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Equivalence checking for weak bi-Kleene algebra
[article]

2021
*
arXiv
*
pre-print

Pomset automata are an operational model of

arXiv:1807.02102v5
fatcat:pgnylodopvddplmfzjfqrdgjt4
*weak**bi*-*Kleene**algebra*, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a ... We characterize a fragment of pomset automata that admits a decision procedure*for*language*equivalence*. ... We would like to thank the anonymous reviewers*for*their insightful comments, which helped to substantially improve the initial version of this paper. ...##
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Convolution and Concurrency
[article]

2020
*
arXiv
*
pre-print

concurrent quantales or

arXiv:2002.02321v1
fatcat:dyjzozvmhzd75cmus2v6hhpwxa
*Kleene**algebras*Q. ... We show how concurrent quantales and concurrent*Kleene**algebras*arise as convolution*algebras*Q^X of functions from structures X with two ternary relations that satisfy relational interchange laws into ... Acknowledgement: The authors would like to thank Tony Hoare*for*discussions on models of concurrent*Kleene**algebras*, and to Brijesh Dongol and Ian Hayes*for*their collaboration on convolution*algebras*...##
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Concurrent Kleene algebra with tests and branching automata

2016
*
Journal of Logical and Algebraic Methods in Programming
*

Highlights • Guarded strings are generalized to guarded series-parallel strings giving a concrete language model

doi:10.1016/j.jlamp.2015.12.005
fatcat:nhu7vxfcijcwbhvixcyulxnfrq
*for*concurrent*Kleene**algebra*with tests that satisfies the*weak*exchange law. • We define ... 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 ... In general it can be difficult to*check*this*equivalence*in the free*algebra*, but*for*KA and KAT the semantic models of all rational languages and all guarded rational languages give a concrete representation ...##
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Concurrent Dynamic Algebra
[article]

2014
*
arXiv
*
pre-print

The modal operators of concurrent dynamic

arXiv:1407.5819v1
fatcat:bfbftlau55czhd6kg6zmqkxiym
*algebra*are obtained from abstract axioms*for*domain and antidomain operators; the*Kleene*star is modelled as a least fixpoint. ... We reconstruct Peleg's concurrent dynamic logic in the context of modal*Kleene**algebras*. ... at Kyushu University*for*a pleasant short stay and financial support. ...##
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Weak Concurrent Kleene Algebra with Application to Algebraic Verification
[article]

2013
*
arXiv
*
pre-print

The

arXiv:1301.7153v1
fatcat:443dnyeoi5ff3l3my6w33fo34i
*algebra*is proved sound with respect to a model of automata modulo a variant of rooted η-simulation*equivalence*. ... We propose a generalisation of concurrent*Kleene**algebra*Hoa09 that can take account of probabilistic effects in the presence of concurrency. ... (Subsection 3.2) forms a*weak*concurrent*Kleene**algebra*. ...##
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PBZ*-Lattices: Structure Theory and Subvarieties
[article]

2019
*
arXiv
*
pre-print

These lattices with additional structure originate in the foundations of quantum mechanics and can be viewed as a common generalisation of orthomodular lattices and

arXiv:1804.08136v3
fatcat:v4xz2xyi7bf7rlftjcknijg52q
*Kleene**algebras*expanded by an extra ... The class of bounded involution lattices is a variety, here denoted by*BI*. The involution of a pseudo-*Kleene**algebra*is called*Kleene*complement. ... The variety of pseudo-*Kleene**algebras*,*for*which see e.g. [10] , is denoted by PKA. Distributive pseudo-*Kleene**algebras*are variously called*Kleene*lattices or*Kleene**algebras*in the literature. ...##
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Layered graph traversals and Hamiltonian path problems — An algebraic approach
[chapter]

1998
*
Lecture Notes in Computer Science
*

In the rst case, we are even able to abstract to the very general setting of

doi:10.1007/bfb0054287
fatcat:bxgkpwzkf5bitiodnkhpdhnleu
*Kleene**algebras*. ... Using an*algebra*of paths we present abstract*algebraic*derivations*for*two problem classes concerning graphs, viz. layer oriented traversal and computing sets of Hamiltonian paths. ... The pointwise extension of join yields the following result*for*unary relations S und T: S 1 T = S \ T : (3) 3*Kleene**Algebras*and Closures*Kleene**Algebras*A*Kleene**algebra*is a quintuple (S; ; ; 0;1 ...##
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PBZ*-Lattices: Structure Theory and Subvarieties

2020
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Reports on Mathematical Logic
*

