Counterexample-guided inductive synthesis for probabilistic systems

• https://dl.acm.org/doi/10.1007/s00165-021-00547-2

Program Sketches, Probabilistic Programming, Markov Chains, Model Checking,
Counterexamples

This paper presents counterexample-guided inductive synthesis (CEGIS) to
automatically synthesise probabilistic models. The starting point is a family of
finite-stateMarkov chains with related but distinct topologies. Such families can
succinctly be described by a sketch of a probabilistic program. Program sketches
are programs containing holes. Every hole has a finite repertoire of possible
program snippets by which it can be filled.We study several synthesis
problems-feasibility, optimal synthesis, and complete partitioning-for a given
quantitative specification . Feasibility amounts to determine a family member
satisfying , optimal synthesis amounts to find a family member that maximises the
probability to satisfy , and complete partitioning splits the family in
satisfying and refuting members. Each of these problems can be considered under
the additional constraint of minimising the total cost of instantiations, e.g.,
what are all possible instantiations for  that are within a certain budget? The
synthesis problems are tackled using a CEGIS approach. The crux is to
aggressively prune the search space by using counterexamples provided by
a probabilistic model checker. Counterexamples can be viewed as sub-Markov chains
that rule out all family members that share this sub-chain. Our CEGIS approach
leverages efficient probabilisticmodel checking,modern SMT solving, and
programsnippets as counterexamples. Experiments on case studies froma diverse
nature-controller synthesis, program sketching, and security-show that synthesis
among up to a million candidate designs can be done using a few thousand
verification queries.