Probabilistic Thread Algebra

Abstract

We add probabilistic features to basic thread algebra and its extensions with thread-service interaction and strategic interleaving. Here, threads represent the behaviours produced by instruction sequences under execution and services represent the behaviours exhibited by the components of execution environments of instruction sequences. In a paper concerned with probabilistic instruction sequences, we proposed several kinds of probabilistic instructions and gave an informal explanation for each of them. The probabilistic features added to the extension of basic thread algebra with thread-service interaction make it possible to give a formal explanation in terms of non-probabilistic instructions and probabilistic services. The probabilistic features added to the extensions of basic thread algebra with strategic interleaving make it possible to cover strategies corresponding to probabilistic scheduling algorithms.

Equational Axioms for Expected Value Operators

“…This paper is a sequel to [4] where a meadow based approach to the equational specification of probability functions was proposed. In [6] probabilistic choice is formalised with the meadow of reals as a number system. The equations in that paper demonstrate, just as well as the equations in Table 9, an attractive compatibility between the requirements of probability calculus and the treatment of division in a meadow.…”