Programmatic Strategy Synthesis: Resolving Nondeterminism in Probabilistic Programs

Proceedings of the ACM on Programming Languages, vol. 8, pp. 2792–2820

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 preconditionstyle 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 reachabilityreward objectives. Finally, we apply our technique to several case studies.

Authors 4

1. Kevin Batz Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

2. Tom Jannik Biskup Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

3. Joost-Pieter Katoen Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

4. Tobias Winkler Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany