Parallel Pushdown Automata and Commutative Context-Free Grammars in Bisimulation Semantics (Extended Abstract)

TL;DR

This paper explores the relationship between parallel pushdown automata and commutative context-free grammars within bisimulation semantics, extending classical automata theory to concurrent process models with parallelism.

Contribution

It extends classical automata-theoretic results to parallel pushdown automata and commutative grammars in a bisimulation framework, incorporating parallelism and value passing.

Findings

Parallel pushdown automata characterize certain process behaviors.

Theoretical connection between parallel automata and commutative grammars established.

Extension of classical automata theorems to concurrent process models.

Abstract

A classical theorem states that the set of languages given by a pushdown automaton coincides with the set of languages given by a context-free grammar. In previous work, we proved the pendant of this theorem in a setting with interaction: the set of processes given by a pushdown automaton coincides with the set of processes given by a finite guarded recursive specification over a process algebra with actions, choice, sequencing and guarded recursion, if and only if we add sequential value passing. In this paper, we look what happens if we consider parallel pushdown automata instead of pushdown automata, and a process algebra with parallelism instead of sequencing.