Denotational Semantics for a Probabilistic Timed Shared-Variable Language

Complex software systems typically involve features like time, concurrency and probability, where probabilistic computations play an increasing role. It is challenging to formalize languages comprising all these features. We have proposed a language, which integrates probability with time and shared-variable concurrency (called PTSC [19]). We also explored its operational semantics, where a set of algebraic laws has been investigated via bisimulation.
In this paper we explore the denotational semantics for our probabilistic language. In order to deal with the above three features and the nondeterminism, we introduce a tree structure, called P-tree, to model concurrent probabilistic programs. The denotational semantics of each statement is formalized in the structure of P-tree. Based on the achieved semantics, a set of algebraic laws is explored; i.e., especially those parallel expansion laws. These laws can be proved via our achieved denotational semantics.