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29
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 27 (3 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
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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Cited by 23 (8 self)
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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
Runtime monitoring of electronic contracts
 In ATVA’08, LNCS
, 2008
"... Abstract. Electronic interorganizational relationships are governed by contracts regulating their interaction. It is necessary to runtime monitor the contracts, as to guarantee their fulfillment. The present work shows how to obtain a runtime monitor for contracts written in CL, a formal specific ..."
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Abstract. Electronic interorganizational relationships are governed by contracts regulating their interaction. It is necessary to runtime monitor the contracts, as to guarantee their fulfillment. The present work shows how to obtain a runtime monitor for contracts written in CL, a formal specification language which allows to write conditional obligations, permissions and prohibitions over actions. The trace semantics of CL formalizes the notion of a trace fulfills a contract. We show how to obtain, for a given contract, an alternating Büchi automaton which accepts exactly the traces that fulfill the contract. This automaton is the basis for obtaining a finite state machine which acts as a runtime monitor for CL contracts. 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 13 (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
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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Cited by 9 (0 self)
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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.
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 8 (3 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.
CL: A Logic for Reasoning about Legal Contracts – Semantics
, 2008
"... The work reported here is concerned with the definition of a logic (which we call CL) for reasoning about legal contracts. The report presents the syntax of the logic and the associated semantics. There are two semantics presented: one is defined with respect to linear structures (i.e. traces of act ..."
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The work reported here is concerned with the definition of a logic (which we call CL) for reasoning about legal contracts. The report presents the syntax of the logic and the associated semantics. There are two semantics presented: one is defined with respect to linear structures (i.e. traces of actions) and is intended for runtime monitoring of executions of contracts; the second semantics is given over branching structures (i.e. Kripkelike structures) and is intended for reasoning about contracts in a static manner (i.e. modelchecking and theorem proving). In the first part of the report we present the theoretical results underlying the branching semantics. It presents an algebra of actions and restates some of previous results presented in another report, as well as new results useful for the definition of the branching semantics and for the proofs. The rest of the report is concerned with the definition of the two semantics. Moreover, several
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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Cited by 4 (2 self)
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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
2 KAT and Hoare Logic with Derivatives ∗
, 2013
"... Kleene algebra with tests (KAT) is an equational system for program verification, which is the combination of Boolean algebra (BA) and Kleene algebra (KA), the algebra of regular expressions. In particular, KAT subsumes the propositional fragment of Hoare logic (PHL) which is a formal system for the ..."
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Cited by 3 (2 self)
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Kleene algebra with tests (KAT) is an equational system for program verification, which is the combination of Boolean algebra (BA) and Kleene algebra (KA), the algebra of regular expressions. In particular, KAT subsumes the propositional fragment of Hoare logic (PHL) which is a formal system for the specification and verification of programs, and that is currently the base of most tools for checking program correctness. Both the equational theory of KAT and the encoding of PHL in KAT are known to be decidable. In this paper we present a new decision procedure for the equivalence of two KAT expressions based on the notion of partial derivatives. We also introduce the notion of derivative modulo particular sets of equations. With this we extend the previous procedure for deciding PHL. Some experimental results are also presented. 1
Reasoning about protocol change and knowledge
 In Proceedings of ICLA
, 2011
"... Abstract. In social interactions, protocols govern our behaviour and assign meaning to actions. In this paper, we investigate the dynamics of protocols and their epistemic effects. We develop two logics, inspired by Propositional Dynamic Logic (PDL) and Public Announcement Logic (PAL), for reasoning ..."
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Cited by 2 (2 self)
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Abstract. In social interactions, protocols govern our behaviour and assign meaning to actions. In this paper, we investigate the dynamics of protocols and their epistemic effects. We develop two logics, inspired by Propositional Dynamic Logic (PDL) and Public Announcement Logic (PAL), for reasoning about protocol change and knowledge updates. We show that these two logics can be translated back to the standard PDL and PAL respectively. 1