Correctness of concurrent processes

A new notion of correctness for concurrent processes is introduced and investigated. It is a relationship P sat S between process terms P built up from operators of CCS [Mi 80], CSP [Ho 85] and COSY [LTS 79] and logical formulas S specifying sets of finite communication sequences as in [Zw 89]. The definition of P sat S is based on a Petri net semantics for process terms [Ol 89]. The main point is that P sat S requires a simple liveness property of the net denoted by P. This implies that P is divergence free and externally deterministic. Process correctness P sat S determines a new semantic model for process terms and logical formulas. It is a modification ℜ* of the readiness semantics [OH 86] which is fully abstract with respect to the relation P sat S. The model ℜ* abstracts from the concurrent behaviour of process terms and certain aspects of their internal activity. In ℜ* process correctness P sat S boils down to semantic equality: ℜ*[P]=ℜ*[S]. The modified readiness equivalence is closely related to failure equivalence [BHR 84] and strong testing equivalence [DH 84]

Hoare Logics for Recursive Procedures and Unbounded Nondeterminism

This paper presents sound and complete Hoare logics for partial and total correctness of recursive parameterless procedures in the context of unbounded nondeterminism. For total correctness, the literature so far has either restricted recursive procedures to be deterministic or has studied unbounded nondeterminism only in conjunction with loops rather than procedures. We consider both single procedures and systems of mutually recursive procedures. All proofs have been checked with the theorem prover Isabelle/HOL

Spatial Reasoning About Motorway Traffic Safety with Isabelle/HOL

Formal verification of autonomous vehicles on motorways is a challenging problem, due to the complex interactions between dynamical behaviours and controller choices of the vehicles. In previous work, we showed how an abstraction of motorway traffic, with an emphasis on spatial properties, can be beneficial. In this paper, we present a semantic embedding of a spatio-temporal multi-modal logic, specifically defined to reason about motorway traffic, into Isabelle/HOL. The semantic model is an abstraction of a motorway, emphasising local spatial properties, and parameterised by the types of sensors deployed in the vehicles. We use the logic to define controller constraints to ensure safety, i.e., the absence of collisions on the motorway. After proving safety with a restrictive definition of sensors, we relax these assumptions and show how to amend the controller constraints to still guarantee safety