Counterexample-guided inductive synthesis for probabilistic systems

Abstract

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 φ . Feasibility amounts to determine a family member satisfying φ , optimal synthesis amounts to find a family member that maximises the probability to satisfy φ , 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 φ 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.

Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants

“…PrIC3 [15] finds quantitative invariants by iteratively overapproximating k-step reachability. Alternative CEGIS approaches synthesize Markov chains [18] and probabilistic programs [5] that satisfy reachability properties. Symbolic Inference.…”

Counterexample Generation for Probabilistic Model Checking Micro-Scale Cyber-Physical Systems

“…Aljzzar et al [29] propose a directed state space search method called XBF (XZ, XUZ) to generate a counterexample, which is the first work of counterexample generation with a heuristic. There are some works in this direction, such as [13,30,31], which optimizes the heuristics to generate a counterexample for DTMC.…”

“…Up to now, existing probabilistic model checking tools cannot provide a counterexample directly. Counterexamples play a very important role in estimating or verifying MCPSs: (1) Counterexamples can feedback which parts of the system violate the requirements and provide diagnostic information; (2) Counterexamples are very effective in model-based testing, which can provide a reference for the design of test cases; (3) In the process of abstract refinement, counterexamples can provide guidance information for the refinement of rough abstract models [13,14]; (4) Counterexamples can be used to obtain the core of feasible plans in planning, such as task scheduling [15]; (5) Counterexamples are recently used to synthesize attacks for showing how confidentiality of systems can be broken, and the quality assurance of multi-agent systems [16].…”