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13
Kleene algebra with tests and program schematology
, 2001
"... The theory of flowchart schemes has a rich history going back to Ianov [6]; see Manna [22] for an elementary exposition. A central question in the theory of program schemes is scheme equivalence. Manna presents several examples of equivalence proofs that work by simplifying the schemes using various ..."
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The theory of flowchart schemes has a rich history going back to Ianov [6]; see Manna [22] for an elementary exposition. A central question in the theory of program schemes is scheme equivalence. Manna presents several examples of equivalence proofs that work by simplifying the schemes using various combinatorial transformation rules. In this paper we present a purely algebraic approach to this problem using Kleene algebra with tests (KAT). Instead of transforming schemes directly using combinatorial graph manipulation, we regard them as a certain kind of automaton on abstract traces. We prove a generalization of Kleene’s theorem and use it to construct equivalent expressions in the language of KAT. We can then give a purely equational proof of the equivalence of the resulting expressions. We prove soundness of the method and give a detailed example of its use. 1
On the coalgebraic theory of Kleene algebra with tests
, 2008
"... We develop a coalgebraic theory of Kleene algebra with tests (KAT) along the lines of Rutten (1998) for Kleene algebra (KA) and Chen and Pucella (2003) for a limited version of KAT, resolving some technical issues raised by Chen and Pucella. Our treatment includes a simple definition of the Brzozows ..."
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Cited by 14 (0 self)
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We develop a coalgebraic theory of Kleene algebra with tests (KAT) along the lines of Rutten (1998) for Kleene algebra (KA) and Chen and Pucella (2003) for a limited version of KAT, resolving some technical issues raised by Chen and Pucella. Our treatment includes a simple definition of the Brzozowski derivative for KAT expressions and an automatatheoretic interpretation involving automata on guarded strings. We also give a complexity analysis, showing that an efficient implementation of coinductive equivalence proofs in this setting is tantamount to a standard automatatheoretic construction. It follows that coinductive equivalence proofs can be generated automatically in PSPACE. This matches the bound of Worthington (2008) for the automatic generation of equational proofs in KAT. 1
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
Assumeguarantee reasoning for deadlock
 IN: PROC. OF FMCAD.
, 2006
"... We extend the learningbased automated assume guarantee paradigm to perform compositional deadlock detection. We define Failure Automata, a generalization of finite automata that accept regular failure sets. We develop a learning algorithm L F that constructs the minimal deterministic failure autom ..."
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Cited by 6 (2 self)
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We extend the learningbased automated assume guarantee paradigm to perform compositional deadlock detection. We define Failure Automata, a generalization of finite automata that accept regular failure sets. We develop a learning algorithm L F that constructs the minimal deterministic failure automaton accepting any unknown regular failure set using a minimally adequate teacher. We show how L F can be used for compositional regular failure language containment, and deadlock detection, using noncircular and circular assume guarantee rules. We present an implementation of our techniques and encouraging experimental results on several nontrivial benchmarks.
A Coalgebraic Approach to Kleene Algebra with Tests
 In volume 82(1) of ENTCS
, 2003
"... Kleene Algebra with Tests is an extension of Kleene Algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene Algebra with Tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata. ..."
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Kleene Algebra with Tests is an extension of Kleene Algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene Algebra with Tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata. Since the known automatatheoretic presentation of Kleene Algebra with Tests does not lend itself to a coalgebraic theory, we define a new interpretation of Kleene Algebra with Tests expressions and a corresponding automatatheoretic presentation. One outcome of the theory is a coinductive proof principle, that can be used to establish equivalence of our Kleene Algebra with Tests expressions.
Substructural logic and partial correctness
 Trans. Computational Logic
"... We formulate a noncommutative sequent calculus for partial correctness that subsumes propositional Hoare Logic. Partial correctness assertions are represented by intuitionistic linear implication. We prove soundness and completeness over relational and trace models. As a corollary we obtain a comple ..."
