Kleene chain completeness and fixedpoint properties
نویسندگان
چکیده
منابع مشابه
Kleene Chain Completeness and Fixedpoint Properties
Fixedpoint theorems play a fundamental role in denotational semantics of programming languages. In 1955, Tarski [6] and Davis [l] showed that a lattice L is complete if and only if every monotonic function f: L + L has a fixedpoint. Since then, other fixedpoint properties are considered, by imposing either the function to be o-continuous or the fixedpoint to be the least fixedpoint. The key que...
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This paper gives a new presentation of Kozen’s proof of Kleene algebra completeness featured in his article A completeness theorem for Kleene algebras and the algebra of regular events. A few new variants are introduced, shortening the proof. Specifically, we directly construct an ε-free automaton to prove an equivalent to Kleene’s representation theorem (implementing Glushkov’s instead of Thom...
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Article history: Received 26 January 2016 Received in revised form 9 June 2017 Accepted 11 June 2017 Available online 16 June 2017
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Kleene algebras with tests provide a rigorous framework for equational speci cation and veri cation They have been used success fully in basic safety analysis source to source 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 language theoretic and relational models We also...
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Concurrent Kleene Algebra (CKA) was introduced by Hoare, Moeller, Struth and Wehrman in 2009 as a framework to reason about concurrent programs. We prove that the semantics proposed in the original paper is the free model of CKA with bounded parallel iteration, meaning the completeness of these axioms. This result settles a conjecture of Hoare and collaborators. Moreover, it allows us to establ...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1983
ISSN: 0304-3975
DOI: 10.1016/0304-3975(83)90037-3