Probabilistic Choice, Reversibility, Loops, and Miracles

Abstract

Abstract. We consider an addition of probabilistic choice to Abrial's Generalised Substitution Language (GSL) in a form that accommodates the backtracking interpretation of nondeterministic 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 nontermination 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 our formalism, which is strict with respect to nontermination. The formal constructs described are incorporated in a reversal virtual machine (RVM).

The stochastic semantics and verification for periodic control systems

“…The characteristics of complexity of software trustworthiness can be also analyzed by dynamical statistical analysis methods at the software life cycle level [26]. At the program level, some work focus on the probabilistic choice in control flow [27,28]. Compared with traditional programs, the probabilistic programs still use concrete program state, and they enrich the choice structure by introducing probabilities.…”

UTP by Example: Designs

“…Other contributions to UTP theories of programming language semantics, including: angelic nondeterminism [22,23,58]; aspect-oriented programming [25]; component systems [76]; event-driven programming [47,77,80]; lazy evaluation semantics [35]; object-oriented programming [18,59,63]; pointer-based programming [37]; probabilistic programming [43,40,64,9,79]; real-time programming [42,38]; reversible computation [65,64]; timed reactive programming [61,62,69,60,66]; and transaction programming [39,40]. Individual programming languages have been given semantics in UTP.…”