Algebraic Synchronization Trees and Processes

TL;DR

This paper explores the expressive power of algebraic recursion schemes over synchronization trees, comparing their capabilities with established process algebra signatures and the Caucal hierarchy, to understand their modeling strength.

Contribution

It introduces and analyzes algebraic synchronization trees and compares their expressiveness with Basic CCS, Basic Process Algebra, and Caucal's hierarchy.

Findings

Algebraic recursion schemes can define synchronization trees up to bisimilarity and language equivalence.

The expressive power of these schemes is comparable to certain levels of Caucal's pushdown hierarchy.

The study clarifies the relative strengths of different algebraic frameworks for process modeling.

Abstract

We study algebraic synchronization trees, i.e., initial solutions of algebraic recursion schemes over the continuous categorical algebra of synchronization trees. In particular, we investigate the relative expressive power of algebraic recursion schemes over two signatures, which are based on those for Basic CCS and Basic Process Algebra, as a means for defining synchronization trees up to isomorphism as well as modulo bisimilarity and language equivalence. The expressiveness of algebraic recursion schemes is also compared to that of the low levels in Caucal's pushdown hierarchy.