Concise Representations of Reversible Automata

Giovanna J Lavado,Luca Prigioniero

doi:10.1142/s0129054119400331

Giovanna J Lavado, Luca Prigioniero

Open Access

https://doi.org/10.1142/s0129054119400331

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Abstract

In this paper, we present two concise representations of reversible automata. Both representations have a size comparable to the size of the minimum equivalent deterministic automaton and can be exponentially smaller than the size of the explicit representations of corresponding reversible automata. Using these representations it is possible to simulate the computations of reversible automata without explicitly writing down their complete descriptions.

Highlights

Reversibility is a fundamental principle in physics: in thermodynamics a transformation is reversible if, after occurring, it can be inverted in order to recover the original state of the system
In this paper we present two concise representations of reversible automata
In the study of computational models, reversibility means that each elementary step can be inverted, recovering the previous state of the system

Summary

Introduction

Reversibility is a fundamental principle in physics: in thermodynamics a transformation is reversible if, after occurring, it can be inverted in order to recover the original state of the system. It is interesting to investigate whether it is possible to obtain a concise representation of it, by avoiding to repeat those patterns To this aim, in this paper we present two concise representations of reversible automata, which can be used to simulate reversible computations without explicitly writing down the description of the reversible automaton. By using such representation, it is possible to simulate the behaviour of a minimal reversible automaton equivalent to A without explicitly representing it. Both representations have polynomial size with respect to the size of the given deterministic automaton A and require a precomputation (of the parameter β and of the function c, respectively) which can be performed in linear time

Preliminaries

1: Let C be an array of size n

Another Concise Representation

1: Let SM be the graph representing the sccs of the transition graph of M

Conclusion