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Partially Observable Concurrent Kleene Algebra [article]

Jana Wagemaker and Paul Brunet and Simon Docherty and Tobias Kappé and Jurriaan Rot and Alexandra Silva
2020 arXiv   pre-print
We introduce 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  ... 
arXiv:2007.07593v2 fatcat:45mi4yoyjrdv3nsc2gsbcjur4u

Partially Observable Concurrent Kleene Algebra

Jana Wagemaker, Paul Brunet, Simon Docherty, Tobias Kappé, Jurriaan Rot, Alexandra Silva, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
We introduce 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).  ... 
doi:10.4230/lipics.concur.2020.20 dblp:conf/concur/WagemakerBDKR020 fatcat:b3yl27z3xjdiparebr46czphs4

Concurrent Kleene algebra with tests and branching automata

Peter Jipsen, M. Andrew Moshier
2016 Journal of Logical and Algebraic Methods in Programming  
Abstract We introduce 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  ... 
doi:10.1016/j.jlamp.2015.12.005 fatcat:nhu7vxfcijcwbhvixcyulxnfrq

Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness [chapter]

Tobias Kappé, Paul Brunet, Alexandra Silva, Jana Wagemaker, Fabio Zanasi
2020 Lecture Notes in Computer Science  
In this paper we provide a solution in the form of 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.  ... 
doi:10.1007/978-3-030-45231-5_20 fatcat:hiblehptwnh2hboxqvqyctx5qi

Concurrent Kleene Algebra [chapter]

C. A. R. Tony Hoare, Bernhard Möller, Georg Struth, Ian Wehrman
2009 Lecture Notes in Computer Science  
A 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.  ... 
doi:10.1007/978-3-642-04081-8_27 fatcat:kzlmps732bghxf44bgf75n2a54

Synchronous Kleene algebra

Cristian Prisacariu
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.  ... 
doi:10.1016/j.jlap.2010.07.009 fatcat:osi22hgbefcrfleg2vmlbl7dr4

Algebra, Logic, Locality, Concurrency [chapter]

Peter W. O'Hearn
2011 Lecture Notes in Computer Science  
others -on models and logics for 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] .  ... 
doi:10.1007/978-3-642-25379-9_2 fatcat:5t7wapdh6jhgzcskoplmzuc7me

Concurrent Dynamic Algebra [article]

Hitoshi Furusawa, Georg Struth
2014 arXiv   pre-print
We reconstruct Peleg's 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.  ... 
arXiv:1407.5819v1 fatcat:bfbftlau55czhd6kg6zmqkxiym

Concurrent Kleene Algebra and its Foundations

Tony Hoare, Bernhard Möller, Georg Struth, Ian Wehrman
2011 The Journal of Logic and Algebraic Programming  
A 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.  ... 
doi:10.1016/j.jlap.2011.04.005 fatcat:7zx4n42mojaqhaktidvrdzl6cq

Kleene Algebra with Observations [article]

Tobias Kappé and Paul Brunet and Jurriaan Rot and Alexandra Silva and Jana Wagemaker and Fabio Zanasi
2019 arXiv   pre-print
In this paper, we propose 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.  ... 
arXiv:1811.10401v3 fatcat:3tbaptzye5gvjel3cbqhc5khni

Automated Engineering of Relational and Algebraic Methods in Isabelle/HOL [chapter]

Simon Foster, Georg Struth, Tjark Weber
2011 Lecture Notes in Computer Science  
We present a new integration of relational and 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.  ... 
doi:10.1007/978-3-642-21070-9_5 fatcat:oszkpd2pfrbsnovtsp7mvn3sha

An Event Structure Model for Probabilistic Concurrent Kleene Algebra [article]

Annabelle McIver and Tahiry Rabehaja and Georg Struth
2013 arXiv   pre-print
We give a new true-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] .  ... 
arXiv:1310.2320v1 fatcat:emhwdn2djrhijmwd6pvjlrawja

An Event Structure Model for Probabilistic Concurrent Kleene Algebra [chapter]

Annabelle McIver, Tahiry Rabehaja, Georg Struth
2013 Lecture Notes in Computer Science  
We give a new true-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] .  ... 
doi:10.1007/978-3-642-45221-5_43 fatcat:qjcyo4yoyvd37cmu7hqoafzqu4

Completeness and Incompleteness of Synchronous Kleene Algebra [chapter]

Jana Wagemaker, Marcello Bonsangue, Tobias Kappé, Jurriaan Rot, Alexandra Silva
2019 Lecture Notes in Computer Science  
Synchronous 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.  ... 
doi:10.1007/978-3-030-33636-3_14 fatcat:bwa44fghl5cifdzjbbvkrjvflm

On the Representation of Kleene Algebras with Tests [chapter]

Dexter Kozen
2006 Lecture Notes in Computer Science  
We investigate conditions under which a given 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.  ... 
doi:10.1007/11821069_6 fatcat:c47kaz377zhuzfcz2qqueadppq
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