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23
Kleene algebra with tests: Completeness and decidability
 IN PROC. OF 10TH INTERNATIONAL WORKSHOP ON COMPUTER SCIENCE LOGIC (CSL’96
, 1996
"... Kleene algebras with tests provide a rigorous framework for equational specification and verification. They have been used successfully in basic safety analysis, sourcetosource program transformation, and concurrency control. We prove the completeness of the equational theory of Kleene algebra w ..."
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Cited by 37 (15 self)
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Kleene algebras with tests provide a rigorous framework for equational specification and verification. They have been used successfully in basic safety analysis, sourcetosource program transformation, and concurrency control. We prove the completeness of the equational theory of Kleene algebra
Completeness and Incompleteness in Nominal Kleene Algebra
, 2014
"... Gabbay and Ciancia (2011) presented a nominal extension of Kleene algebra as a framework for trace semantics with dynamic allocation of resources, along with a semantics consisting of nominal languages. They also provided an axiomatization that captures the behavior of the scoping operator and its ..."
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Cited by 1 (1 self)
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interaction with the Kleene algebra operators and proved soundness over nominal languages. In this paper we show that the axioms are complete and describe the free language models. 1
Synchronous Kleene Algebra
, 2009
"... The work presented here investigates the combination of Kleene algebra with the synchrony model of concurrency from Milner’s SCCS calculus. The resulting algebraic structure is called synchronous Kleene algebra. Models are given in terms of sets of synchronous strings and finite automata accepting s ..."
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Cited by 4 (2 self)
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. Decidability follows from completeness. Kleene algebra with synchrony should be included in the class of true concurrency models. In this direction, a comparison with Mazurkiewicz traces is made which yields their incomparability with synchronous Kleene algebras (one cannot simulate the other). On the other
Kleene Algebra with Equations
"... We identify sufficient conditions for the construction of free language models for systems of Kleene algebra with additional equations. The construction applies to a broad class of extensions of KA and provides a uniform approach to deductive completeness and coalgebraic decision procedures. ..."
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Cited by 1 (1 self)
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We identify sufficient conditions for the construction of free language models for systems of Kleene algebra with additional equations. The construction applies to a broad class of extensions of KA and provides a uniform approach to deductive completeness and coalgebraic decision procedures.
On the relation between Concurrent Separation Logic and Concurrent Kleene Algebra
"... We investigate the connection between a general form of Concurrent Separation Logic (CSL), a logic for modular reasoning about concurrent programs, and Concurrent Kleene Algebra (CKA), which provides an axiomatic approach to models of concurrency. We show how the proof theory of a general form of CS ..."
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We investigate the connection between a general form of Concurrent Separation Logic (CSL), a logic for modular reasoning about concurrent programs, and Concurrent Kleene Algebra (CKA), which provides an axiomatic approach to models of concurrency. We show how the proof theory of a general form
WaitFree Data Structures in the Asynchronous PRAM Model
 In Proceedings of the 2nd Annual Symposium on Parallel Algorithms and Architectures
, 2000
"... In the asynchronous PRAM model, processes communicate by atomically reading and writing shared memory locations. This paper investigates the extent to which asynchronous PRAM permits longlived, highly concurrent data structures. An implementation of a concurrent object is waitfree if every operati ..."
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Cited by 60 (13 self)
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In the asynchronous PRAM model, processes communicate by atomically reading and writing shared memory locations. This paper investigates the extent to which asynchronous PRAM permits longlived, highly concurrent data structures. An implementation of a concurrent object is waitfree if every
Models of nondeterministic regular expressions
 J. Comput. Sys. Sci
, 1999
"... Nondeterminism is a direct outcome of interactions and is, therefore a central ingredient for modelling concurrent systems. Trees are very useful for modelling nondeterministic behaviour. We aim at a treebased interpretation of regular expressions and study the effect of removing the idempotence la ..."
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Cited by 7 (1 self)
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law X+X=X and the distribution law X v(Y+Z)=X vY+X vZ from Kleene algebras. We show that the free model of the new set of axioms is a class of trees labelled over A. We also equip regular expressions with a twolevel behavioural semantics. The basic level is described in terms of a class of labelled
Contents
, 2008
"... The work reported here investigates the introduction of synchrony into Kleene algebra. The resulting algebraic structure is called synchronous Kleene algebra. Models are given in terms of regular sets of concurrent strings and finite automata accepting concurrent strings. The extension of synchrono ..."
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of synchronous Kleene algebra with Boolean tests is presented together with models on regular sets of guarded concurrent strings and the associated automata on guarded concurrent strings. Completeness w.r.t. the standard interpretations is given in each case. Decidability follows from completeness. A comparison
ALGEBRAIC ALGORITHMS1
, 2012
"... This is a preliminary version of a Chapter on Algebraic Algorithms in the up ..."
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This is a preliminary version of a Chapter on Algebraic Algorithms in the up
Derivative Based Methods for Deciding SKA and SKAT
, 2014
"... Synchronous Kleene algebra (SKA) is a decidable framework that combines Kleene algebra (KA) with a synchrony model of concurrency. Elements of SKA can be seen as processes taking place within a fixed discrete time frame and that, at each time step, may execute one or more basic actions or then come ..."
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Synchronous Kleene algebra (SKA) is a decidable framework that combines Kleene algebra (KA) with a synchrony model of concurrency. Elements of SKA can be seen as processes taking place within a fixed discrete time frame and that, at each time step, may execute one or more basic actions or then come
Results 1  10
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23