History-Register Automata

TL;DR

History-Register Automata (HRA) provide a powerful automata-theoretic framework for modeling programs with dynamic resource allocation, extending previous models and approaching the limits of decidability for reachability analysis.

Contribution

Introduction of HRAs, a novel automata model with unbounded memory sets, capable of simulating counter machines and supporting various regular operations, advancing the analysis of resource-aware programs.

Findings

HRAs extend expressiveness of previous models.

HRAs can simulate counter machines.

Closure under all regular operations except complementation.

Abstract

Programs with dynamic allocation are able to create and use an unbounded number of fresh resources, such as references, objects, files, etc. We propose History-Register Automata (HRA), a new automata-theoretic formalism for modelling such programs. HRAs extend the expressiveness of previous approaches and bring us to the limits of decidability for reachability checks. The distinctive feature of our machines is their use of unbounded memory sets (histories) where input symbols can be selectively stored and compared with symbols to follow. In addition, stored symbols can be consumed or deleted by reset. We show that the combination of consumption and reset capabilities renders the automata powerful enough to imitate counter machines, and yields closure under all regular operations apart from complementation. We moreover examine weaker notions of HRAs which strike different balances between expressiveness and effectiveness.