Probabilistic Inference for Predicate Constraint Satisfaction

Abstract

In this paper, we present a novel constraint solving method for a class of predicate Constraint Satisfaction Problems (pCSP) where each constraint is represented by an arbitrary clause of first-order predicate logic over predicate variables. The class of pCSP properly subsumes the well-studied class of Constrained Horn Clauses (CHCs) where each constraint is restricted to a Horn clause. The class of CHCs has been widely applied to verification of linear-time safety properties of programs in different paradigms. In this paper, we show that pCSP further widens the applicability to verification of branching-time safety properties of programs that exhibit finitely-branching non-determinism. Solving pCSP (and CHCs) however is challenging because the search space of solutions is often very large (or unbounded), high-dimensional, and non-smooth. To address these challenges, our method naturally combines techniques studied separately in different literatures: counterexample guided inductive synthesis (CEGIS) and probabilistic inference in graphical models. We have implemented the presented method and obtained promising results on existing benchmarks as well as new ones that are beyond the scope of existing CHC solvers.

Competition Report: CHC-COMP-21

“…PCSat is based on CounterExample-Guided Inductive Synthesis (CEGIS), with the support of multiple synthesis engines including template-based [21], decision-tree-based [14], and graphical-modelbased [19] ones.…”

An Overview of the HFL Model Checking Project

“…where disjunction may occur in the head (here, P i , Q j are unknown predicate variables and ψ(x,ỹ) is a formula of integer arithmetic). Solving this generalized form of constrained clauses [39] is the current major bottleneck of this approach; work is under way to extend the ICE-based CHC solving approach [6,13] to deal with the generalized constrained clauses. Despite the bottleneck mentioned above, the refinement type-based approach to νHFL(Z) validity checking is generally faster than the predicate abstraction-based approach, while the latter tends to be more precise.…”

Decision Tree Learning in CEGIS-Based Termination Analysis

“…A pCSP WF (C, R) is called CHCs (constrained Horn clauses, [9]) if R = ∅ and ℓ ≤ 1 for all clauses c ∈ C. The class of CHCs has been widely studied in the verification community [12,14,26,33].…”

“…CEGIS has been applied not only to program verification tasks (synthesis of inductive invariants [17,18,23,24], that of ranking functions [19], etc.) but also to constraint solving (for CHC [12,14,26,33], for pCSP WF (T ) [28], etc.). The In contrast, in other methods such as [5-8, 22, 25], synthesizers receive logical constraints that are much more binding.…”