The notion of quantum weakest precondition was introduced by D’Hondt and P. Panangaden (Mathematical Structures in Computer Science 16(2006)429-451), and they presented a representation of weakest precondition of a quantum program in the operatorsum form. In this letter, we give an intrinsic characterization of the weakest precondition of a quantum program given in a systemenvironment model. Fu...

This paper is a systematic study of verification conditions and their use in the context of program verification. We take Hoare logic as a starting point and study in detail how a verification conditions generator can be obtained from it. The notion of program annotation is essential in this process. Weakest preconditions and the use of updates are also studied as alternative approaches to veri...

In a recent paper [17] Miro-Roig, Mezzetti and Ottaviani highlight the link between rational varieties satisfying a Laplace equation and artinian ideals failing the Weak Lefschetz Property. Continuing their work we extend this link to the more general situation of artinian ideals failing the Strong Lefschetz Property. We characterize the failure of the SLP (which includes WLP) by the existence ...

Generalisation of the quantum weakest precondition result of D’Hondt and Panangaden is presented. In particular the most general notion of quantum predicate as positive operator valued measure (POVM) is introduced. The previously known quantum weakest precondition result has been extended to cover the case of POVM playing the role of a quantum predicate. Additionally, our result is valid in inf...

The paper aims at providing a formal system, motivated by Dijkstra’s weakest precondition logic, for specifying mobile network. The paper shows how mobility can be specified using a state and transition based approach, which allows mobile hosts to be treated as nodes in a traditional statically structured distributed system. Another goal is to reason formally about the possible behaviors of a s...

This paper introduces a technique for localizing model checking of concurrent state-based systems. The technique, called partial model checking, is fully automatic and performs model checking by gradually specializing the speciication with respect to the concurrent components one by one, computing a \concurrent weakest precondition." Speciications are invariance properties and the concurrent co...

We present a procedure for deriving the weakest precondition for a database update and an integrity constraint. We show how to simplify the weakest precondition to produce a condition to be evaluated before the update is performed. This provides an efficient means to ensure that database updates maintain integrity constraints.

This short note contains random thoughts about a factorization theorem for closure/interior operators on a powerset which is reminiscent to the notion of resolution for a monad/comonad. The question originated from formal topology but is interesting in itself. The result holds constructively (even if it classically has several variations); but usually not predicatively (in the sense that the in...

The cost of developing and maintaining high quality software remains at a premium. In this paper we introduce a practical approach for enhancement of software quality, based on calculation of strongest postconditions of program components. The method provides a powerful means for detecting and removing by transformation various forms of redundancy and inconsistency in programs. The feasibility ...