Mechanizing the Minimization of Deterministic Generalized Büchi Automata

Deterministic Buchi automata (DBA) are useful to (probabilistic) model checking and synthesis. We survey techniques used to obtain and minimize DBAs for different classes of properties. We extend these techniques to support DBA that have generalized and transition-based acceptance (DTGBA) as they can be even smaller. Our minimization technique—a reduction to a SAT problem—synthesizes a DTGBA equivalent to the input DTGBA for any given number of states and number of acceptance sets (assuming such automaton exists). We present benchmarks using a framework that implements all these techniques.

[1]  Alexandre Duret-Lutz,et al.  LTL translation improvements in spot , 2011 .

[2]  Sven Schewe,et al.  Tight Bounds for the Determinisation and Complementation of Generalised Büchi Automata , 2012, ATVA.

[3]  Andreas Podelski,et al.  ACSAR: Software Model Checking with Transfinite Refinement , 2007, SPIN.

[4]  Robert K. Brayton,et al.  Deterministic w Automata vis-a-vis Deterministic Buchi Automata , 1994, ISAAC.

[5]  Rüdiger Ehlers,et al.  Minimising Deterministic Büchi Automata Precisely Using SAT Solving , 2010, SAT.

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

[7]  Sven Schewe,et al.  Beyond Hyper-Minimisation---Minimising DBAs and DPAs is NP-Complete , 2010, FSTTCS.

[8]  Moshe Y. Vardi,et al.  A Multi-encoding Approach for LTL Symbolic Satisfiability Checking , 2011, FM.

[9]  Roberto Grossi,et al.  Mathematical Foundations Of Computer Science 2003 , 2003 .

[10]  Wolfram Schulte,et al.  FM 2011: Formal Methods - 17th International Symposium on Formal Methods, Limerick, Ireland, June 20-24, 2011. Proceedings , 2011, FM.

[11]  Lorenzo Clemente,et al.  Advanced automata minimization , 2012, POPL.

[12]  J. Eisinger,et al.  Mechanizing the Powerset Construction for Restricted Classes of ω-Automata ⋆ , 2007 .

[13]  Gilles Audemard,et al.  Predicting Learnt Clauses Quality in Modern SAT Solvers , 2009, IJCAI.

[14]  Kavita Ravi,et al.  Efficient Decision Procedures for Model Checking of Linear Time Logic Properties , 1999, CAV.

[15]  Zohar Manna,et al.  A hierarchy of temporal properties (invited paper, 1989) , 1990, PODC '90.

[16]  Alexandre Duret-Lutz,et al.  Compositional Approach to Suspension and Other Improvements to LTL Translation , 2013, SPIN.

[17]  Jan Kretínský,et al.  Rabinizer: Small Deterministic Automata for LTL(F, G) , 2012, ATVA.

[18]  Ofer Strichman,et al.  Theory and Applications of Satisfiability Testing – SAT 2010 , 2010, Lecture Notes in Computer Science.

[19]  Denis Poitrenaud,et al.  On-the-Fly Emptiness Checks for Generalized Büchi Automata , 2005, SPIN.

[20]  Mohamed Nassim Seghir,et al.  A Lightweight Approach for Loop Summarization , 2011, ATVA.

[21]  Ivana Cerná,et al.  Relating Hierarchy of Temporal Properties to Model Checking , 2003, MFCS.

[22]  Pierre Wolper,et al.  On the Use of Weak Automata for Deciding Linear Arithmetic with Integer and Real Variables , 2001, IJCAR.

[23]  C. Baier,et al.  Experiments with Deterministic ω-Automata for Formulas of Linear Temporal Logic , 2005 .

[24]  Bernd Finkbeiner,et al.  Uniform distributed synthesis , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

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

[26]  Larry Wos,et al.  What Is Automated Reasoning? , 1987, J. Autom. Reason..