2,544 research outputs found
Commutativity of quantum weakest preconditions
The notion of quantum weakest precondition was introduced by D'Hondt and P. Panangaden [E. D'Hondt, P. Panangaden, Quantum weakest preconditions, Mathematical Structures in Computer Science 16 (2006) 429-451], and they presented a representation of weakest precondition of a quantum program in the operator-sum form. In this Letter, we give an intrinsic characterization of the weakest precondition of a quantum program given in a system-environment model. Furthermore, some sufficient conditions for commutativity of quantum weakest preconditions are presented. © 2007 Elsevier B.V. All rights reserved
Simple characterizations for commutativity of quantum weakest preconditions
In a recent letter [Information Processing Letters~104 (2007) 152-158], it
has shown some sufficient conditions for commutativity of quantum weakest
preconditions. This paper provides some alternative and simple
characterizations for the commutativity of quantum weakest preconditions, i.e.,
Theorem 3.1, Theorem 3.2 and Proposition 3.3 in what follows. We also show that
to characterize the commutativity of quantum weakest preconditions in terms of
() is hard in the sense of Proposition 4.1 and Proposition 4.2.Comment: Re-written, comments are welcom
Deciding Conditional Termination
We address the problem of conditional termination, which is that of defining
the set of initial configurations from which a given program always terminates.
First we define the dual set, of initial configurations from which a
non-terminating execution exists, as the greatest fixpoint of the function that
maps a set of states into its pre-image with respect to the transition
relation. This definition allows to compute the weakest non-termination
precondition if at least one of the following holds: (i) the transition
relation is deterministic, (ii) the descending Kleene sequence
overapproximating the greatest fixpoint converges in finitely many steps, or
(iii) the transition relation is well founded. We show that this is the case
for two classes of relations, namely octagonal and finite monoid affine
relations. Moreover, since the closed forms of these relations can be defined
in Presburger arithmetic, we obtain the decidability of the termination problem
for such loops.Comment: 61 pages, 6 figures, 2 table
Knowledge and regularity in planning
The field of planning has focused on several methods of using domain-specific knowledge. The three most common methods, use of search control, use of macro-operators, and analogy, are part of a continuum of techniques differing in the amount of reused plan information. This paper describes TALUS, a planner that exploits this continuum, and is used for comparing the relative utility of these methods. We present results showing how search control, macro-operators, and analogy are affected by domain regularity and the amount of stored knowledge
Fifty years of Hoare's Logic
We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin
Abstraction and Learning for Infinite-State Compositional Verification
Despite many advances that enable the application of model checking
techniques to the verification of large systems, the state-explosion problem
remains the main challenge for scalability. Compositional verification
addresses this challenge by decomposing the verification of a large system into
the verification of its components. Recent techniques use learning-based
approaches to automate compositional verification based on the assume-guarantee
style reasoning. However, these techniques are only applicable to finite-state
systems. In this work, we propose a new framework that interleaves abstraction
and learning to perform automated compositional verification of infinite-state
systems. We also discuss the role of learning and abstraction in the related
context of interface generation for infinite-state components.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455
Computation calculus bridging a formalization gap
AbstractWe present an algebra that is intended to bridge the gap between programming formalisms that have a high level of abstraction and the operational interpretations these formalisms have been designed to capture. In order to prove a high-level formalism sound for its intended operational interpretation, one needs a mathematical handle on the latter. To this end we design the computation calculus. As an expression mechanism, it is sufficiently transparent to avoid begging the question. As an algebra, it is quite powerful and relatively simple
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