“…As observed by de Bakker and Meertens [4], the operator sp is a dual of wlp; for every property of wlp there is a corresponding dual property of sp. For example, the following are the duals of WLP2 and WLP3.…”
The weakest liberal precondition and strongest postcondition predicate transformers are generalized to the weakest invariant and strongest invariant.These new predicate transformers are useful for reasoning about concurrent programs containing operations in which the grain of atomicity is unspecified. They can also be used to replace behavioral arguments with more rigorous assertional ones.
“…As observed by de Bakker and Meertens [4], the operator sp is a dual of wlp; for every property of wlp there is a corresponding dual property of sp. For example, the following are the duals of WLP2 and WLP3.…”
The weakest liberal precondition and strongest postcondition predicate transformers are generalized to the weakest invariant and strongest invariant.These new predicate transformers are useful for reasoning about concurrent programs containing operations in which the grain of atomicity is unspecified. They can also be used to replace behavioral arguments with more rigorous assertional ones.
“…From the proof we can extract all intermediate assertions about atomic substatements of the original program. Since proofs are finite, we obtain a finite system of intermediate assertions, thus apparently contradicting the result of [2]. Also [ 4] and [6] avoid the necessity of an infinite number of assertions by using an extension of the inductive assertion method.…”
Section: Introduction De Bakker and Meertens Proved Inmentioning
confidence: 81%
“…The purpose of this paper is to investigate this issue in the 'relational framework of [2] and to obtain, within that framework, a unification of the (essence of the) results of [2] and of [ 4], [5] and [6]. The solution of the apparent contradiction lies in the fact that in [4], [5] and [6] auxiliary variables are used (to store the initial values of variables).…”
Section: Introduction De Bakker and Meertens Proved Inmentioning
confidence: 99%
“…
[2] shows that for W one could also take the set of all so-called index-triple sequences, so that these two completeness results differ only in the choice of the extended state space. Our choice is both more economical and easier to use in the concrete proofs.
[2] shows that for W one could also take the set of all so-called index-triple sequences, so that these two completeness results differ only in the choice of the extended state space. Our choice is both more economical and easier to use in the concrete proofs.
“…The weakest-precondition was developed by (de Bakker and de Roever, 1972;de Bakker and Meertens, 1975) and popularised by Dijkstra (1976). This notion is connected with the Hoare triple {f 1 }P {f 2 } (Hoare, 1969), where f 1 and f 2 denote some predicates and P is a program.…”
A general definition of a quantum predicate and quantum labelled transition systems for finite quantum computation systems is presented. The notion of a quantum predicate as a positive operator-valued measure is developed. The main results of this paper are a theorem about the existence of generalised predicates for quantum programs defined as completely positive maps and a theorem about the existence of a GSOS format for quantum labelled transition systems. The first theorem is a slight generalisation of D'Hondt and Panagaden's theorem about the quantum weakest precondition in terms of discrete support positive operator-valued measures.Keywords: quantum computation, predicate notion for quantum programs, quantum labelled transition systems.
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