Sequential Composition in the Presence of Intermediate Termination

TL;DR

This paper revises the operational semantics of sequential composition with intermediate termination to eliminate transparency, restoring the correspondence between context-free and pushdown processes and proving the expressive power of TCP.

Contribution

It introduces a new operational semantics for sequential composition that removes transparency, enabling better process modeling and analysis.

Findings

Elimination of transparency in sequential composition.

Restoration of the correspondence between context-free and pushdown processes.

Proof of reactive Turing power of TCP with the revised semantics.

Abstract

The standard operational semantics of the sequential composition operator gives rise to unbounded branching and forgetfulness when transparent process expressions are put in sequence. Due to transparency, the correspondence between context-free and pushdown processes fails modulo bisimilarity, and it is not clear how to specify an always terminating half counter. We propose a revised operational semantics for the sequential composition operator in the context of intermediate termination. With the revised operational semantics, we eliminate transparency. As a consequence, we establish a correspondence between context-free processes and pushdown processes. Moreover, we prove the reactive Turing powerfulness of TCP with iteration and nesting with the revised operational semantics for sequential composition.