2010 | OriginalPaper | Buchkapitel
Probabilistic Choice, Reversibility, Loops, and Miracles
verfasst von : Bill Stoddart, Pete Bell
Erschienen in: Unifying Theories of Programming
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
We consider an addition of probabilistic choice to Abrial’s Generalised Substitution Language (GSL) in a form that accommodates the backtracking interpretation of non-deterministic choice. Our formulation is introduced as an extension of the Prospective Values formalism we have developed to describe the results from a backtracking search. Significant features are that probabilistic choice is governed by feasibility, and non-termination is strict. The former property allows us to use probabilistic choice to generate search heuristics. In this paper we are particularly interested in iteration. By demonstrating sub-conjunctivity and monotonicity properties of expectations we give the basis for a fixed point semantics of iterative constructs, and we consider the practical proof treatment of probabilistic loops. We discuss loop invariants, loops with probabilistic behaviour, and probabilistic termination in the context of a formalism in which a small probability of non-termination can dominate our calculations, proposing a method of limits to avoid this problem. The formal programming constructs described have been implemented in a reversible virtual machine (RVM).