A Note on Undecidability of Observation Consistency for Non-Regular Languages

TL;DR

This paper proves that checking observation consistency, a key condition in hierarchical control of discrete-event systems, is undecidable for non-regular languages, highlighting limits of automation in system analysis.

Contribution

It establishes the undecidability of observation consistency for non-regular languages, extending understanding of computational limits in hierarchical control.

Findings

Observation consistency is undecidable for non-regular languages.

Decidability for regular languages remains an open question.

Highlights computational boundaries in system observability analysis.

Abstract

One of the most interesting questions concerning hierarchical control of discrete-event systems with partial observations is a condition under which the language observability is preserved between the original and the abstracted plant. Recently, we have characterized two such sufficient conditions---observation consistency and local observation consistency. In this paper, we prove that the condition of observation consistency is undecidable for non-regular (linear, deterministic context-free) languages. The question whether the condition is decidable for regular languages is open.