Language Preservation Problems in Parametric Timed Automata

TL;DR

This paper investigates the decidability of language and trace preservation in parametric timed automata, showing undecidability in general but identifying specific decidable subclasses and robust variants.

Contribution

It establishes undecidability results for general PTA and L/U-PTA, and identifies decidable subclasses such as 1-clock and deterministic L/U-PTA.

Findings

Undecidability of language and trace preservation in general PTA

Decidability results for 1-clock PTA and deterministic L/U-PTA

Introduction of robust preservation problems with intermediate valuations

Abstract

Parametric timed automata (PTA) are a powerful formalism to model and reason about concurrent systems with some unknown timing delays. In this paper, we address the (untimed) language- and trace-preservation problems: given a reference parameter valuation, does there exist another parameter valuation with the same untimed language, or with the same set of traces? We show that these problems are undecidable both for general PTA and for the restricted class of L/U-PTA, even for integer-valued parameters, or over bounded time. On the other hand, we exhibit decidable subclasses: 1-clock PTA, and 1-parameter deterministic L-PTA and U-PTA. We also consider robust versions of these problems, where we additionally require that the language be preserved for all valuations between the reference valuation and the new valuation.