These lattices with additional structure originate in the foundations of quantum mechanics and can be viewed as a common generalisation of orthomodular lattices and

doi:10.4467/20842589rm.20.001.12433
fatcat:lei2p5utx5dnxisbyqmuogrq4i
*Kleene**algebras*expanded by an extra ... Finally, we thank an anonymous referee*for*her/his precious comments. ... The class of bounded involution lattices is a variety, here denoted by*BI*. The involution of a pseudo-*Kleene**algebra*is called*Kleene*complement. ...##
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Commutative integral bounded residuated lattices with an added involution

2009
*
Annals of Pure and Applied Logic
*

Since these conditions are rather restrictive (

doi:10.1016/j.apal.2009.05.008
fatcat:i4yxfu54sfgltgorrokwtsfok4
*for*instance, on a symmetric Heyting*algebra*ε is an interior operator if and only the equation (x → 0) ∨ ((x → 0) → 0) = 1 is satisfied) we consider when ... We give necessary and sufficient conditions*for*ε being an interior operator. ... (ii) A satisfies the*Kleene*equation (2.16). (iii) A is normal. Hence it follows from Lemmas 1.5 and 1.6 that (i) and (ii) are*equivalent*. ...##
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Concurrent Kleene Algebra and its Foundations

2011
*
The Journal of Logic and Algebraic Programming
*

A Concurrent

doi:10.1016/j.jlap.2011.04.005
fatcat:7zx4n42mojaqhaktidvrdzl6cq
*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 ... On this basis, we develop a series of richer*algebras*; the richest validates a proof calculus*for*programs similar to that of a Jones style rely/guarantee calculus. ... Acknowledgements We are grateful*for*valuable comments by J. Desharnais ...##
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On the Fine-Structure of Regular Algebra

2014
*
Journal of automated reasoning
*

We use Isabelle/HOL

doi:10.1007/s10817-014-9318-9
fatcat:tt7toa7wwbdghgymeqowvzxkdu
*for*a detailed systematic study of the regular*algebra*axioms given by Boffa, Conway, Kozen and Salomaa. ... Regular*algebra*is the*algebra*of regular expressions as induced by regular language identity. ... We would like to thank Christian Urban and Tobias Nipkow*for*information on the implementation of regular languages in Isabelle, and the anonymous referees*for*comments and suggestions that helped us to ...##
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Monoids with tests and the algebra of possibly non-halting programs
[article]

2014
*
arXiv
*
pre-print

composition, if-then-else and while-do defined in terms of a Boolean

arXiv:1408.4498v1
fatcat:vf2a5y2vufferblustxp3cwtwi
*algebra*of conditions. ... All*algebras*considered turn out to be enrichments of the notion of a (one-sided) restriction semigroup. ... Within*weak*comparison monoids, quasi-equational law (32)*for*disagreeable monoids is*equivalent*to the following equational laws: T (X) is closed under*weak*comparison, where the operation is called ...##
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Monoids with tests and the algebra of possibly non-halting programs

2015
*
Journal of Logical and Algebraic Methods in Programming
*

composition, if-then-else and while-do defined in terms of a Boolean

doi:10.1016/j.jlamp.2014.08.007
fatcat:6g36upllqnhihjjxt5l3hbomxi
*algebra*of conditions. ... All*algebras*considered turn out to be enrichments of the notion of a (one-sided) restriction semigroup. ... Within*weak*comparison monoids, quasi-equational law (32)*for*disagreeable monoids is*equivalent*to the following equational laws: T (X) is closed under*weak*comparison, where the operation is called ...##
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Concurrent Kleene Algebra with Tests
[chapter]

2014
*
Lecture Notes in Computer Science
*

Concurrent

doi:10.1007/978-3-319-06251-8_3
fatcat:tnekgiex4jfsbpeesa52q2vt7a
*Kleene**algebras*were introduced by Hoare, Möller, Struth and Wehrman in [HMSW09,HMSW09a,HMSW11] as idempotent bisemirings that satisfy a concurrency inequation and have a*Kleene*-star*for*both ... Concurrent*Kleene**algebras*with tests (CKAT) combine these concepts and give a relatively simple*algebraic*model*for*reasoning about operational semantics of concurrent programs. ... The*bi*-*Kleene**algebra*of series-rational gsp-languages 1 , denoted by C Σ,T , is the subalgebra generated by {G(t) : t ∈ T } ∪ {G(p) : p ∈ Σ}. ...##
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Convolution, Separation and Concurrency
[article]

2014
*
arXiv
*
pre-print

A notion of convolution is presented in the context of formal power series together with lifting constructions characterising

arXiv:1410.4235v1
fatcat:lk4kbkkrkzdq3p4ng677vabn44
*algebras*of such series, which usually are quantales. ... separation logics, where convolution is separating conjunction in an assertion quantale; interval logics, where convolution is the chop operation; and stream interval functions, where convolution is used*for*... over X,*for*instance a*Kleene**algebra*with constants from X. ...
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