Symbolic Representation of Algorithmic Game Semantics

TL;DR

This paper introduces a symbolic automata framework for representing second-order recursion free Idealized Algol with infinite data types, enabling finite automata representations and more efficient verification.

Contribution

It generalizes regular-language representations to symbolic automata, reducing state space and improving verification of terms with infinite data types.

Findings

Finite symbolic automata represent infinite data types.

State space reductions enable efficient verification.

Illustrated with practical examples.

Abstract

In this paper we revisit the regular-language representation of game semantics of second-order recursion free Idealized Algol with infinite data types. By using symbolic values instead of concrete ones we generalize the standard notion of regular-language and automata representations to that of corresponding symbolic representations. In this way terms with infinite data types, such as integers, can be expressed as finite symbolic-automata although the standard automata interpretation is infinite. Moreover, significant reductions of the state space of game semantics models are obtained. This enables efficient verification of terms, which is illustrated with several examples.