Modeling and Verification of Hybrid Systems Based on Equations

Abstract

We describe hybrid observational transition systems, or HOTSs. HOTSs are written in terms of equations and verified by means of equational reasoning. More concretely, CafeOBJ, an algebraic specification language, is used to specify HOTSs and verify that HOTSs have properties by writing proofs, or proof scores. One case study is used to demonstrate how to model hybrid systems as HOTSs, specify HOTSs in CafeOBJ and verify that HOTSs have properties with the CafeOBJ system.

Formal verification of multitask hybrid systems by the OTS/CafeOBJ method

“…A real-time system is regarded as a hybrid system where only time is its continuous data. In the literature [4], a way to describe and verify formal specifications of hybrid systems based on CafeOBJ has been proposed, however, only a single-task system is considered. In this study, we propose a way to describe a formal specification of a multitask hybrid system as an observational transition system in CafeOBJ algebraic specification language by extending the existing results, and verify it by the proof score method based on equational reasoning implemented in CafeOBJ interpreter.…”

Specification description and verification of multitask hybrid systems in the OTS/CafeOBJ method

“…A real-time system is regarded as a hybrid system where only time is its continuous data. In the literature [7], a way to describe and verify formal specifications of hybrid systems based on CafeOBJ has been proposed, however, only a single-task system is considered. In this study, we propose a way to describe a formal specification of a multitask hybrid system as an observational transition system in CafeOBJ algebraic specification language by extending the existing results, and verify it by the proof score method based on equational reasoning implemented in CafeOBJ interpreter (Table 1).…”

Generating Test Cases for Invariant Properties from Proof Scores in the OTS/CafeOBJ Method

“…In this method, it is verified that a specification satisfies a given desired property by describing a proof score. There are many successful case studies of formal verification with proof scores [6], [8]- [10]. On the other hand, there is no established method to obtain test cases which test whether an implementation satisfies the property verified by a proof score.…”