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56
A completeness theorem for Kleene algebras and the algebra of regular events
 Information and Computation
, 1994
"... We givea nitary axiomatization of the algebra of regular events involving only equations and equational implications. Unlike Salomaa's axiomatizations, the axiomatization given here is sound for all interpretations over Kleene algebras. 1 ..."
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Cited by 250 (28 self)
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We givea nitary axiomatization of the algebra of regular events involving only equations and equational implications. Unlike Salomaa's axiomatizations, the axiomatization given here is sound for all interpretations over Kleene algebras. 1
Computation orchestration: A basis for widearea computing
 Journal of Software and Systems Modeling
, 2006
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Action Logic and Pure Induction
 Logics in AI: European Workshop JELIA '90, LNCS 478
, 1991
"... In FloydHoare logic, programs are dynamic while assertions are static (hold at states). In action logic the two notions become one, with programs viewed as onthefly assertions whose truth is evaluated along intervals instead of at states. Action logic is an equational theory ACT conservatively ex ..."
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Cited by 67 (6 self)
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In FloydHoare logic, programs are dynamic while assertions are static (hold at states). In action logic the two notions become one, with programs viewed as onthefly assertions whose truth is evaluated along intervals instead of at states. Action logic is an equational theory ACT conservatively extending the equational theory REG of regular expressions with operations preimplication a!b (had a then b) and postimplication b/a (b ifever a). Unlike REG, ACT is finitely based, makes a reflexive transitive closure, and has an equivalent Hilbert system. The crucial axiom is that of pure induction, (a!a) = a!a. This work was supported by the National Science Foundation under grant number CCR8814921. 1 Introduction Many logics of action have been proposed, most of them in the past two decades. Here we define action logic, ACT, a new yet simple juxtaposition of old ideas, and show off some of its attractive aspects. The language of action logic is that of equational regular expressio...
A language for task orchestration and its semantic properties
 In Proceedings of Concur’06
, 2006
"... Abstract. Orc is a new language for task orchestration, a form of concurrent programming with applications in workflow, business process management, and web service orchestration. Orc provides constructs to orchestrate the concurrent invocation of services – while managing timeouts, priorities, and ..."
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Cited by 49 (5 self)
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Abstract. Orc is a new language for task orchestration, a form of concurrent programming with applications in workflow, business process management, and web service orchestration. Orc provides constructs to orchestrate the concurrent invocation of services – while managing timeouts, priorities, and failure of services or communication. In this paper, we show a tracebased semantic model for Orc, which induces a congruence on Orc programs and facilitates reasoning about them. Despite the simplicity of the language and its semantic model, Orc is able to express a variety of useful orchestration tasks. 1
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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Cited by 37 (16 self)
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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
On Fixed Point Equations over Commutative Semirings
, 2007
"... Fixed point equations x = f(x) overωcontinuous semirings can be seen as the mathematical foundation of interprocedural program analysis. The sequence 0, f(0), f 2 (0),...converges to the least fixed point μf. The convergence can be accelerated if the underlying semiring is commutative. We show tha ..."
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Cited by 19 (11 self)
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Fixed point equations x = f(x) overωcontinuous semirings can be seen as the mathematical foundation of interprocedural program analysis. The sequence 0, f(0), f 2 (0),...converges to the least fixed point μf. The convergence can be accelerated if the underlying semiring is commutative. We show that accelerations in the literature, namely Newton’s method for the arithmetic semiring [4] and an acceleration for commutative Kleene algebras due to Hopkins and Kozen [5], are instances of a general algorithm for arbitrary commutative ωcontinuous semirings. In a second contribution, we improve the O(3 n) bound of [5] and show that their acceleration reaches μf after n iterations, where n is the number of equations. Finally, we apply the HopkinsKozen acceleration to itself and study the resulting hierarchy of increasingly fast accelerations.
Certified sizechange termination
 In Proc. 21st CADE, volume 4603 of LNAI
, 2007
"... Abstract. We develop a formalization of the SizeChange Principle in Isabelle/HOL and use it to construct formally certified termination proofs for recursive functions automatically. 1 ..."
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Abstract. We develop a formalization of the SizeChange Principle in Isabelle/HOL and use it to construct formally certified termination proofs for recursive functions automatically. 1
Total Parser Combinators
, 2009
"... A monadic parser combinator library which guarantees termination of parsing, while still allowing many forms of left recursion, is described. The library’s interface is similar to that of many other parser combinator libraries, with two important differences: one is that the interface clearly specif ..."
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Cited by 16 (4 self)
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A monadic parser combinator library which guarantees termination of parsing, while still allowing many forms of left recursion, is described. The library’s interface is similar to that of many other parser combinator libraries, with two important differences: one is that the interface clearly specifies which parts of the constructed parsers may be infinite, and which parts have to be finite, using a combination of induction and coinduction; and the other is that the parser type is unusually informative. The library comes with a formal semantics, using which it is proved that the parser combinators are as expressive as possible. The implementation
Newtonian Program Analysis
, 2010
"... This article presents a novel generic technique for solving dataflow equations in interprocedural dataflow analysis. The technique is obtained by generalizing Newton’s method for computing a zero of a differentiable function to ωcontinuous semirings. Complete semilattices, the common program analy ..."
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Cited by 15 (5 self)
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This article presents a novel generic technique for solving dataflow equations in interprocedural dataflow analysis. The technique is obtained by generalizing Newton’s method for computing a zero of a differentiable function to ωcontinuous semirings. Complete semilattices, the common program analysis framework, are a special class of ωcontinuous semirings. We show that our generalized method always converges to the solution, and requires at most as many iterations as current methods based on Kleene’s fixedpoint theorem. We also show that, contrary to Kleene’s method, Newton’s method always terminates for arbitrary idempotent and commutative semirings. More precisely, in the latter setting the number of iterations required to solve a system of n equations is at most n.
On Action Algebras
, 1993
"... Action algebras have been proposed by Pratt [22] as an alternative to Kleene algebras [8, 9]. Their chief advantage over Kleene algebras is that they form a finitelybased equational variety, so the essential properties of (iteration) are captured purely equationally. However, unlike Kleene algebras ..."
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Cited by 15 (1 self)
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Action algebras have been proposed by Pratt [22] as an alternative to Kleene algebras [8, 9]. Their chief advantage over Kleene algebras is that they form a finitelybased equational variety, so the essential properties of (iteration) are captured purely equationally. However, unlike Kleene algebras, they are not closed under the formation of matrices, which renders them inapplicable in certain constructions in automata theory and the design and analysis of algorithms. In this paper we consider a class of action algebras called action lattices. An action lattice is simply an action algebra that forms a lattice under its natural order. Action lattices combine the best features of Kleene algebras and action algebras: like action algebras, they form a finitelybased equational variety; like Kleene algebras, they are closed under the formation of matrices. Moreover, they form the largest subvariety of action algebras for which this is true. All common examples of Kleene algebras appearing in automata theory, logics of programs, relational algebra, and the design and analysis of algorithms are action lattices.