Everything You Always Wanted to Know About Generalization of Proof Obligations in PDR

TL;DR

This paper investigates the generalization of proof obligations in PDR, analyzing complexity, limitations, new approaches, and evaluating their effectiveness on benchmarks from hardware and AI planning.

Contribution

It introduces novel proof obligation generalization methods for PDR and provides a comprehensive theoretical and empirical evaluation of these techniques.

Findings

New proof obligation generalization methods outperform existing ones

Complexity analysis clarifies the computational limits of the problem

Empirical results demonstrate improved efficiency on hardware and AI benchmarks

Abstract

In this paper we revisit the topic of generalizing proof obligations in bit-level Property Directed Reachability (PDR). We provide a comprehensive study which (1) determines the complexity of the problem, (2) thoroughly analyzes limitations of existing methods, (3) introduces approaches to proof obligation generalization that have never been used in the context of PDR, (4) compares the strengths of different methods from a theoretical point of view, and (5) intensively evaluates the methods on various benchmarks from hardware model checking as well as from AI planning.