1. Title: SAT-based Decision Procedures for Knowledge Representation and Formal Verification

Author: Armando Tacchella

Advisor: Proff. Enrico Giunchiglia and Mauro Di Manzo

Defense date: February 2001

Institution:Dipartimento di Informatica, Sistemistica e Telematica, Università degli Studi di Genova, Italia

Abstract: This work focuses on the development of computer procedures for automated deduction in the following logics:

• propositional logic (or Boolean logic) and the related satisfiability problem, i.e., establishing whether a given a sentence in propositional logic is contradictory or not;
• modal logics, i.e., the extension of propositional logic to deal with modalities such as time and knowledge;
• quantified propositional logic, i.e., the extension of propositional logic to deal with quantifications

The contribution of this thesis is the design, the implementation and the experimental testing of three systems:

• SIM (Satisfiability Internal Modules), a library of efficient decision procedures based on the Davis-Putnam-Logemann-Loveland (DPLL) method for propositional satisfiability.
• *SAT (Everything on SAT), a platform for the development of SAT-based, and particularly, DPLL-based decision procedures for various modal logics.
• QuBE (Quantified Boolean formulas Evaluator), a collection of decision procedures for quantified Boolean logic.

• SIM compares favorably with the systems presented in [BS97, Zha97, LA97, Fre95] and it can outperform them using the same techniques they use, but combining them to foster effectiveness;
• *SAT is continuously under development; the current version 3.2 embeds SATO [Zha97a] as the internal DPLL solver and it compared well with the systems presented in [PS98, Hor97, HS97]; we are currently developing a new version which will include SIM as the internal solver and will be able to handle expressive modal logics.
• QuBE is faster than other comparable state-of-the-art systems (such as the one presented in [CGS98]) and it features some newly introduced technique as well.

The systems that we developed are interesting not only from the research perspective, but also from an application point of view. SIM is at the heart of two technology-transfer projects. The first one is THUNDER, an open architecture for SAT-based verification of hardware designs developed by the Logic Validation Technologies Group at the Israel Development Center of Intel Corp. An object oriented version of SIM (SIMO) has been recently integrated into THUNDER and used to debug the design of some Pentium IV components. THUNDER(SIMO) outperforms other traditional validation technologies [CF+01]. The second technology transfer project centered around SIM is in cooperation with Istituto per la Ricerca Scientifica e Tecnologica (IRST-ITC) in Trento and involves the integration of SIM into the NuSMV [CC+98] model checker, a tool for debugging and verifying hardware designs and software protocols.

On-line resources
SIM and QuBE homepages under Software Tools for Automated Reasoning (STAR) pages.
*SAT homepage, including source code distribution, manual, papers and more.

Bibliography
[BS97] R. J. Bayardo Jr. and R. C. Schrag. Using CSP Look-Back Techniques to Solve Real-World SAT instances. In Proc. of AAAI, pages 203--208. AAAI Press, 1997.
[CC+98] A. Cimatti, E. Clarke, F. Giunchiglia and M. Roveri. NuSMV: a new symbolic model checker. Journal on Software Tools for Technology Transfer, 2:4, pages 410--425, Springer Verlag, 2000.
[CF+01] F. Copty, L. Fix, Ranan Fraer, E. Giunchiglia, G. Kamhi, A. Tacchella and M. Y. Vardi. Benefits of Bounded Model Checking at an Industrial Setting. In Proc. of CAV, 2001.
[CGS98] M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified boolean formulae. In Proc. of AAAI, 1998.
[Fre95] J. W. Freeman. Improvements to propositional satisfiability search algorithms. PhD thesis, University of Pennsylvania, 1995 .
[Hor97] I. Horrocks. Optimizing Tableaux Decision Procedures for Description Logics. PhD thesis, University of Manchester, 1997.
[HS97] U. Hustadt and R.A. Schmidt. On evaluating decision procedures for modal logic. In \em Proc. of IJCAI, 1997.
[LA97] C. M. Li and Anbulagan. Heuristics Based on Unit Propagation for Satisfiability Problems. In Proc. of IJCAI, pages 366--371. Morgan-Kauffmann, 1997 .
[PS98] P. F. Patel-Schneider. DLP System Description. In Collected Papers from the International Description Logics Workshop (DL'98). CEUR Workshop Proceedings, 1998 .
[Zha97] H. Zhang. SATO: An efficient propositional prover. In Proc. of CADE, volume 1249 of LNAI, pages 272--275. Springer Verlag, 1997 .