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Algebraic Approaches to Nondeterminism  an Overview
 ACM Computing Surveys
, 1997
"... this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University ..."
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Cited by 23 (3 self)
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this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University
NonDeterministic Extensions of Untyped λcalculus
 INFO. AND COMP
, 1995
"... The main concern of this paper is the study of the interplay between functionality and non determinism. Indeed the first question we ask is whether the analysis of parallelism in terms of sequentiality and non determinism, which is usual in the algebraic treatment of concurrency, remains correct in ..."
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Cited by 6 (0 self)
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The main concern of this paper is the study of the interplay between functionality and non determinism. Indeed the first question we ask is whether the analysis of parallelism in terms of sequentiality and non determinism, which is usual in the algebraic treatment of concurrency, remains correct in presence of functional application and abstraction. We identify non determinism in the setting of λcalculus with the absence of the ChurchRosser property plus the inconsistency of the equational theory obtained by the symmetric closure of the reduction relation. We argue in favour of a distinction between non determinism and parallelism, due to the conjunctive nature of the former in contrast to the disjunctive character of the latter. This is the basis of our analysis of the operational and denotational semantics of non deterministiccalculus, which is the classical calculus plus a choice operator, and of our election of bounded indeterminacy as the semantical counterpart of conjunctive non determinism. This leads to operational semantics based on...
A Convex Powerdomain over Lattices: its Logic and λCalculus
, 1997
"... . To model at the same time parallel and nondeterministic functional calculi we define a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D ! D]? ). We derive f ..."
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Cited by 1 (1 self)
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. To model at the same time parallel and nondeterministic functional calculi we define a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D ! D]? ). We derive from the algebras of P the logic of D 1 , that is the axiomatic description of its compact elements. We then define a calculus and a type assignment system using the logic of D 1 as the related type theory. We prove that the filter model of this calculus, which is isomorphic to D 1 , is fully abstract with respect to the observational preorder of the calculus. Keywords: calculus, Nondeterminism, Full Abstraction, Powerdomain Construction, Intersection Type Disciplines. 1. Introduction One of the main issues in the design of programming languages is the achievement of a good compromise between the multiplicity of control structures and data types and the unicity of the mathematica...
NonDeterministic untyped λcalculus  A study about explicit non determinism in higherorder functional calculi
, 1991
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Under consideration for publication in Formal Aspects of Computing Characterisations of Testing Preorders for a Finite Probabilistic πCalculus
"... Abstract. We consider two characterisations of the may and must testing preorders for a probabilistic extension of the finite πcalculus: one based on notions of probabilistic weak simulations, and the other on a probabilistic extension of a fragment of MilnerParrowWalker modal logic for the πcal ..."
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Abstract. We consider two characterisations of the may and must testing preorders for a probabilistic extension of the finite πcalculus: one based on notions of probabilistic weak simulations, and the other on a probabilistic extension of a fragment of MilnerParrowWalker modal logic for the πcalculus. We base our notions of simulations on similar concepts used in previous work for probabilistic CSP. However, unlike the case with CSP (or other nonvaluepassing calculi), there are several possible definitions of simulation for the probabilistic πcalculus, which arise from different ways of scoping the name quantification. We show that in order to capture the testing preorders, one needs to use the “earliest ” simulation relation (in analogy to the notion of early (bi)simulation in the nonprobabilistic case). The key ideas in both characterisations are the notion of a “characteristic formula ” of a probabilistic process, and the notion of a “characteristic test ” for a formula. As in an earlier work on testing equivalence for the πcalculus by Boreale and De Nicola, we extend the language of the πcalculus with a mismatch operator, without which the formulation of a characteristic test will not be possible.