In [19], Migliore–Miró-Roig–Nagel show that the Weak Lefschetz property can fail for an ideal I ⊆ K[x 1 ,. .. , x 4 ] generated by powers of linear forms. This is in contrast to the analogous situation in K[x 1 , x 2 , x 3 ], where WLP always holds [24]. We use the inverse system dictionary to connect I to an ideal of fat points, and show that failure of WLP for powers of linear forms is connec...

In a recent paper, F. Zanello showed that level Artinian algebras in 3 variables can fail to have the Weak Lefschetz Property (WLP), and can even fail to have unimodal Hilbert function. We show that the same is true for the Artinian reduction of reduced, level sets of points in projective 3-space. Our main goal is to begin an understanding of how the geometry of a set of points can prevent its ...

The lack of a method for developing programs from Z specifications is a widely recognized difficulty. In response to this problem, different approaches to the integration of Z with a refinement calculus have been proposed. These programming techniques are promising, but as far as we know, have not been formalized. Since they are based on refinement calculi formalized in terms of weakest precond...

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.