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Kleene Algebra with Domain
, 2003
"... We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressibility of Kleene algebra, in particular for the specification and analysis of state transition systems. We ..."
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Cited by 42 (29 self)
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We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressibility of Kleene algebra, in particular for the specification and analysis of state transition systems. We develop the basic calculus, discuss some related theories and present the most important models of KAD. We demonstrate applicability by two examples: First, an algebraic reconstruction of Noethericity and wellfoundedness. Second, an algebraic reconstruction of propositional Hoare logic.
Modal Kleene Algebra And Applications  A Survey
, 2004
"... Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various other calculi and allows treating quite a variety of areas. We survey ..."
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Cited by 11 (5 self)
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Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various other calculi and allows treating quite a variety of areas. We survey
KATML: An interactive theorem prover for Kleene Algebra with Tests
 University of Manchester
, 2003
"... Abstract. We describe an implementation of an interactive theorem prover for Kleene algebra with tests (KAT). The system is designed to reflect the natural style of reasoning with KAT that one finds in the literature. We illustrate its use with some examples. 1 ..."
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Cited by 8 (1 self)
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Abstract. We describe an implementation of an interactive theorem prover for Kleene algebra with tests (KAT). The system is designed to reflect the natural style of reasoning with KAT that one finds in the literature. We illustrate its use with some examples. 1
Omega Algebra, Demonic Refinement Algebra and Commands
 IN 9TH INTERNATIONAL CONFERENCE ON RELATIONAL METHODS IN COMPUTER SCIENCE AND 4TH INTERNATIONAL WORKSHOP ON APPLICATIONS OF KLEENE ALGEBRA, LECTURE
, 2006
"... Weak omega algebra and demonic refinement algebra are two ways of describing systems with finite and infinite iteration. We show that these independently introduced kinds of algebras can actually be defined in terms of each other. By defining modal operators on the underlying weak semiring, that res ..."
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Cited by 4 (3 self)
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Weak omega algebra and demonic refinement algebra are two ways of describing systems with finite and infinite iteration. We show that these independently introduced kinds of algebras can actually be defined in terms of each other. By defining modal operators on the underlying weak semiring, that result directly gives a demonic refinement algebra of commands. This yields models in which extensionality does not hold. Since in predicatetransformer models extensionality always holds, this means that the axioms of demonic refinement algebra do not characterise predicatetransformer models uniquely. The omega and the demonic refinement algebra of commands both utilise the convergence operator that is analogous to the halting predicate of modal µcalculus. We show that the convergence operator can be defined explicitly in terms of infinite iteration and domain if and only if domain coinduction for infinite iteration holds.
Reasoning algebraically about probabilistic loops
 In International Conference on Formal Engineering Methods, volume 4260 of LNCS
, 2006
"... Abstract. Back and von Wright have developed algebraic laws for reasoning about loops in the refinement calculus. We extend their work to reasoning about probabilistic loops in the probabilistic refinement calculus. We apply our algebraic reasoning to derive transformation rules for probabilistic ac ..."
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Cited by 1 (0 self)
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Abstract. Back and von Wright have developed algebraic laws for reasoning about loops in the refinement calculus. We extend their work to reasoning about probabilistic loops in the probabilistic refinement calculus. We apply our algebraic reasoning to derive transformation rules for probabilistic action systems. In particular we focus on developing data refinement rules for probabilistic action systems. Our extension is interesting since some well known transformation rules that are applicable to standard programs are not applicable to probabilistic ones: we identify some of these important differences and we develop alternative rules where possible. In particular, our probabilistic action system data refinement rules are new. 1
Refinement Algebra Extended with Operators for Enabledness and Termination
, 2005
"... Refinement algebras are axiomatisations intended for reasoning about programs in a total correctness framework. We reduce von Wright’s demonic refinement algebra to only allow strong iteration and introduce two operators for modelling enabledness and termination of programs, respectively. We show ho ..."
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Cited by 1 (1 self)
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Refinement algebras are axiomatisations intended for reasoning about programs in a total correctness framework. We reduce von Wright’s demonic refinement algebra to only allow strong iteration and introduce two operators for modelling enabledness and termination of programs, respectively. We show how the operators can be used for expressing properties between programs and apply the algebra to reasoning about action systems.
On Two Dually Nondeterministic Refinement Algebras
 MONIKA SEISENBERGER (EDS.): CALCO YOUNG RESEARCHERS WORKSHOP 2005, SELECTED PAPERS. UNIV. OF WALES, SWANSEA, TECHNICAL REPORT CSR
, 2005
"... A dually nondeterministic refinement algebra with a negation operator is proposed. The algebra facilitates reasoning about totalcorrectness preserving program transformations and nondeterministic programs. The negation operator is used to express enabledness and termination operators through a usefu ..."
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A dually nondeterministic refinement algebra with a negation operator is proposed. The algebra facilitates reasoning about totalcorrectness preserving program transformations and nondeterministic programs. The negation operator is used to express enabledness and termination operators through a useful explicit definition. As a small application, a property of action systems is proved employing the algebra. A dually nondeterministic refinement algebra without the negation operator is also discussed.
Algebra of Monotonic Boolean Transformers
, 2013
"... Algebras of imperative programming languages have been successful in reasoning about programs. In general an algebra of programs is an algebraic structure with programs as elements and with program compositions (sequential composition, choice, skip) as algebra operations. Various versions of these a ..."
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Algebras of imperative programming languages have been successful in reasoning about programs. In general an algebra of programs is an algebraic structure with programs as elements and with program compositions (sequential composition, choice, skip) as algebra operations. Various versions of these algebras were introduced to model partial correctness, total correctness, refinement, demonic choice, and other aspects. We formalize here an algebra which can be used to model total correctness, refinement, demonic and angelic choice. The basic model of this algebra are monotonic Boolean transformers (monotonic