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Using probabilistic Kleene algebra pKA for protocol verification

A.K. McIver, C. Gonzalia, E. Cohen, C.C. Morgan
2008 The Journal of Logic and Algebraic Programming  
We propose a method 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.  ... 
doi:10.1016/j.jlap.2007.10.005 fatcat:nuuhuzvb3bgrlcqykiw7opbw7a

Using Probabilistic Kleene Algebra for Protocol Verification [chapter]

A. K. McIver, E. Cohen, C. C. Morgan
2006 Lecture Notes in Computer Science  
We propose a method 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).  ... 
doi:10.1007/11828563_20 fatcat:nlh7zni2bzgtnaws4uuoze6nve

Towards Automated Proof Support for Probabilistic Distributed Systems [chapter]

Annabelle K. McIver, Tjark Weber
2005 Lecture Notes in Computer Science  
In this paper we propose a framework 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.  ... 
doi:10.1007/11591191_37 fatcat:ehhm7ahxnzh6rl2pt56jdnfpaa

Author Index – Volume76

2008 The Journal of Logic and Algebraic Programming  
Morgan, 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.  ... 
doi:10.1016/s1567-8326(08)00058-1 fatcat:nhdejrmpcfe7hjrm4olg55xixq

Probabilistic Rely-guarantee Calculus [article]

Annabelle McIver and Tahiry Rabehaja and Georg Struth
2015 arXiv   pre-print
We 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.  ... 
arXiv:1409.0582v3 fatcat:boxc7vsutrdydfyfaw6ow6225a

Layered reasoning for randomized distributed algorithms

Mani Swaminathan, Joost-Pieter Katoen, Ernst-Rüdiger Olderog
2012 Formal Aspects of Computing  
, Gonzalia, Cohen, and Morgan. • Central to the pGCL/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.  ... 
doi:10.1007/s00165-012-0231-x fatcat:ztjarcqotzhzxeokidd4umq26i

Algebraic verification of probabilistic and concurrent systems

Mananjanahary Tahiry Rabehaja
2022
This thesis provides an 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  ... 
doi:10.25949/19430699 fatcat:ljd3wsisizeppodkv2lfxmm624

Layered Reduction for Modal Specification Theories [chapter]

Arpit Sharma, Joost-Pieter Katoen
2014 Lecture Notes in Computer Science  
Modal transition systems (MTSs) are a well-known formalism 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.  ... 
doi:10.1007/978-3-319-07602-7_20 fatcat:64tfnguu6jaynabjscbs7ofqty

Event fairness and non-interleaving concurrency

Marta Z. Kwiatkowska
1989 Formal Aspects of Computing  
Abstract Fairness in a non-interleaving semantic model 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.  ... 
doi:10.1007/bf01887206 fatcat:whv7zhxnczeuvhq4j752mvpa6e