A Unified Framework for DPLL(T) + Certificates

Min Zhou,Jiaguang Sun,Bow-Yaw Wang,Ming Gu,Fei He

doi:10.1155/2013/964682

Abstract

Satisfiability Modulo Theories (SMT) techniques are widely used nowadays. SMT solvers are typically used as verification backends. When an SMT solver is invoked, it is quite important to ensure the correctness of its results. To address this problem, we propose a unified certificate framework based on DPLL(T), including a uniform certificate format, a unified certificate generation procedure, and a unified certificate checking procedure. The certificate format is shown to be simple, clean, and extensible to different background theories. The certificate generation procedure is well adapted to most DPLL(T)-based SMT solvers. The soundness and completeness for DPLL(T) + certificates were established. The certificate checking procedure is straightforward and efficient. Experimental results show that the overhead for certificates generation is only 10%, which outperforms other methods, and the certificate checking procedure is quite time saving.

Highlights

IntroductionIn an satisfiability problem (SAT) community, people consider to generate certificates along with the DPLL framework, and the certificates (for unsatisfiability instances) are unified as chains of linear regular resolutions which can lead from the initial clauses to an empty clause [4, 5]
This paper considers the DPLL(T) framework, which is extended from DPLL and has been widely used in state-ofthe-art Satisfiability Modulo Theories (SMT) solvers
(ii) The certificate generation procedure is well adapted to most DPLL(T)-based SMT solvers

Summary

Introduction

In an SAT community, people consider to generate certificates along with the DPLL framework, and the certificates (for unsatisfiability instances) are unified as chains of linear regular resolutions which can lead from the initial clauses to an empty clause [4, 5] With this uniform format, the generation and checking procedures for certificates can be unified. Upon this format, a unified procedure for certificates generation is proposed This procedure can be integrated into DPLL(T)-based SMT solvers. If we focus on quantifier-free problems, the proof format and proof checking could be simplified Solvers such as CVC3 and Z3 can generate certificates, but their formats are quite different because they use different proof rules. (ii) The certificate generation procedure is well adapted to most DPLL(T)-based SMT solvers. This algorithm will terminate under weak assumption and is proven sound and complete [9]

The Certificate Format

Define C2 Define C3 Define

The Certificate Checking

Experiments

Conclusion