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We formulate a noncommutative sequent calculus for partial correctness that subsumes propositional Hoare Logic. Partial correctness assertions are represented by intuitionistic linear implication. We prove soundness and completeness over relational and trace models. As a corollary we obtain a complete sequent calculus for inclusion and equivalence of regular expressions. Categories and Subject Descriptors: D.2.2 [Software Engineering]: Tools and Techniques— structured programming; D.2.4 [Software Engineering]: Program Verification—correctness
Hidden Protocols
"... When agents know a protocol, this leads them to have expectations about future observations. Agents can update their knowledge by matching their actual observations with the expected ones. They eliminate states where they do not match. In this paper, we study how agents perceive protocols that are n ..."
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Cited by 1 (1 self)
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When agents know a protocol, this leads them to have expectations about future observations. Agents can update their knowledge by matching their actual observations with the expected ones. They eliminate states where they do not match. In this paper, we study how agents perceive protocols that are not commonly known, and propose a logic to reason about knowledge in such scenarios. Categories and Subject Descriptors
KAT and PHL in Coq
"... In this article we describe an implementation of Kleene algebra with tests (KAT) in the Coq theorem prover. KAT is an equational system that has been successfully applied in program verification and, in particular, it subsumes the propositional Hoare logic (PHL). We also present an PHL encoding in K ..."
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In this article we describe an implementation of Kleene algebra with tests (KAT) in the Coq theorem prover. KAT is an equational system that has been successfully applied in program verification and, in particular, it subsumes the propositional Hoare logic (PHL). We also present an PHL encoding in KAT, by deriving its deduction rules as theorems of KAT. Some examples of simple program's formal correctness are given. This work is part of a study of the feasibility of using KAT in the automatic production of certificates in the context of (sourcelevel) ProofCarryingCode (PCC).
The Böhm–Jacopini Theorem is False, Propositionally
"... Abstract. The Böhm–Jacopini theorem (Böhm and Jacopini, 1966) is a classical result of program schematology. It states that any deterministic flowchart program is equivalent to a while program. The theorem is usually formulated at the firstorder interpreted or firstorder uninterpreted (schematic) ..."
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Abstract. The Böhm–Jacopini theorem (Böhm and Jacopini, 1966) is a classical result of program schematology. It states that any deterministic flowchart program is equivalent to a while program. The theorem is usually formulated at the firstorder interpreted or firstorder uninterpreted (schematic) level, because the construction requires the introduction of auxiliary variables. Ashcroft and Manna (1972) and Kosaraju (1973) showed that this is unavoidable. As observed by a number of authors, a slightly more powerful structured programming construct, namely loop programs with multilevel breaks, is sufficient to represent all deterministic flowcharts without introducing auxiliary variables. Kosaraju (1973) established a strict hierarchy determined by the maximum depth of nesting allowed. In this paper we give a purely propositional account of these results. We reformulate the problems at the propositional level in terms of automata on guarded strings, the automatatheoretic counterpart to Kleene algebra with tests. Whereas the classical approaches do not distinguish between firstorder and propositional levels of abstraction, we find that the purely propositional formulation allows a more streamlined mathematical treatment, using algebraic and topological concepts such as bisimulation and coinduction. Using these tools, we can give more mathematically rigorous formulations and simpler and more revealing proofs. 1
Kleene Coalgebra – an overview
"... Abstract. Coalgebras provide a uniform framework for the study of dynamical systems, including several types of automata. The coalgebraic view on systems has recently been proved relevant by the development of a number of expression calculi which generalize classical results by Kleene, on regular ex ..."
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Abstract. Coalgebras provide a uniform framework for the study of dynamical systems, including several types of automata. The coalgebraic view on systems has recently been proved relevant by the development of a number of expression calculi which generalize classical results by Kleene, on regular expressions, and by Kozen, on Kleene algebra. This note contains an overview of the motivation and results of the generic framework we developed – Kleene Coalgebra – to uniformly derive the aforementioned calculi. We present an historical overview of work on regular expressions and axiomatizations, as well a discussion of related work. We show applications of the framework to three types of probabilistic systems: simple Segala, stratified and PnueliZuck. 1