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Modal Kleene Algebra and Partial Correctness
 INSTITUT FÜR INFORMATIK, UNIVERSITÄT AUGSBURG
, 2003
"... We enrich Kleene algebra by domain and codomain operators. These ..."
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We enrich Kleene algebra by domain and codomain operators. These
Some results in dynamic model theory
 Science of Computer Programming
, 2004
"... Firstorder structures over a xed signature give rise to a family of tracebasedandrelational Kleene algebras with tests de ned in terms of Tarskian frames. A Tarskian frame is a Kripke frame whose states are valuations of program variables andwhose atomic actions are state changes e ectedby variabl ..."
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Cited by 4 (3 self)
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Firstorder structures over a xed signature give rise to a family of tracebasedandrelational Kleene algebras with tests de ned in terms of Tarskian frames. A Tarskian frame is a Kripke frame whose states are valuations of program variables andwhose atomic actions are state changes e ectedby variable assignments x: = e, where e is aterm. The Kleene algebras with tests that arise in this way play a role in dynamic model theory akin to the role played by Lindenbaum algebras in classical rstorder model theory. Given a rstorder theory T over, we exhibit a Kripke frame U whose trace algebra TrU is universal for the equational theory of Tarskian trace algebras over satisfying T, although U itself is not Tarskian in general. The corresponding relation algebra RelU is not universal for the equational theory of relation algebras of Tarskian frames, but it is so modulo observational equivalence.
Kleene Algebra with Tests and Coq Tools for While Programs
, 2013
"... Abstract. We present a Coq library about Kleene algebra with tests, including a proof of their completeness over the appropriate notion of languages, a decision procedure for their equational theory, and tools for exploiting hypotheses of a certain kind in such a theory. Kleene algebra with tests ma ..."
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Abstract. We present a Coq library about Kleene algebra with tests, including a proof of their completeness over the appropriate notion of languages, a decision procedure for their equational theory, and tools for exploiting hypotheses of a certain kind in such a theory. Kleene algebra with tests make it possible to represent ifthenelse statements and while loops in most imperative programming languages. They were actually introduced by Kozen as an alternative to propositional Hoare logic. We show how to exploit the corresponding Coq tools in the context of program verification by proving equivalences of while programs, correctness of some standard compiler optimisations, Hoare rules for partial correctness, and a particularly challenging equivalence of flowchart schemes.
Kleene Algebra with Equations
"... Abstract. 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 procedur ..."
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Abstract. 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. 1
KAT + B!
"... It is known that certain program transformations require a small amount of mutable state, a feature not explicitly provided by Kleene algebra with tests (KAT). In this paper we show how to axiomatically extend KAT with this extra feature in the form of mutable tests. The extension is conservative an ..."
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It is known that certain program transformations require a small amount of mutable state, a feature not explicitly provided by Kleene algebra with tests (KAT). In this paper we show how to axiomatically extend KAT with this extra feature in the form of mutable tests. The extension is conservative and is formulated as a general commutative coproduct construction. We give several results on deductive completeness and complexity of the system, as well as some examples of its use. Categories and Subject Descriptors F.3.3 [Logics and Meanings of Programs]: Studies of Program Constructs—Program and recursion schemes
KAT + B!
"... Abstract—It is known that certain program transformations require a small amount of mutable state, a feature not explicitly provided by Kleene algebra with tests (KAT). In this paper we show how to axiomatically extend KAT with this extra feature in the form of mutable tests. The extension is conser ..."
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Abstract—It is known that certain program transformations require a small amount of mutable state, a feature not explicitly provided by Kleene algebra with tests (KAT). In this paper we show how to axiomatically extend KAT with this extra feature in the form of mutable tests. The extension is conservative and is formulated as a general commutative coproduct construction. We give several results on deductive completeness and complexity of the system, as well as some examples of its use. I.
KAT + B!
"... It is known that certain program transformations require a small amount of mutable state, a feature not explicitly provided by Kleene algebra with tests (KAT). In this paper we show how to axiomatically extend KAT with this extra feature in the form of mutable tests. The extension is conservative an ..."
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It is known that certain program transformations require a small amount of mutable state, a feature not explicitly provided by Kleene algebra with tests (KAT). In this paper we show how to axiomatically extend KAT with this extra feature in the form of mutable tests. The extension is conservative and is formulated as a general commutative coproduct construction. We give several results on deductive completeness and complexity of the system, as well as some examples of its use. Categories and Subject Descriptors F.3.3 [Logics and Meanings of Programs]: Studies of Program Constructs—Program and recursion schemes
unknown title
"... epistemic logic. Kleene algebra plays a prominent role in this work. I will first describe my existing work in Kleene algebra (section 1); then I will describe my proposed research in epistemic logic and “webs of distrust ” (sections 2 and 3), which also involves Kleene algebra. Finally, I will disc ..."
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epistemic logic. Kleene algebra plays a prominent role in this work. I will first describe my existing work in Kleene algebra (section 1); then I will describe my proposed research in epistemic logic and “webs of distrust ” (sections 2 and 3), which also involves Kleene algebra. Finally, I will discuss some joint work with Alan Taylor on “infinite hat problems ” (section 4). The material in sections 1–3 is closely related mathematically, while section 4 is largely independent. For space reasons, I must be sparing with details, and completely omit discussion of much miscellaneous work, such as my solution [7] to a problem posed by Francis Su concerning the combinatorics of approval voting [13, 1]. 1 The Horn theory of relational Kleene algebra This was the subject of my thesis [9], and constitutes a substantial amount of my work [8, 4, 3, 5, 6]. A meaningful discussion requires some background; fortunately, this will also assist the discussion in sections 2 and 3. Background and motivation Kleene algebra (KA) arises in many areas of computer science, such as automata theory, the design and analysis of algorithms, dynamic logic, and program semantics. Kleene algebra with tests (KAT) is essentially
unknown title
"... Brief summary of research interests. I am interested in mathematical logic and theoretical computer science. Specifically, I am interested in program logics, particularly Kleene algebra with tests and dynamic logic. (Within Kleene algebra, I am most interested in describing the theory of relational ..."
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Brief summary of research interests. I am interested in mathematical logic and theoretical computer science. Specifically, I am interested in program logics, particularly Kleene algebra with tests and dynamic logic. (Within Kleene algebra, I am most interested in describing the theory of relational Kleene algebras.) I am also interested in epistemic logic. My planned research after graduation involves two areas: the Horn theory of relational Kleene algebra, and revelation in epistemic logic. I will discuss the Kleene algebra aspects first, which will require me to give some background information, and then discuss the epistemic logic, at a level that will not require any background. Background and Motivation Kleene algebra (KA) arises in many areas of computer science, such as automata theory, the design and analysis of algorithms, dynamic logic, and program semantics. Kleene algebra with tests (KAT) is essentially the result of combining KA with Boolean algebra, and this adaptation is particularly useful in dynamic logic and program semantics. For a detailed introduction see [6]. Before defining KA or KAT explicitly, I will give an example that is particularly important in motivating my research. Consider the set R of all binary relations on a set X. We will think of R as an algebra with
MODULARIZING THE ELIMINATION OF r = 0 IN KLEENE ALGEBRA
, 2005
"... Vol. 1 (3:2) 2005, pp. 1–15 ..."
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