States in Process Calculi

TL;DR

This paper introduces a method to extract explicit state information from process calculi with structural congruence, enabling easier assertional reasoning about distributed algorithms.

Contribution

It provides a formal semantics for state-informative representatives of congruence classes, bridging action-based and state-based reasoning in process calculi.

Findings

Extracted state-informative representatives from congruence classes

Enabled assertional reasoning on process calculus models

Improved analysis of distributed algorithms

Abstract

Formal reasoning about distributed algorithms (like Consensus) typically requires to analyze global states in a traditional state-based style. This is in contrast to the traditional action-based reasoning of process calculi. Nevertheless, we use domain-specific variants of the latter, as they are convenient modeling languages in which the local code of processes can be programmed explicitly, with the local state information usually managed via parameter lists of process constants. However, domain-specific process calculi are often equipped with (unlabeled) reduction semantics, building upon a rich and convenient notion of structural congruence. Unfortunately, the price for this convenience is that the analysis is cumbersome: the set of reachable states is modulo structural congruence, and the processes' state information is very hard to identify. We extract from congruence classes of reachable states individual state-informative representatives that we supply with a proper formal semantics. As a result, we can now freely switch between the process calculus terms and their representatives, and we can use the stateful representatives to perform assertional reasoning on process calculus models.