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Partially Observable Concurrent Kleene Algebra
[article]

2020
*
arXiv
*
pre-print

We introduce

arXiv:2007.07593v2
fatcat:45mi4yoyjrdv3nsc2gsbcjur4u
*partially**observable**concurrent**Kleene**algebra*(POCKA), an*algebraic*framework to reason about*concurrent*programs with control structures, such as conditionals and loops. ... We prove that POCKA is a sound and complete axiomatisation of a model of*partial**observations*, and show the semantics passes an important check for sequential consistency. ... To that end, we propose*Partially**Observable**Concurrent**Kleene**Algebra*(POCKA), an*algebraic*theory built on top of CKA that allows for an analysis of*concurrent*programs manipulating memory, such as the ...##
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Partially Observable Concurrent Kleene Algebra

2020
*
International Conference on Concurrency Theory
*

We introduce

doi:10.4230/lipics.concur.2020.20
dblp:conf/concur/WagemakerBDKR020
fatcat:b3yl27z3xjdiparebr46czphs4
*partially**observable**concurrent**Kleene**algebra*(POCKA), an*algebraic*framework to reason about*concurrent*programs with variables as well as control structures, such as conditionals and loops ... We prove that POCKA is a sound and complete axiomatisation of a model of*partial**observations*, and show the semantics passes an important check for sequential consistency. ... Definition*Partially**Observable**Concurrent**Kleene**Algebra*In this section we define*partially**observable**concurrent**Kleene**algebra*(POCKA). ...##
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Concurrent Kleene algebra with tests and branching automata

2016
*
Journal of Logical and Algebraic Methods in Programming
*

Abstract We introduce

doi:10.1016/j.jlamp.2015.12.005
fatcat:nhu7vxfcijcwbhvixcyulxnfrq
*concurrent**Kleene**algebra*with tests (CKAT) as a combination of*Kleene**algebra*with tests (KAT) of Kozen and Smith with*concurrent**Kleene**algebras*(CKA), introduced by Hoare, Möller ... To express basic*concurrent*algorithms, we define*concurrent*deterministic flowchart schemas and relate them to branching automata and to*concurrent**Kleene**algebras*with tests. ...*Kleene**algebras*with*concurrency*A*concurrent**Kleene**algebra*(CKA) [12] is of the form (A, +, 0, ||, ·, 1, * ) such that (A, +, 0, ·, 1, * ) is a*Kleene**algebra*, (A, +, 0, ||, 1) is a commutative idempotent ...##
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Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness
[chapter]

2020
*
Lecture Notes in Computer Science
*

In this paper we provide a solution in the form of

doi:10.1007/978-3-030-45231-5_20
fatcat:hiblehptwnh2hboxqvqyctx5qi
*Concurrent**Kleene**Algebra*with*Observations*(CKAO). Our main contribution is a completeness theorem for CKAO. ...*Concurrent**Kleene**Algebra*(CKA) extends basic*Kleene**algebra*with a parallel composition operator, which enables reasoning about*concurrent*programs. ... This work was*partially*supported by the ERC Starting Grant ProFoundNet, grant code 679127. We acknowledge support from the EPSRC grants EP/S028641/1 (A. Silva); EP/R020604/1 (F. ...##
###
Concurrent Kleene Algebra
[chapter]

2009
*
Lecture Notes in Computer Science
*

A

doi:10.1007/978-3-642-04081-8_27
fatcat:kzlmps732bghxf44bgf75n2a54
*concurrent**Kleene**algebra*offers, next to choice and iteration, operators for sequential and*concurrent*composition, related by an inequational form of the exchange law. ... We show applicability of the*algebra*to a*partially*-ordered trace model of program execution semantics and demonstrate its usefulness by validating familiar proof rules for sequential programs (Hoare triples ... setting of*Concurrent**Kleene**Algebras*. ...##
###
Synchronous Kleene algebra

2010
*
The Journal of Logic and Algebraic Programming
*

*Kleene*

*algebra*with synchrony should be included in the class of true

*concurrency*models. ... The work presented here investigates the combination of

*Kleene*

*algebra*with the synchrony model of

*concurrency*from Milner's SCCS calculus. ...

*Concurrent*

*Kleene*

*algebra*Recently

*Concurrent*

*Kleene*

*algebra*(CKA) was proposed in [21] as a general formalism for reasoning about

*concurrent*programs. ...

