Roberto Vaglica

A reconstruction algorithm for L-convex polyominoes

We give an algorithm that uniquely reconstruct an L-convex polyomino from the size of some special paths, called bordered L-paths.

Recognizable picture languages and polyominoes

An irrigation system includes an irrigation line and a wind brace assembly which can be automatically disengaged from the irrigation line preparatory to moving the irrigation line across a field to a new position. The assembly is automatically engaged with the irrigation line in the new position to prevent wind from moving the irrigation line.

A graph theoretic approach to automata minimality

The paper presents a graph-theoretic approach to test the minimality of a deterministic automaton. In particular, we focus on problems concerning the dependence of the minimality of an automaton on the choice of the set F of final states or on the cardinality of the set F. We introduce different minimality conditions of an automaton and show that such conditions can be characterized in graph-theoretic terms.

Some remarks on automata minimality

It is well known that the minimization problem of deterministic finite automata (DFAs) is related to the indistinguishability notion of states (cf. [HMU00]). Indeed, a well known technique to minimize a DFA, essentially, consists in finding pairs of states that are equivalent (or indistinguishable), namely pairs of states (p,q) such that it is impossible to assert the difference between p and q only by starting in each of the two states and asking whether or not a given input string leads to a final state. Since, in the testing states equivalence, the notion of initial state is irrelevant, some of the main techniques for the minimization of automata, such as Moore’s algorithm [Moo56] and Hopcroft’s algorithm [Hop71], do not care what is the initial state of the automaton, when applied to accessible automata (i.e. such that all states can be reached from the initial state). Therefore a natural question that arises is, for accessible automata, on what does minimality depend? Obviously, it depends on both the automata transitions and the set of final states. In this paper, our main focus is to investigate to what extent minimality depends on the particular subset of final states.