Practical Stutter-Invariance Checks for ω-Regular Languages

An $$\omega $$-regular language is stutter-invariant if it is closed by the operation that duplicates some letter in a word or that removes some duplicate letter. Model checkers can use powerful reduction techniques when the specification is stutter-invariant. We propose several automata-based constructions that check whether a specification is stutter-invariant. These constructions assume that a specification and its negation can be translated into Buchi automata, but aside from that, they are independent of the specification formalism. These transformations were inspired by a construction due to Holzmann and Kupferman, but that we broke down into two operations that can have different realizations, and that can be combined in different ways. As it turns out, implementing only one of these operations is needed to obtain a functional stutter-invariant check. Finally we have implemented these techniques in a tool so that users can easily check whether an LTL or PSL formula is stutter-invariant.

[1]  Viktor Schuppan,et al.  Evaluating LTL Satisfiability Solvers , 2011, ATVA.

[2]  Alfons Laarman,et al.  Guard-based partial-order reduction , 2013, International Journal on Software Tools for Technology Transfer.

[3]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[4]  Doron A. Peled,et al.  Stutter-Invariant Temporal Properties are Expressible Without the Next-Time Operator , 1997, Inf. Process. Lett..

[5]  Max Michel.  Algebre de machines et logique temporelle , 1984, STACS.

[6]  Jaco Geldenhuys,et al.  Larger Automata and Less Work for LTL Model Checking , 2006, SPIN.

[7]  Paul Gastin,et al.  Fast LTL to Büchi Automata Translation , 2001, CAV.

[8]  Christel Baier,et al.  Principles of Model Checking (Representation and Mind Series) , 2008 .

[9]  Wojciech Penczek,et al.  Stuttering-Insensitive Automata for On-the-fly Detection of Livelock Properties , 2002, Electron. Notes Theor. Comput. Sci..

[10]  Lubos Brim,et al.  Parallel Partial Order Reduction with Topological Sort Proviso , 2010, 2010 8th IEEE International Conference on Software Engineering and Formal Methods.

[11]  Alexandre Duret-Lutz.  Manipulating LTL Formulas Using Spot 1.0 , 2013, ATVA.

[12]  Kousha Etessami,et al.  A note on a question of Peled and Wilke regarding stutter-invariant LTL , 2000, Inf. Process. Lett..

[13]  Dimitra Giannakopoulou,et al.  From States to Transitions: Improving Translation of LTL Formulae to Büchi Automata , 2002, FORTE.

[14]  Jean-Michel Couvreur,et al.  On-the-Fly Verification of Linear Temporal Logic , 1999, World Congress on Formal Methods.

[15]  Gerard J. Holzmann,et al.  Not checking for closure under stuttering , 1996, The Spin Verification System.

[16]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[17]  Fabrice Kordon,et al.  Three SCC-Based Emptiness Checks for Generalized Büchi Automata , 2013, LPAR.

[18]  Dimitrie O. Paun,et al.  On Closure Under Stuttering , 2003, Formal Aspects of Computing.

[19]  Gerard J. Holzmann,et al.  The SPIN Model Checker - primer and reference manual , 2003 .

[20]  Kousha Etessami,et al.  Computer Aided Verification , 2008 .

[21]  Christel Baier,et al.  Principles of model checking , 2008 .

[22]  Heikki Tauriainen,et al.  Nested emptiness search for generalized Buchi automata , 2004, Proceedings. Fourth International Conference on Application of Concurrency to System Design, 2004. ACSD 2004..

[23]  Christian Dax,et al.  Specification Languages for Stutter-Invariant Regular Properties , 2009, ATVA.

[24]  Zhenhua Duan,et al.  A note on stutter-invariant PLTL , 2009, Inf. Process. Lett..

[25]  Vojtech Rehák,et al.  LTL to Büchi Automata Translation: Fast and More Deterministic , 2012, TACAS.

[26]  Alexandre Duret-Lutz,et al.  LTL translation improvements in Spot 1.0 , 2014, Int. J. Crit. Comput. Based Syst..

[27]  Christel Baier,et al.  On-the-Fly Stuttering in the Construction of Deterministic ω-Automata , 2007 .

[28]  Jan Kretínský,et al.  The Hanoi Omega-Automata Format , 2015, CAV.

[29]  Pierre Wolper,et al.  An Algorithmic Approach for Checking Closure Properties of Temporal Logic Specifications and Omega-Regular Languages , 1998, Theor. Comput. Sci..