Fresh-register automata

Abstract

What is a basic automata-theoretic model of computation with names and fresh-name generation? We introduce Fresh-Register Automata (FRA), a new class of automata which operate on an infinite alphabet of names and use a finite number of registers to store fresh names, and to compare incoming names with previously stored ones. These finite machines extend Kaminski and Francez's Finite-Memory Automata by being able to recognise globally fresh inputs, that is, names fresh in the whole current run. We examine the expressivity of FRA's both from the aspect of accepted languages and of bisimulation equivalence. We establish primary properties and connections between automata of this kind, and answer key decidability questions. As a demonstrating example, we express the theory of the pi-calculus in FRA's and characterise bisimulation equivalence by an appropriate, and decidable in the finitary case, notion in these automata.

Bisimilarity in Fresh-Register Automata

“…Our approach for RAs relied on symbolic bisimulations and the group-theoretic structure that emanated from them. While we can express bisimilarity in FRAs symbolically following [27], we shall see that such symbolic bisimulations do not support the group-theoretic representations. The reason is the treatment of the history of the computation, which affects bisimilarity in subtle ways, especially in the initial stages of the bisimulation game.…”

“…The condition i = 0, which stipulates that every name encountered by the automaton be stored in some register, also originates from [14], [19]. The class FRA(S# 0 ) follow the register assignment discipline of the automata defined in [27].…”

“…While register automata can detect symbols that are currently not stored in registers (local freshness), the bounded number of registers means that they are not in general capable of recognising inputs that are genuinely fresh in the sense that they occur in the computation for the first time (global freshness). Because such a feature is desirable in many contexts, notably dynamic resource allocation, the formalism has been extended in [27] to fresh-register automata, which do account for global freshness. This paper is concerned with the problem of bisimilarity testing for register and fresh-register automata.…”

“…Since value passing can be seen as a purely functional proxy for multiple register assignments, this result neatly reflects our findings for RA(M #). Finally, decidability of bisimilarity for FRA(S# 0 ) was proven in [27], albeit without a proper study of its complexity (the procedure given in loc. cit.…”

Game Semantic Analysis of Equivalence in IMJ

“…The automata are also equipped with a visible pushdown stack which can also store names; these names are communicated between the registers and the stack via push/pop operations. They are therefore pushdown extensions of Fresh-Register Automata [15,10].…”