Weakly and Strongly Irreversible Regular Languages

Abstract

Finite automata whose computations can be reversed, at any point, by knowing the last k symbols read from the input, for a fixed k, are considered. These devices and their accepted languages are called k-reversible automata and k-reversible languages, respectively. The existence of k-reversible languages which are not (k-1)-reversible is known, for each k>1. This gives an infinite hierarchy of weakly irreversible languages, i.e., languages which are k-reversible for some k. Conditions characterizing the class of k-reversible languages, for each fixed k, and the class of weakly irreversible languages are obtained. From these conditions, a procedure that given a finite automaton decides if the accepted language is weakly or strongly (i.e., not weakly) irreversible is described. Furthermore, a construction which allows to transform any finite automaton which is not k-reversible, but which accepts a k-reversible language, into an equivalent k-reversible finite automaton, is presented.Comment: In Proceedings AFL 2017, arXiv:1708.0622

Concise Representations of Reversible Automata

“…Recently, the definition of reversibility for finite automata has been deepened and relaxed, thus allowing different degrees of reversibility, the degree one corresponding to reversible automata [9]. In particular, finite automata whose computations can be reversed deterministically by knowing the last k symbols read from the input, for a fixed k (reversed k-lookahead ), have led to the notion of weak irreversibility [13]. It could be interesting to extend the results about the succinctness of representations of rev-dfa to weakly irreversible automata.…”

Foundations of Reversible Computation

“…Because of the narrowness of the power of reversible finite automata with respect to the irreversible ones, the definition of reversibility has been relaxed, by considering finite automata whose computations can be reversed, at any point, by accessing the last k symbols read from the input, for a fixed k. These devices are said to be "weakly irreversible". Characterisations of languages accepted by weakly irreversible automata and languages not having any weakly irreversible automaton ("strongly irreversible" languages) have been given [124].…”

Finite automata with undirected state graphs

“…The observation that loss of information results in heat dissipation [12] strongly suggests to study computations without loss of information. Recent results on reversible finite automata can be found, for example, in [7][8][9]13].…”