##
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Algebra, Logic, Locality, Concurrency
[chapter]

2011
*
Lecture Notes in Computer Science
*

others -on models and logics for

doi:10.1007/978-3-642-25379-9_2
fatcat:5t7wapdh6jhgzcskoplmzuc7me
*concurrent*processes [10, 6, 5] . The approach we are taking abstracts from syntax or particular models. ... Message passing and shared memory process interaction, and strong (interleaving) and weak (*partial*order) approaches to sequencing, are accomodated as different models of the same core axioms. ... This law was was noticed in work on pomsets and traces in the 1980s and 1990s [4, 1] , and emphasized recently in the formulation of*Concurrent**Kleene**Algebra*[5] . ...##
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Concurrent Dynamic Algebra
[article]

2014
*
arXiv
*
pre-print

We reconstruct Peleg's

arXiv:1407.5819v1
fatcat:bfbftlau55czhd6kg6zmqkxiym
*concurrent*dynamic logic in the context of modal*Kleene**algebras*. ... The modal operators of*concurrent*dynamic*algebra*are obtained from abstract axioms for domain and antidomain operators; the*Kleene*star is modelled as a least fixpoint. ... They are grateful to Yde Vedema for drawing their attention to*concurrent*dynamic logic, and to Yasuo Kawahara, Koki Nishizawa, Toshinori Takai and Norihiro Tsumagari for enlightening discussions. ...##
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Concurrent Kleene Algebra and its Foundations

2011
*
The Journal of Logic and Algebraic Programming
*

A

doi:10.1016/j.jlap.2011.04.005
fatcat:7zx4n42mojaqhaktidvrdzl6cq
*Concurrent**Kleene**Algebra*offers two composition operators, related by a weak version of an exchange law: when applied in a trace model of program semantics, one of them stands for sequential execution ... and the other for*concurrent*execution of program components. ... setting of*Concurrent**Kleene**Algebras*. ...##
###
Kleene Algebra with Observations
[article]

2019
*
arXiv
*
pre-print

In this paper, we propose

arXiv:1811.10401v3
fatcat:3tbaptzye5gvjel3cbqhc5khni
*Kleene**algebra*with*observations*(KAO), a variant of KAT, as an alternative foundation for extending KAT to a*concurrent*setting. ...*Kleene**algebra*with tests (KAT) is an*algebraic*framework for reasoning about the control flow of sequential programs. ...*Partial*derivatives Derivatives [8] are a powerful tool in*Kleene**algebra*variants. ...##
###
Automated Engineering of Relational and Algebraic Methods in Isabelle/HOL
[chapter]

2011
*
Lecture Notes in Computer Science
*

We present a new integration of relational and

doi:10.1007/978-3-642-21070-9_5
fatcat:oszkpd2pfrbsnovtsp7mvn3sha
*algebraic*methods in the Isabelle/HOL theorem proving environment. ... It consists of a fine grained hierarchy of*algebraic*structures based on Isabelle's type classes and locales, and a repository of more than 800 facts obtained by automated theorem proving. ... Structures such as*concurrent**Kleene**algebras*, action*algebras*and action lattices, and*Kleene**algebras*with converse are under development. ...##
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An Event Structure Model for Probabilistic Concurrent Kleene Algebra
[article]

2013
*
arXiv
*
pre-print

We give a new true-

arXiv:1310.2320v1
fatcat:emhwdn2djrhijmwd6pvjlrawja
*concurrent*model for probabilistic*concurrent**Kleene**algebra*. ... Finally, the*algebraic*properties of the model are summarised to the extent that they can be used to derive techniques such as probabilistic rely/guarantee inference rules. ... of*concurrent**Kleene**algebra*[2] . ...##
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An Event Structure Model for Probabilistic Concurrent Kleene Algebra
[chapter]

2013
*
Lecture Notes in Computer Science
*

We give a new true-

doi:10.1007/978-3-642-45221-5_43
fatcat:qjcyo4yoyvd37cmu7hqoafzqu4
*concurrent*model for probabilistic*concurrent**Kleene**algebra*. ... Finally, the*algebraic*properties of the model are summarised to the extent that they can be used to derive techniques such as probabilistic rely/guarantee inference rules. ⋆ ... of*concurrent**Kleene**algebra*[2] . ...##
###
Completeness and Incompleteness of Synchronous Kleene Algebra
[chapter]

2019
*
Lecture Notes in Computer Science
*

Synchronous

doi:10.1007/978-3-030-33636-3_14
fatcat:bwa44fghl5cifdzjbbvkrjvflm
*Kleene**algebra*(SKA), an extension of*Kleene**algebra*(KA), was proposed by Prisacariu as a tool for reasoning about programs that may execute synchronously, i.e., in lock-step. ... We provide a countermodel witnessing that the axioms of SKA are incomplete w.r.t. its language semantics, by exploiting a lack of interaction between the synchronous product operator and the*Kleene*star ... In the context of*Kleene**algebra*based frameworks for*concurrent*reasoning, a synchronous product is just one possible interpretation of*concurrency*. ...##
###
On the Representation of Kleene Algebras with Tests
[chapter]

2006
*
Lecture Notes in Computer Science
*

We investigate conditions under which a given

doi:10.1007/11821069_6
fatcat:c47kaz377zhuzfcz2qqueadppq
*Kleene**algebra*with tests is isomorphic to an*algebra*of binary relations. ... An*algebraic*condition is identified that is necessary and sufficient for the construction to produce a standard representation. ... Not all*algebras*are so representable, even star-continuous ones; as*observed*above, the min,+*algebra*is not. ...
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