The quotient complexity of a regular language L is the number of left quotients of L, which is the same as the state complexity of L. Suppose that L and L′ are binary regular languages with quotient complexities m and n, and that the transition semigroups of the minimal deterministic automata accepting L and L′ are the symmetric groups Sm and Sn of degrees m and n, respectively. Denote by ◦ any...

We propose linear systems of hedge language equations (LSH) as a formalism to represent regular hedge languages. These linear systems are suitable for several computations in the algebra of regular hedge languages. We indicate algorithms to translate between representations by hedge automata and LSH, and for the computation of LSH for the intersection, quotient, left and right factors of regula...

We introduce the notion of double permutation in order to study particular classes of transformations of the one-dimensional cellular automata rule space. These classes of transformations are characterized according to different sets of metrical, language theoretic, and dynamical properties they preserve. Each set of transformations we propose induces an equivalence relation over the cellular a...

We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language – which is the number of its (left) quotients, and is the same as its state complexity – we also consider the size of its syntactic semigroup and the quotient complexity of its atoms – basic components of every...

Algebraic properties and structures of intuitionistic $$L-$$ fuzzy multiset finite automata (ILFMA) are discussed through congruences on a semigroup in this paper. Firstly, we put forward the notion compatible relation, monoid associated with relation can be effectively constructed, construct two monoids different congruence relations given ILFMA, then prove that they isomorphic. Furthermore, u...

We study bisimulation and minimization for weighted automata, relying on a geometrical representation of the model, linear weighted automata (lwa). In a lwa, the state-space of the automaton is represented by a vector space, and the transitions and weighting maps by linear morphisms over this vector space. Weighted bisimulations are represented by sub-spaces that are invariant under the transit...

This paper is devoted to the study of nondeterministic closure automata, that is, nondeterministic finite automata (nfas) equipped with a strict closure operator on the set of states and continuous transition structure. We prove that for each regular language L there is a unique minimal nondeterministic closure automaton whose underlying nfa accepts L. Here minimality means no proper sub or quo...

The synthesis of controllers for discrete event systems, as introduced by Ramadge and Wonham, amounts to computing winning strategies in parity games. We show that in this framework it is possible to extend the specifications of the supervised systems as well as the constraints on the controllers by expressing them in the modal μ-calculus. In order to express unobservability constraints, we pro...

The Besicovitch pseudodistance measures the relative size of the set of points where two functions take different values; the quotient space modulo the induced equivalence relation is endowed with a natural metric. We study the behaviour of cellular automata in the new topology and show that, under suitable additional hypotheses, they retain certain properties possessed in the usual product top...

The Besicovitch pseudodistance measures the relative size of the set of points where two functions take different values; the quotient space modulo the induced equivalence relation is endowed with a natural metric. We study the behaviour of cellular automata in the new topology and show that, under suitable additional hypotheses, they retain certain properties possessed in the usual product top...