Compositional verification of hybrid systems with discrete interaction using simulation relations

Abstract

Abstract-Simulation relations can be used to verify refinement between a system and its specification, or between models of different complexity. It is known that for the verification of safety properties, simulation between hybrid systems can be defined based on their labeled transition system semantics. We show that for hybrid systems without shared variables, which therefore only interact at discrete events, this simulation preorder is compositional, and present assume-guarantee rules that help to counter the state explosion problem. Some experimental results for simulation checking of linear hybrid automata are provided using a prototype tool with exact arithmetic and unlimited digits.

Assume-guarantee reasoning for hybrid I/O-automata by over-approximation of continuous interaction

“…The semi-algorithms for checking simulation and A/Gsimulation were implemented in C++ as part of a tool for verifying linear hybrid automata called PHAVer, of which an earlier version was presented in [10]. For operations on convex polyhedra it uses the Parma Polyhedra Library (PPL) by Roberto Bagnara et al [12], which employs exact arithmetic with unlimited digits.…”

“…Depending on the system, this can tremendously speed up or slow down the convergence [10]. A simple semi-algorithm to compute simulation relations is shown in Fig.…”

“…3. For a more detailed discussion of simulation relations for hybrid automata, see [10], and more advanced algorithms for computing simulation relations can be found, e.g., in [11].…”

Hybrid Automata Dicretising Agents for Formal Modelling of Robots

“…Discrete interaction between two hybrid automata can be modelled by means of synchronization on common labels, see Frehse (2005). A discrete synchronization in the parallel composition of two hybrid automata exists, if the intersection of their finite set of labels is not an empty set, Lab 1 ∩ Lab 2 = / 0.…”

Compositional Abstraction in Real-Time Model Checking

“…The idea to use simulations (or refinements) as a compositional abstraction device is well-known, both in untimed and timed settings, and has already been studied theoretically and practically in many papers during the last three decades, see for instance [28,23,19,26,22,20,1,27,16,17,14,12,21]. Nevertheless, when we attempted to apply these existing approaches to fight state space explosions in a model of an industrial protocol [13], we ran into the problem that these approaches do not handle two fundamental modeling concepts that are frequently used in Uppaal.…”