From LTL to deterministic automata

We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula $$\varphi $$φ. The automaton is the product of a co-Büchi automaton for $$\varphi $$φ and an array of Rabin automata, one for each $${\mathbf {G}}$$G-subformula of $$\varphi $$φ. The Rabin automaton for $${\mathbf {G}}\psi $$Gψ is in charge of recognizing whether $${\mathbf {F}}{\mathbf {G}}\psi $$FGψ holds. This information is passed to the co-Büchi automaton that decides on acceptance. As opposed to standard procedures based on Safra’s determinization, the states of all our automata have a clear logical structure, which allows for various optimizations. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.

[1]  Jan Strejcek,et al.  Comparison of LTL to Deterministic Rabin Automata Translators , 2013, LPAR.

[2]  Salomon Sickert.  Converting Linear Temporal Logic to Deterministic (Generalised) Rabin Automata , 2015, Arch. Formal Proofs.

[3]  George S. Avrunin,et al.  Patterns in property specifications for finite-state verification , 1999, Proceedings of the 1999 International Conference on Software Engineering (IEEE Cat. No.99CB37002).

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

[5]  Jan Strejcek,et al.  Effective Translation of LTL to Deterministic Rabin Automata: Beyond the (F, G)-Fragment , 2013, ATVA.

[6]  Nir Piterman,et al.  From Nondeterministic Buchi and Streett Automata to Deterministic Parity Automata , 2006, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06).

[7]  Jan Kretínský,et al.  Rabinizer 3: Safraless Translation of LTL to Small Deterministic Automata , 2014, ATVA.

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

[9]  Krishnendu Chatterjee,et al.  Automata with Generalized Rabin Pairs for Probabilistic Model Checking and LTL Synthesis , 2013, CAV.

[10]  Moshe Y. Vardi.  Probabilistic Linear-Time Model Checking: An Overview of the Automata-Theoretic Approach , 1999, ARTS.

[11]  Orna Kupferman,et al.  Safraless Compositional Synthesis , 2006, CAV.

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

[13]  Fausto Giunchiglia,et al.  Improved Automata Generation for Linear Temporal Logic , 1999, CAV.

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

[15]  Amir Pnueli,et al.  On the Merits of Temporal Testers , 2008, 25 Years of Model Checking.

[16]  Christel Baier,et al.  Experiments with deterministic omega-automata for formulas of linear temporal logic , 2006, Theor. Comput. Sci..

[17]  Jan Kretínský,et al.  Deterministic Automata for the (F,G)-fragment of LTL , 2012, CAV.

[18]  Tobias Nipkow,et al.  Isabelle/HOL , 2002, Lecture Notes in Computer Science.

[19]  Carsten Fritz,et al.  Constructing Büchi Automata from Linear Temporal Logic Using Simulation Relations for Alternating Büchi Automata , 2003, CIAA.

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

[21]  Rajeev Alur,et al.  Deterministic generators and games for Ltl fragments , 2004, TOCL.

[22]  Christel Baier,et al.  On-the-Fly Stuttering in the Construction of Deterministic omega -Automata , 2007, CIAA.

[23]  Orna Kupferman,et al.  Safraless decision procedures , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

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

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

[26]  Sven Schewe,et al.  Tighter Bounds for the Determinisation of Büchi Automata , 2009, FoSSaCS.

[27]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

[28]  Mads Dam,et al.  Fixed Points of Büchi Automata , 1992, FSTTCS.

[29]  Marta Z. Kwiatkowska,et al.  PRISM 4.0: Verification of Probabilistic Real-Time Systems , 2011, CAV.

[30]  Jean-François Raskin,et al.  Safraless Procedures for Timed Specifications , 2010, FORMATS.

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

[32]  Orna Kupferman,et al.  Recent Challenges and Ideas in Temporal Synthesis , 2012, SOFSEM.

[33]  Pierre Wolper,et al.  Reasoning About Infinite Computations , 1994, Inf. Comput..

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

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

[36]  Amir Pnueli,et al.  A Framework for the Synthesis of Reactive Modules , 1988, Concurrency.

[37]  S. Safra,et al.  On the complexity of omega -automata , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[38]  Jan Kretínský,et al.  From LTL to Deterministic Automata: A Safraless Compositional Approach , 2014, CAV.

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

[40]  Jan Kretínský,et al.  Rabinizer 2: Small Deterministic Automata for LTL ∖ GU , 2013, ATVA.

[41]  Radek Pelánek,et al.  BEEM: Benchmarks for Explicit Model Checkers , 2007, SPIN.

[42]  Tobias Nipkow,et al.  A Fully Verified Executable LTL Model Checker , 2013, CAV.

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

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