Related papers: Testing the Equivalence of Regular Languages
We study a connection between synchronizing automata and its set $M$ of minimal reset words, i.e., such that no proper factor is a reset word. We first show that any synchronizing automaton having the set of minimal reset words whose set of…
Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or…
We present a few classes of synchronizing automata exhibiting certain extremal properties with regard to synchronization. The first is a series of automata with subsets whose shortest extending words are of length $\varTheta(n^2)$, where…
In the computational-mechanics structural analysis of one-dimensional cellular automata the following automata-theoretic analogue of the \emph{change-point problem} from time series analysis arises: \emph{Given a string $\sigma$ and a…
We present an algorithm for regular expression parsing and submatch extraction based on tagged deterministic finite automata. The algorithm works with different disambiguation policies. We give detailed pseudocode for the algorithm,…
We introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every…
We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…
We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…
The main aim of the paper is to give a short self-contained proof of the decidability of language equivalence for deterministic pushdown automata, which is the famous problem solved by G. Senizergues, for which C. Stirling has derived a…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
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…
We first show that given a $k_1$-letter quantum finite automata $\mathcal{A}_1$ and a $k_2$-letter quantum finite automata $\mathcal{A}_2$ over the same input alphabet $\Sigma$, they are equivalent if and only if they are…
An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far…
We introduce Symbolic Alternating Finite Automata (s-AFA) as an expressive, succinct, and decidable model for describing sets of finite sequences over arbitrary alphabets. Boolean operations over s-AFAs have linear complexity, which is in…
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…
We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…
Automatic evaluation of various text quality criteria produced by data-driven intelligent methods is very common and useful because it is cheap, fast, and usually yields repeatable results. In this paper, we present an attempt to automate…
We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the…