Reasoning about Idealized ALGOL Using Regular Languages

Abstract

Abstract. We explain how recent developments in game semantics can be applied to reasoning about equivalence of terms in a non-trivial fragment of Idealized Algol (IA) by expressing sets of complete plays as regular languages. Being derived directly from the fully abstract game semantics for IA, our method of reasoning inherits its desirable theoretical properties. The method is mathematically elementary and formal, which makes it uniquely suitable for automation. We show that reasoning can be carried out using only a meta-language of extended regular expressions, a language for which equivalence is formally decidable.

Angelic Semantics of Fine-Grained Concurrency

“…We can make straightforward arguments about ground-type equivalences such as Brookes's laws of parallel programming [1], or other typical second-order equivalences. In order for such arguments to be formalized, and even automated, it is necessary to find a concrete representation of strategies, along the lines of [14]. For this purpose, the most convenient representations are those which are finite-state, such as regular expressions, regular languages, labelled transitions systems, etc.…”

Reachability Games and Game Semantics: Comparing Nondeterministic Programs

“…In recent years a subarea, called algorithmic game semantics [1], was born, which seeks to establish connections between game semantics and models of computation with a view to applying them to software verification. The insights obtained this way have already contributed several verification tools [1,11,14,7,22] and helped to prove new decidability/undecidability results in program verification [13,32,27,31,29,30,33].…”

Events, Causality and Symmetry

“…The techniques here, based on symmetry, extend unfoldings and their characterization to general nets, and begin to push Petri nets into the new territory of higher-order processes (although we have concentrated on event structures, similar ideas are working for nets). The compact, often finite, representations afforded by Petri nets accede to the known decision procedures for Petri nets and regular languages, and so potentially tools for the analysis of higher-order processes (in the manner of algorithmic game theory [39]). Symmetry is already exploited in model checking [30], and its potential role in netunfolding techniques should be investigated.…”