On MITL and Alternating Timed Automata

One clock alternating timed automata (OCATA) have been recently introduced as natural extension of (one clock) timed automata to express the semantics of MTL [12]. We consider the application of OCATA to problem of model-checking MITL formulas (a syntactic fragment of MTL) against timed automata. We introduce a new semantics for OCATA where, intuitively, clock valuations are intervals instead of single values in ℝ. Thanks to this new semantics, we show that we can bound the number of clock copies that are necessary to allow an OCATA to recognise the models of an MITL formula. Equipped with this technique, we propose a new algorithm to translate an MITL formula into a timed automaton, and we sketch several ideas to define new model checking algorithms for MITL.

[1]  Thomas A. Henzinger,et al.  The temporal specification and verification of real-time systems , 1991 .

[2]  Jean-François Raskin,et al.  Antichains: Alternative Algorithms for LTL Satisfiability and Model-Checking , 2008, TACAS.

[3]  Paritosh K. Pandya,et al.  The Unary Fragments of Metric Interval Temporal Logic: Bounded versus Lower Bound Constraints , 2012, ATVA.

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

[5]  Pierre-Yves Schobbens,et al.  The Logic of Event Clocks - Decidability, Complexity and Expressiveness , 1998, J. Autom. Lang. Comb..

[6]  Dejan Nickovic,et al.  From MITL to Timed Automata , 2006, FORMATS.

[7]  Thomas Brihaye,et al.  On MITL and Alternating Timed Automata over Infinite Words , 2014, FORMATS.

[8]  Slawomir Lasota,et al.  Alternating timed automata , 2005, TOCL.

[9]  Joël Ouaknine,et al.  On the decidability and complexity of Metric Temporal Logic over finite words , 2007, Log. Methods Comput. Sci..

[10]  Jean-François Raskin,et al.  Antichain Algorithms for Finite Automata , 2010, TACAS.

[11]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[12]  Ron Koymans,et al.  Specifying real-time properties with metric temporal logic , 1990, Real-Time Systems.

[13]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[14]  Thomas A. Henzinger,et al.  The benefits of relaxing punctuality , 1991, PODC '91.

[15]  Stephan Merz,et al.  Model Checking , 2000 .

[16]  Joël Ouaknine,et al.  On the decidability of metric temporal logic , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

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