Constructing Büchi Automata from Linear Temporal Logic Using Simulation Relations for Alternating Büchi Automata

We present a new procedure for the translation of propositional linear-time temporal logic (LTL) formulas to equivalent nondeterministic Buchi automata. Our procedure is based on simulation relations for alternating Buchi automata. Whereas most of the procedures that have been described in the past compute simulation relations in the last step of the translation (after a nondeterministic Buchi automaton has already been constructed), our procedure computes simulation relations for alternating Buchi automata in an early stage and uses them in an on the-fly fashion. This decreases the time and space consumption without sacrificing the potential of simulation relations. We present experimental results that demonstrate the advantages of our approach: Our procedure is faster than TMP but produces, on the average, automata of about the same size; LTL2BA is faster than our procedure but produces larger automata.

[1]  Thomas A. Henzinger,et al.  Computing simulations on finite and infinite graphs , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[2]  Keijo Heljanko,et al.  Testing LTL formula translation into Büchi automata , 2002, International Journal on Software Tools for Technology Transfer.

[3]  Marcin Jurdzinski,et al.  Small Progress Measures for Solving Parity Games , 2000, STACS.

[4]  Carsten Fritz,et al.  State Space Reductions for Alternating Büchi Automata Quotienting by Simulation Equivalences , 2002 .

[5]  Moshe Y. Vardi.  An Automata-Theoretic Approach to Linear Temporal Logic , 1996, Banff Higher Order Workshop.

[6]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[7]  David E. Muller,et al.  Alternating Automata. The Weak Monadic Theory of the Tree, and its Complexity , 1986, ICALP.

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

[9]  Pierre Wolper,et al.  Simple on-the-fly automatic verification of linear temporal logic , 1995, PSTV.

[10]  Fabio Somenzi,et al.  Fair Simulation Minimization , 2002, CAV.

[11]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[12]  Robin Milner,et al.  An Algebraic Definition of Simulation Between Programs , 1971, IJCAI.

[13]  Thomas A. Henzinger,et al.  Fair Simulation , 1997, Inf. Comput..

[14]  Kousha Etessami,et al.  Optimizing Büchi Automata , 2000, CONCUR.

[15]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[16]  Westone,et al.  Home Page , 2004, 2022 2nd International Conference on Intelligent Cybernetics Technology & Applications (ICICyTA).

[17]  Thomas A. Henzinger,et al.  Fair Bisimulation , 2000, TACAS.

[18]  Kousha Etessami,et al.  Fair Simulation Relations, Parity Games, and State Space Reduction for Büchi Automata , 2001, ICALP.

[19]  Faron Moller.  Logics for concurrency: structure versus automata , 1996, CSUR.

[20]  Thomas A. Henzinger,et al.  Alternating Refinement Relations , 1998, CONCUR.

[21]  Thomas Wilke,et al.  Simulation relations for alternating Büchi automata , 2005, Theor. Comput. Sci..

[22]  Alan J. Hu,et al.  Checking for Language Inclusion Using Simulation Preorders , 1991, CAV.

[23]  Luigi Santocanale,et al.  Ambiguous Classes in the Games µ-Calculus Hierarchy , 2003, FoSSaCS.

[24]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[25]  Fabio Somenzi,et al.  Efficient Büchi Automata from LTL Formulae , 2000, CAV.