BLACK: A Fast, Flexible and Reliable LTL Satisfiability Checker

BLACK, short for Bounded Ltl sAtisfiability ChecKer, is a recently developed software tool for satisfiability checking of Linear Temporal Logic (LTL) formulas. It supports formulas using both future and past operators, interpreted over both infinite and finite traces. At its core, BLACK uses an incremental SAT encoding of the one-pass tree-shaped tableau for LTL recently developed by Reynolds, which guarantees completeness thanks to its particular pruning rule. This paper gives an overview of the tool, surveys the main design choices underlying its implementation, describes its features and discusses potential future developments.

[1]  Mark Reynolds,et al.  A Parallel Linear Temporal Logic Tableau , 2017, GandALF.

[2]  Pierre Wolper Temporal Logic Can Be More Expressive , 1983, Inf. Control..

[3]  Claude Castelluccia,et al.  Extending SAT Solvers to Cryptographic Problems , 2009, SAT.

[4]  Marco Esposito,et al.  Simulation-Based Synthesis of Personalised Therapies for Colorectal Cancer , 2021, OVERLAY@GandALF.

[5]  Carsten Lutz,et al.  Temporalising Tableaux , 2004, Stud Logica.

[6]  Nikolaj Bjørner,et al.  Z3: An Efficient SMT Solver , 2008, TACAS.

[7]  Stefan Schwendimann,et al.  A New One-Pass Tableau Calculus for PLTL , 1998, TABLEAUX.

[8]  Aaron R. Bradley,et al.  SAT-Based Model Checking without Unrolling , 2011, VMCAI.

[9]  Moshe Y. Vardi,et al.  LTL Satisfiability Checking , 2007, SPIN.

[10]  Alessandro Cimatti,et al.  Reverse engineering with P-stable Abstractions , 2021, OVERLAY@GandALF.

[11]  Angelo Montanari,et al.  One-Pass and Tree-Shaped Tableau Systems for TPTL and TPTLb+Past , 2018, GandALF.

[12]  Amir Pnueli,et al.  Propositional Temporal Logics: Decidability and Completeness , 2000, Log. J. IGPL.

[13]  Giuseppe De Giacomo,et al.  Linear Temporal Logic and Linear Dynamic Logic on Finite Traces , 2013, IJCAI.

[14]  Michael Fisher,et al.  A Resolution Method for Temporal Logic , 1991, IJCAI.

[15]  Niklas Sörensson,et al.  An Extensible SAT-solver , 2003, SAT.

[16]  Marco Roveri,et al.  The nuXmv Symbolic Model Checker , 2014, CAV.

[17]  Angelo Montanari,et al.  Past Matters: Supporting LTL+Past in the BLACK Satisfiability Checker , 2021, TIME.

[18]  Angelo Montanari,et al.  A One-Pass Tree-Shaped Tableau for LTL+Past , 2017, LPAR.

[19]  Angelo Montanari,et al.  A SAT-Based Encoding of the One-Pass and Tree-Shaped Tableau System for LTL , 2019, TABLEAUX.

[20]  A. Prasad Sistla,et al.  The complexity of propositional linear temporal logics , 1982, STOC '82.

[21]  Mark Reynolds A New Rule for LTL Tableaux , 2016, GandALF.

[22]  Marco Esposito,et al.  AI-guided optimal deployments of drone-intercepting systems in large critical areas , 2021, OVERLAY@GandALF.

[23]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[24]  Giuseppe De Giacomo,et al.  Synthesis for LTL and LDL on Finite Traces , 2015, IJCAI.

[25]  Michael Fisher,et al.  A Normal Form for Temporal Logics and its Applications in Theorem-Proving and Execution , 1997, J. Log. Comput..

[26]  Angelo Montanari,et al.  Leviathan: A New LTL Satisfiability Checking Tool Based on a One-Pass Tree-Shaped Tableau , 2016, IJCAI.

[27]  Lijun Zhang,et al.  Aalta: an LTL satisfiability checker over Infinite/Finite traces , 2014, SIGSOFT FSE.

[28]  Alberto Griggio,et al.  The MathSAT5 SMT Solver , 2013, TACAS.

[29]  Carla Limongelli,et al.  Linear temporal logic as an executable semantics for planning languages , 2007, J. Log. Lang. Inf..