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Using probabilistic Kleene algebra pKA for protocol verification

2008
*
The Journal of Logic and Algebraic Programming
*

We propose a method

doi:10.1016/j.jlap.2007.10.005
fatcat:nuuhuzvb3bgrlcqykiw7opbw7a
*for**verification*of*probabilistic*distributed systems in which a variation of Kozen's*Kleene**Algebra*with Tests [Dexter Kozen,*Kleene**algebra*with tests, ACM Trans. ... We describe*pKA*, a*probabilistic**Kleene*-style*algebra*, based on a widely accepted model of*probabilistic*/demonic computation [Jifeng He, K. Seidel, A.K. ... In Fig. 2 we set out the rules*for*the*probabilistic**Kleene**algebra*,*pKA*. ...##
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Using Probabilistic Kleene Algebra for Protocol Verification
[chapter]

2006
*
Lecture Notes in Computer Science
*

We propose a method

doi:10.1007/11828563_20
fatcat:nlh7zni2bzgtnaws4uuoze6nve
*for**verification*of*probabilistic*distributed systems in which a variation of Kozen's*Kleene**Algebra*with Tests [11] is*used*to take account of the well-known interaction of probability ... We describe*pKA*, a*probabilistic**Kleene*-style*algebra*, based on a widely accepted model of*probabilistic*/demonic computation [7, 25, 17] . ... In Fig.2 we set out the rules*for*the*probabilistic**Kleene**algebra*,*pKA*. We shall also*use*tests, whose denotations are programs of the kind (4). ...##
###
Towards Automated Proof Support for Probabilistic Distributed Systems
[chapter]

2005
*
Lecture Notes in Computer Science
*

In this paper we propose a framework

doi:10.1007/11591191_37
fatcat:ehhm7ahxnzh6rl2pt56jdnfpaa
*for**verification*of*probabilistic*distributed systems based on the generalisation of*Kleene**algebra*with tests that has been*used*as a basis*for*development of concurrency ... The mechanisation of proofs*for**probabilistic*systems is particularly challenging due to the*verification*of real-valued properties that probability entails: experience indicates [12, 4, 11] that there ... In Fig. 2 we set out the rules*for*the*probabilistic**Kleene**algebra*,*pKA*. ...##
###
Author Index – Volume76

2008
*
The Journal of Logic and Algebraic Programming
*

Morgan,

doi:10.1016/s1567-8326(08)00058-1
fatcat:nhdejrmpcfe7hjrm4olg55xixq
*Using**probabilistic**Kleene**algebra**pKA**for**protocol**verification*(1) 90 McKinley, R., Soft Linear Set Theory (2) 226 Möller, B., see Hö fner, P. (1) 35 Morgan, C.C., see McIver, A.K. (1) 90 Schmid ... Kozen, Local variable scoping and*Kleene**algebra*with tests (1) 3 Andrew Moshier, M., see Jung, A. (2) 16 Baboolal, D. and P.P. ...##
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Probabilistic Rely-guarantee Calculus
[article]

2015
*
arXiv
*
pre-print

We

arXiv:1409.0582v3
fatcat:boxc7vsutrdydfyfaw6ow6225a
*use*an*algebraic*approach which combines and adapts*probabilistic**Kleene**algebras*with concurrent*Kleene**algebra*. ... The*use*of these rules is illustrated by a detailed*verification*of a simple*probabilistic*concurrent program: a faulty Eratosthenes sieve. ... Since H 1 Ω is a*probabilistic**Kleene**algebra*[27] , the right induction law of*pKA*implies r * = δ+r. ...##
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Layered reasoning for randomized distributed algorithms

2012
*
Formal Aspects of Computing
*

, Gonzalia, Cohen, and Morgan. • Central to the pGCL/

doi:10.1007/s00165-012-0231-x
fatcat:ztjarcqotzhzxeokidd4umq26i
*pKA*approach in [MGCM08] is the exploitation of the separation theorems introduced earlier in [Coh00]*for*the non-randomized setting. ... Layered composition is*used*to establish*probabilistic*counterparts of the CCL laws that exploit independence and / or precedence conditions between the constituent PA. ... We wish to thank Annabelle McIver*for*her feedback via email on the paper [MGCM08] . The comments from the reviewers helped in improving the presentation of our paper. ...##
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Algebraic verification of probabilistic and concurrent systems

2022

This thesis provides an

doi:10.25949/19430699
fatcat:ljd3wsisizeppodkv2lfxmm624
*algebraic*modelling and*verification*of*probabilistic*concurrent systems in the style of*Kleene**algebra*. ... These two*algebras*are then \merged" to provide*probabilistic*concurrent*Kleene**algebra*which is*used*to discover and prove development rules*for**probabilistic*concurrent systems (e.g. rely/guarantee calculus ...*Probabilistic**Kleene**algebra**Probabilistic**Kleene**algebras*have been introduced*for*resolving nondeterministic choice as they occur,*for*instance, in*probabilistic**protocols*that involve adversarial scheduling ...##
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Layered Reduction for Modal Specification Theories
[chapter]

2014
*
Lecture Notes in Computer Science
*

Modal transition systems (MTSs) are a well-known formalism

doi:10.1007/978-3-319-07602-7_20
fatcat:64tfnguu6jaynabjscbs7ofqty
*used*as an abstraction theory*for*labeled transition systems (LTSs). ... MTS specifications support compositionality together with a step-wise refinement methodology, and thus are*useful**for*component-oriented design and analysis of distributed systems. ... The authors thank Ian Larson*for*modeling the randomized mutual exclusion algorithm case study in PRISM and conducting the experiments. ...##
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Event fairness and non-interleaving concurrency

1989
*
Formal Aspects of Computing
*

Abstract Fairness in a non-interleaving semantic model

doi:10.1007/bf01887206
fatcat:whv7zhxnczeuvhq4j752mvpa6e
*for*concurrency has been investigated. ... First, trace languages have been enhanced to allow*for*infmite traces; this was achieved by introducing trace preorder relation on possibly infinite strings. ...*Protocol**Verification*The*verification*of network communication*protocols*is of increasing importance. ...