On Conditional Decomposability

TL;DR

This paper introduces polynomial-time algorithms for verifying and extending conditional decomposability of languages in discrete-event systems, and explores its relation to nonblockingness, enhancing the analysis of modular control systems.

Contribution

It provides the first polynomial-time algorithms for checking and extending conditional decomposability, and clarifies its relationship to nonblockingness in discrete-event systems.

Findings

Polynomial-time algorithm for verification of conditional decomposability

Polynomial-time algorithm for extending the common alphabet

Conditional decomposability is weaker than nonblockingness

Abstract

The requirement of a language to be conditionally decomposable is imposed on a specification language in the coordination supervisory control framework of discrete-event systems. In this paper, we present a polynomial-time algorithm for the verification whether a language is conditionally decomposable with respect to given alphabets. Moreover, we also present a polynomial-time algorithm to extend the common alphabet so that the language becomes conditionally decomposable. A relationship of conditional decomposability to nonblockingness of modular discrete-event systems is also discussed in this paper in the general settings. It is shown that conditional decomposability is a weaker condition than nonblockingness.