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Kleene algebra with tests: Completeness and decidability
 In Proc. of 10th International Workshop on Computer Science Logic (CSL’96
, 1996
"... Abstract. Kleene algebras with tests provide a rigorous framework for equational speci cation and veri cation. 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 alg ..."
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Abstract. Kleene algebras with tests provide a rigorous framework for equational speci cation and veri cation. 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 with tests and *continuous Kleene algebra with tests over languagetheoretic and relational models. We also show decidability. Cohen's reduction of Kleene algebra with hypotheses of the form r = 0 to Kleene algebra without hypotheses is simpli ed and extended to handle Kleene algebras with tests. 1
Universality and Semicomputability for Nondeterministic Programming Languages over Abstract Algebras
, 2006
"... The Universal Function Theorem (UFT) originated in 1930s with the work of Alan Turing, who proved the existence of a universal Turing machine for computations on strings over a finite alphabet. This stimulated the development of storedprogram computers. Classical computability theory, including the ..."
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The Universal Function Theorem (UFT) originated in 1930s with the work of Alan Turing, who proved the existence of a universal Turing machine for computations on strings over a finite alphabet. This stimulated the development of storedprogram computers. Classical computability theory, including the UFT and the theory of semicomputable sets, has been extended by Tucker and Zucker to abstract manysorted algebras, with algorithms formalized as deterministic While programs. This paper investigates the extension of this work to the nondeterministic programming languages While RA consisting of While programs extended by random assignments, as well as sublanguages of While RA formed by restricting the random assignments to booleans or naturals only. It also investigates the nondeterministic language GC of guarded commands. There are two topics algebras in these languages; (2) concepts of semicomputability for these languages, and the extent to which they coincide with semicomputability for the deterministic While language. data types, abstract computability, random assignments, guarded commands, nondeterminism.
Kleene Algebra with Tests
, 2004
"... In semantics and logics of programs, Kleene algebra forms an essential component of Propositional Dynamic Logic (PDL) [6], in which it is mixed with Boolean algebra and modal logic ..."
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In semantics and logics of programs, Kleene algebra forms an essential component of Propositional Dynamic Logic (PDL) [6], in which it is mixed with Boolean algebra and modal logic