Programmatic Strategy Synthesis: Resolving Nondeterminism in Probabilistic Programs

TL;DR

This paper presents a semi-automatic method for synthesizing deterministic strategies in probabilistic programs with nondeterminism, ensuring they meet specified quantitative outcomes, and extends techniques from Markov decision processes to looped programs.

Contribution

It introduces a deductive verification-based approach for deriving memoryless deterministic strategies in probabilistic programs, including those with loops, using weakest precondition reasoning.

Findings

Strategies can be obtained for loop-free programs with correctness guarantees.

The approach extends to loopy programs with suitable invariants.

Case studies demonstrate practical applicability and effectiveness.

Abstract

We consider imperative programs that involve both randomization and pure nondeterminism. The central question is how to find a strategy resolving the pure nondeterminism such that the so-obtained determinized program satisfies a given quantitative specification, i.e., bounds on expected outcomes such as the expected final value of a program variable or the probability to terminate in a given set of states. We show how memoryless and deterministic (MD) strategies can be obtained in a semi-automatic fashion using deductive verification techniques. For loop-free programs, the MD strategies resulting from our weakest precondition-style framework are correct by construction. This extends to loopy programs, provided the loops are equipped with suitable loop invariants - just like in program verification. We show how our technique relates to the well-studied problem of obtaining strategies in countably infinite Markov decision processes with reachability-reward objectives. Finally, we apply our technique to several case studies.