A practical theory of programming
A practical theory of programming
Probabilistic predicate transformers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Probabilistic models for the guarded command language
Science of Computer Programming - Special issue: on formal specifications: foundations, methods, tools and applications: selected papers from the FMTA '95 conference (29–31 May 1995, Konstancin n. Warsaw, Poland)
A Formal Approach to Probabilistic Termination
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Algebraic reasoning for probabilistic action systems and while-loops
Acta Informatica
A Virtual Machine for Supporting Reversible Probabilistic Guarded Command Languages
Electronic Notes in Theoretical Computer Science (ENTCS)
Probabilistic termination in B
ZB'03 Proceedings of the 3rd international conference on Formal specification and development in Z and B
Preference and non-deterministic choice
ICTAC'10 Proceedings of the 7th International colloquium conference on Theoretical aspects of computing
A design-based model of reversible computation
UTP'06 Proceedings of the First international conference on Unifying Theories of Programming
UTP'06 Proceedings of the First international conference on Unifying Theories of Programming
A prospective-value semantics for the GSL
ZB'05 Proceedings of the 4th international conference on Formal Specification and Development in Z and B
| Hi-index | 0.00 |
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).