MightyL: A Compositional Translation from MITL to Timed Automata

Metric Interval Temporal Logic (MITL) was first proposed in the early 1990s as a specification formalism for real-time systems. Apart from its appealing intuitive syntax, there are also theoretical evidences that make MITL a prime real-time counterpart of Linear Temporal Logic (LTL). Unfortunately, the tool support for MITL verification is still lacking to this day. In this paper, we propose a new construction from MITL to timed automata via very-weak one-clock alternating timed automata. Our construction subsumes the well-known construction from LTL to Buchi automata by Gastin and Oddoux and yet has the additional benefits of being compositional and integrating easily with existing tools. We implement the construction in our new tool MightyL and report on experiments using Uppaal and LTSmin as back-ends.

[1]  Nikolaj Bjørner,et al.  Satisfiability modulo theories , 2011, Commun. ACM.

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

[3]  Marco Roveri,et al.  Symbolic Implementation of Alternating Automata , 2006, CIAA.

[4]  Baruch Sterin,et al.  A circuit approach to LTL model checking , 2013, 2013 Formal Methods in Computer-Aided Design.

[5]  Georgios E. Fainekos,et al.  Formal Requirement Elicitation and Debugging for Testing and Verification of Cyber-Physical Systems , 2016, ArXiv.

[6]  Thomas Wilke,et al.  Specifying Timed State Sequences in Powerful Decidable Logics and Timed Automata , 1994, FTRTFT.

[7]  Orna Kupferman,et al.  Weak alternating automata are not that weak , 1997, Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems.

[8]  Ufuk Topcu,et al.  Computational methods for stochastic control with metric interval temporal logic specifications , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

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

[10]  Marco Pistore,et al.  NuSMV 2: An OpenSource Tool for Symbolic Model Checking , 2002, CAV.

[11]  Yoram Hirshfeld,et al.  Logics for Real Time: Decidability and Complexity , 2004, Fundam. Informaticae.

[12]  Yann Thierry-Mieg,et al.  Symbolic Model-Checking Using ITS-Tools , 2015, TACAS.

[13]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

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

[15]  Thomas Brihaye,et al.  On MITL and Alternating Timed Automata , 2013, FORMATS.

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

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

[18]  John S. Baras,et al.  Timed automata approach for motion planning using metric interval temporal logic , 2016, 2016 European Control Conference (ECC).

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

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

[21]  Ezio Bartocci,et al.  A Temporal Logic Approach to Modular Design of Synthetic Biological Circuits , 2013, CMSB.

[22]  Silvano Dal-Zilio,et al.  A formal framework to specify and verify real-time properties on critical systems , 2014, Int. J. Crit. Comput. Based Syst..

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

[24]  Erion Plaku,et al.  Motion planning with temporal-logic specifications: Progress and challenges , 2015, AI Commun..

[25]  Sertac Karaman,et al.  Optimal planning with temporal logic specifications , 2009 .

[26]  Patricia Bouyer,et al.  Symbolic Optimal Reachability in Weighted Timed Automata , 2016, CAV.

[27]  Alfons Laarman,et al.  LTSmin: High-Performance Language-Independent Model Checking , 2015, TACAS.

[28]  Marcello M. Bersani,et al.  A tool for deciding the satisfiability of continuous-time metric temporal logic , 2013, 2013 20th International Symposium on Temporal Representation and Reasoning.

[29]  Thomas A. Henzinger,et al.  Real-time logics: complexity and expressiveness , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[30]  Thomas A. Henzinger,et al.  The benefits of relaxing punctuality , 1991, JACM.

[31]  Lubos Brim,et al.  DiVinE 3.0 - An Explicit-State Model Checker for Multithreaded C & C++ Programs , 2013, CAV.

[32]  Kim G. Larsen,et al.  Efficient controller synthesis for a fragment of $$\hbox {MTL}_{0, \infty }$$MTL0,∞ , 2013, Acta Informatica.

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

[34]  Kim Guldstrand Larsen,et al.  Efficient controller synthesis for a fragment of MTL 0 , &infin , 2014 .

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

[36]  Georgios E. Fainekos,et al.  Formal Requirement Debugging for Testing and Verification of Cyber-Physical Systems , 2016, ACM Trans. Embed. Comput. Syst..

[37]  Yoram Hirshfeld,et al.  An Expressive Temporal Logic for Real Time , 2006, MFCS.

[38]  Thomas A. Henzinger,et al.  Real-Time Logics: Complexity and Expressiveness , 1993, Inf. Comput..

[39]  Wang Yi,et al.  Uppaal in a nutshell , 1997, International Journal on Software Tools for Technology Transfer.

[40]  Marco Pistore,et al.  Nusmv version 2: an opensource tool for symbolic model checking , 2002, CAV 2002.

[41]  Stephan Merz,et al.  Truly On-The-Fly LTL Model Checking , 2005, TACAS.

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