Beyond vacuity: towards the strongest passing formula

Given an LTL formula φ in negation normal form, it can be strengthened by replacing some of its literals with false. Given such a formula and a model M that satisfies it, vacuity and mutual vacuity attempt to find one or a maximal set of literals, respectively, with which φ can be strengthened while still being satisfied by M. We study the problem of finding the strongest LTL formula that satisfies M and is in the Boolean closure of strengthened versions of φ as defined above. This formula is stronger or equally strong to any formula that can be obtained by vacuity and mutual vacuity. We present our algorithms in the framework of lattice automata.

[1]  Helmut Veith,et al.  Parameterized Vacuity , 2004, FMCAD.

[2]  ANNA CICAK,et al.  Oxygen in the Gas Vacuole of the Rhizopod Protozoan, ARCELLA , 1963, Nature.

[3]  Ofer Strichman,et al.  Beyond Vacuity: Towards the Strongest Passing Formula , 2008, FMCAD.

[4]  Marsha Chechik,et al.  How Vacuous Is Vacuous? , 2004, TACAS.

[5]  Orna Kupferman,et al.  Sanity Checks in Formal Verification , 2006, CONCUR.

[6]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[7]  Marsha Chechik,et al.  Generating Counterexamples for Multi-valued Model-Checking , 2003, FME.

[8]  Orna Kupferman,et al.  Vacuity Detection in Temporal Model Checking , 1999, CHARME.

[9]  Ilan Beer,et al.  Efficient Detection of Vacuity in Temporal Model Checking , 2001, Formal Methods Syst. Des..

[10]  Edmund M. Clarke,et al.  Efficient generation of counterexamples and witnesses in symbolic model checking , 1995, DAC '95.

[11]  Randal E. Bryant,et al.  Formally Verifying a Microprocessor Using a Simulation Methodology , 1994, 31st Design Automation Conference.

[12]  Fabio Somenzi,et al.  Vacuum Cleaning CTL Formulae , 2002, CAV.

[13]  Marsha Chechik,et al.  Multi-valued symbolic model-checking , 2003, TSEM.

[14]  Kedar S. Namjoshi.  An Efficiently Checkable, Proof-Based Formulation of Vacuity in Model Checking , 2004, CAV.

[15]  Edmund M. Clarke,et al.  Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic , 1981, Logic of Programs.

[16]  Joseph Sifakis,et al.  Specification and verification of concurrent systems in CESAR , 1982, Symposium on Programming.

[17]  Orna Kupferman,et al.  Lattice Automata , 2007, VMCAI.

[18]  Dana Fisman,et al.  A Framework for Inherent Vacuity , 2009, Haifa Verification Conference.

[19]  Marsha Chechik,et al.  Model-checking infinite state-space systems with fine-grained abstractions using SPIN , 2001, SPIN '01.

[20]  Amir Pnueli,et al.  Checking that finite state concurrent programs satisfy their linear specification , 1985, POPL.

[21]  Ofer Strichman,et al.  Easier and More Informative Vacuity Checks , 2007, 2007 5th IEEE/ACM International Conference on Formal Methods and Models for Codesign (MEMOCODE 2007).