Nominal Regular Expressions for Languages over Infinite Alphabets. Extended Abstract

TL;DR

This paper introduces nominal regular expressions that incorporate resource names to model resource-aware computations over infinite alphabets, extending classical regular expressions with operators for resource management.

Contribution

It extends classical regular expressions with nominal techniques, providing a formal framework for resource-aware languages and establishing Kleene theorems for their automata representations.

Findings

Defined classes of nominal regular expressions

Provided interpretations over infinite alphabets

Established Kleene theorems for nominal automata

Abstract

We propose regular expressions to abstractly model and study properties of resource-aware computations. Inspired by nominal techniques -- as those popular in process calculi -- we extend classical regular expressions with names (to model computational resources) and suitable operators (for allocation, deallocation, scoping of, and freshness conditions on resources). We discuss classes of such nominal regular expressions, show how such expressions have natural interpretations in terms of languages over infinite alphabets, and give Kleene theorems to characterise their formal languages in terms of nominal automata.