications, computers are required to compute approximations to univariate elementary and special functions such as $\exp$ and $\arctan$ to modest accuracy. This paper proposes a new heuristic for automating the design of such…
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
This paper presents the main features of a system that aims to transform regular expressions into shorter equivalent expressions. The system is also capable of computing other operations useful for simplification, such as checking the…