A Semantic Account of Rigorous Simulation

Abstract

Hybrid systems are a powerful formalism for modeling cyberphysical systems. Reachability analysis is a general method for checking safety properties, especially in the presence of uncertainty and nondeterminism. Rigorous simulation is a convenient tool for reachability analysis of hybrid systems. However, to serve as proof tool, a rigorous simulator must be correct wrt a clearly defined notion of reachability, which captures what is intuitively reachable in finite time. As a step towards addressing this challenge, this paper presents a rigorous simulator in the form of an operational semantics and a specification in the form of a denotational semantics. We show that, under certain conditions about the representation of enclosures, the rigorous simulator is correct. We also show that finding a representation satisfying these assumptions is non-trivial.

Open Source Languages and Methods for Cyber-Physical System Development: Overview and Case Studies

“…Foundational issues in relation to the development of Acumen include showing that there are methods for correctly simulating Zeno systems [15] without diverging or sacrificing correctness. More recent work has focused on developing categorical semantics [16] for hybrid systems modeling languages.…”