Exploratory Functions on Nondeterministic Strategies, up to Lower Bisimilarity

Authors:
Paul Blain Levy;Kidane Yemane Weldemariam
Affiliations:
University of Birmingham, Birmingham, B15 2TT, UK;University of Birmingham, Birmingham, B15 2TT, UK
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2009

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Abstract

We consider a typed lambda-calculus with no function types, only alternating sum and product types, so that closed terms represent strategies. We add nondeterminism and consider strategies up to lower (i.e. divergence-insensitive) bisimilarity. We investigate the question: when is a function on strategies definable by an open term (with sufficiently large nondeterminism)? The answer is: when it is ''exploratory''. This is a kind of iterated continuity property, coinductively defined, that is decidable in the case of a function between finite types. In particular, any exploratory function between countably nondeterministic strategies is definable by a continuum nondeterministic term.