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33
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 188 (23 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
"... ..."
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 51 (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 33 (3 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 22 (11 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
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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Cited by 14 (1 self)
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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
On Action Algebras
 Logic and Information Flow
, 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 algeb ..."
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Cited by 10 (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 appeari...
On the Complexity of Reasoning in Kleene Algebra
 Information and Computation
, 1997
"... We study the complexity of reasoning in Kleene algebra and *continuous Kleene algebra in the presence of extra equational assumptions E; that is, the complexity of deciding the validity of universal Horn formulas E ! s = t, where E is a finite set of equations. We obtain various levels of complexi ..."
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Cited by 10 (5 self)
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We study the complexity of reasoning in Kleene algebra and *continuous Kleene algebra in the presence of extra equational assumptions E; that is, the complexity of deciding the validity of universal Horn formulas E ! s = t, where E is a finite set of equations. We obtain various levels of complexity based on the form of the assumptions E. Our main results are: for * continuous Kleene algebra, ffl if E contains only commutativity assumptions pq = qp, the problem is \Pi 0 1 complete; ffl if E contains only monoid equations, the problem is \Pi 0 2 complete; ffl for arbitrary equations E, the problem is \Pi 1 1  complete. The last problem is the universal Horn theory of the *continuous Kleene algebras. This resolves an open question of Kozen (1994). 1 Introduction Kleene algebra (KA) is fundamental and ubiquitous in computer science. Since its invention by Kleene in 1956, it has arisen in various forms in program logic and semantics [17, 28], relational algebra [27, 32], aut...
Transaction Orchestration
"... The internet promises a truly global computer where all services and data are available to all users at all time. True internet computing, which we call widearea computing, will combine multiple available services in much the same way as we compose functions by combining individual statements in a ..."
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Cited by 8 (0 self)
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The internet promises a truly global computer where all services and data are available to all users at all time. True internet computing, which we call widearea computing, will combine multiple available services in much the same way as we compose functions by combining individual statements in a sequential program. However, it is astoundingly difficult to program the ”internet computer ” for seemingly simple tasks. Consider a university department in which the calendars of all professors are available online. Also available are the room reservation charts. It is still a major software engineering task to automatically schedule a meeting among a group of professors and reserve a room where the meeting is to be held. Add to this the reasonable requirements that (1) the staff should be contacted to provide the appropriate audiovisual equipment for the meeting, (2) the meeting should be rescheduled if more than one third of the members later decide that they can not meet at that time, and (3) a new room should be found if the assigned room is later preempted for a meeting by the chairman of the department. This small example embodies the computational pattern inherent in many widearea applications: acquire data from one or more remote services, calculate with these data, and invoke