A Generalized Hybrid Hoare Logic

Deductive verification of hybrid systems (HSs) increasingly attracts more attention in recent years because of its power and scalability, where a powerful specification logic for HSs is the cornerstone. Often, HSs are naturally modelled by concurrent processes that communicate with each other. However, existing specification logics cannot easily handle such models. In this paper, we present a specification logic and proof system for Hybrid Communicating Sequential Processes (HCSP), that extends CSP with ordinary differential equations (ODE) and interrupts to model interactions between continuous and discrete evolution. Because it includes a rich set of algebraic operators, complicated hybrid systems can be easily modelled in an algebra-like compositional way in HCSP. Our logic can be seen as a generalization and simplification of existing hybrid Hoare logics (HHL) based on duration calculus (DC), as well as a conservative extension of existing Hoare logics for concurrent programs. Its assertion logic is the first-order theory of differential equations (FOD), together with assertions about traces recording communications, readiness, and continuous evolution. We prove continuous relative completeness of the logic w.r.t. FOD, as well as discrete relative completeness in the sense that continuous behaviour can be arbitrarily approximated by discretization. Besides, we discuss how to simplify proofs using the logic by providing a simplified assertion language and a set of sound and complete rules for differential invariants for ODEs. Finally, we implement a proof assistant for the logic in Isabelle/HOL, and apply it to verify two case studies to illustrate the power and scalability of our logic

Using Hoare Logic in a Process Algebra Setting

This paper concerns the relation between process algebra and Hoare logic. We investigate the question whether and how a Hoare logic can be used for reasoning about how data change in the course of a process when reasoning equationally about that process. We introduce an extension of ACP (Algebra of Communicating Processes) with features that are relevant to processes in which data are involved, present a Hoare logic for the processes considered in this process algebra, and discuss the use of this Hoare logic as a complement to pure equational reasoning with the equational axioms of the process algebra

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

Extending Hybrid CSP with Probability and Stochasticity

Probabilistic and stochastic behavior are omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of fundamental properties of nature, uncertain environments, or simplifications to overcome complexity. Tightly intertwining discrete, continuous and stochastic dynamics complicates modelling, analysis and verification of stochastic hybrid systems (SHSs). In the literature, this issue has been extensively investigated, but unfortunately it still remains challenging as no promising general solutions are available yet. In this paper, we give our effort by proposing a general compositional approach for modelling and verification of SHSs. First, we extend Hybrid CSP (HCSP), a very expressive and process algebra-like formal modeling language for hybrid systems, by introducing probability and stochasticity to model SHSs, which is called stochastic HCSP (SHCSP). To this end, ordinary differential equations (ODEs) are generalized by stochastic differential equations (SDEs) and non-deterministic choice is replaced by probabilistic choice. Then, we extend Hybrid Hoare Logic (HHL) to specify and reason about SHCSP processes. We demonstrate our approach by an example from real-world.Comment: The conference version of this paper is accepted by SETTA 201

Constraint Identification Using Modified Hoare Logic on Hybrid Models of Gene Networks

We present a new hybrid Hoare logic dedicated for a class of linear hybrid automata well suited to model gene regulatory networks. These automata rely on Thomas\u27 discrete framework in which qualitative parameters have been replaced by continuous parameters called celerities. The identification of these parameters remains one of the keypoints of the modelling process, and is difficult especially because the modelling framework is based on a continuous time. We introduce Hoare triples which handle biological traces and pre/post-conditions. Observed chronometrical biological traces play the role of an imperative program for classical Hoare logic and our hybrid Hoare logic, defined by inference rules, is proved to be sound. Furthermore, we present a weakest precondition calculus (a la Dijkstra) which leads to constraints on dynamical parameters. Finally, we illustrate our "constraints generator" with a simplified circadian clock model describing the rhythmicity of cells in mammals on a 24-hour period

ON FORMAL TOOLS IN THE SOFTWARE ENGINEERING

This paper presents an overview of different approaches to a creation of the technique of software application development based on the integrated development environment which contains a model and tools for its implementation. Our results in this field are also presented. We study a formal model specification and analysis tools which may have potential for the software application development

ON FORMAL TOOLS IN THE SOFTWARE ENGINEERING

This paper presents an overview of different approaches to a creation of the technique of software application development based on the integrated development environment which contains a model and tools for its implementation. Our results in this field are also presented. We study a formal model specification and analysis tools which may have potential for the software application development

Symbolic Semantics for CSP

Communicating Sequential Processes (CSP) is a well-known formal language for describing concur- rent systems. Brookes, Hoare and Roscoe [2] have given a transition semantics for CSP that underlies common approaches to model checking properties of CSP programs. In this paper, we present a gen- eralized transition semantics of CSP, which we call HCSP, that merges the original transition system with ideas from Floyd-Hoare Logic and symbolic computation. This generalized semantics is shown to be sound and complete with respect to the original trace semantics. Traces in our system are sym- bolic representations of families of traces as given by the original semantics. This more compact representation allows us to expand the original CSP systems to effectively model check some CSP programs which are difficult for other CSP systems to analyze. In particular, our system can han- dle certain classes of non-deterministic choices as a single transition, while the original semantics would treat each choice separately, possibly leading to large or unbounded case analyses. All work described in this paper has been carried out in the theorem prover Isabelle. This then provides us with a framework for automated and interactive analysis of CSP processes. It also give us the ability to extract Ocaml code for an HCSP-based simulator directly from Isabelle.NSF 0917218NASA Contract NNA10DE79Cunpublishednot peer reviewe