Nominal Regular Expressions for Languages over Infinite Alphabets

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

A Characterisation of Languages on Infinite Alphabets with Nominal Regular Expressions

International audienceWe give a characterisation of languages on infinite alphabets in a variant of nominal regular expressions with permutations (p-NREs). We also introduce automata with fresh name generations and permutations (fp-automata), inspired by history-dependent automata (HDAs) and fresh-register automata. Noteworthy, permutations require to deal with dynamic context-dependent expressions. Finally, we give a Kleene theorem for p-NREs and fp-automata to formally characterise languages on infinite alphabets