Thomas Ferrère
Amir Pnueli
Skip Abstract Section
Abstract
We show how to construct temporal testers for the logic MITL, a prominent linear-time logic for real-time systems. A temporal tester is a transducer that inputs a signal holding the Boolean value of atomic propositions and outputs the truth value of a formula along time. Here we consider testers over continuous-time Boolean signals that use clock variables to enforce duration constraints, as in timed automata. We first rewrite the MITL formula into a “simple” formula using a limited set of temporal modalities. We then build testers for these specific modalities and show how to compose testers for simple formulae into complex ones. Temporal testers can be turned into acceptors, yielding a compositional translation from MITL to timed automata. This construction is much simpler than previously known and remains asymptotically optimal. It supports both past and future operators and can easily be extended.
- 2010. IEEE Std 1850-2010 (Revision of IEEE Std 1850-2005). IEEE Standard for Property Specification Language (PSL).Google Scholar
- 2012. ANSI/IEEE 1800-2012. IEEE Standard for SystemVerilog. Unified Hardware Design, Specification, and Verification Language.Google Scholar
- Rajeev Alur. 1999. Timed automata. In Proceedings of the International Conference on Computer Aided Verification. Springer, 8--22. Google ScholarDigital Library
- Rajeev Alur and David L. Dill. 1994. A theory of timed automata. Theor. Comput. Sci. 126, 2 (1994), 183--235. Google ScholarDigital Library
- Rajeev Alur, Tomás Feder, and Thomas A Henzinger. 1996. The benefits of relaxing punctuality. J. ACM 43, 1 (1996), 116--146. Google ScholarDigital Library
- Rajeev Alur and Thomas A. Henzinger. 1992. Back to the future: Towards a theory of timed regular languages. In Foundations of Computer Science. IEEE, 177--186. Google ScholarDigital Library
- Rajeev Alur and Thomas A. Henzinger. 1992. Logics and models of real time: A survey. In Real-Time: Theory in Practice. Springer, 74--106. Google ScholarDigital Library
- Rajeev Alur and Thomas A. Henzinger. 1994. A really temporal logic. J. ACM 41, 1 (1994), 181--203. Google ScholarDigital Library
- Eugene Asarin. 2004. Challenges in timed languages: From applied theory to basic theory. Bull. Eur. Assoc. Theor. Comput. Sci. 83 (2004), 106--120.Google Scholar
- Eugene Asarin, Paul Caspi, and Oded Maler. 2002. Timed regular expressions. J. ACM 49, 2 (2002), 172--206. Google ScholarDigital Library
- Eugene Asarin and Cătălin Dima. 2003. Balanced timed regular expressions1. Electr. Not. Theor. Comput. Sci. 68, 5 (2003).Google Scholar
- Christel Baier, Joost-Pieter Katoen, and Kim Guldstrand Larsen. 2008. Principles of Model Checking. MIT Press. Google ScholarDigital Library
- David Basin, Srđan Krstić, and Dmitriy Traytel. 2017. Almost event-rate independent monitoring of metric dynamic logic. In Runtime Verification. Springer, 85--102. Google ScholarDigital Library
- Béatrice Bérard, Michel Bidoit, Alain Finkel, François Laroussinie, Antoine Petit, Laure Petrucci, and Philippe Schnoebelen. 2013. Systems and Software Verification: Model-checking Techniques and Tools. Springer Science 8 Business Media.Google Scholar
- Marcello M. Bersani, Matteo Rossi, and Pierluigi San Pietro. 2015. An SMT-based approach to satisfiability checking of MITL. Inf. Comput. 245 (2015), 72--97. Google ScholarDigital Library
- Patricia Bouyer, Uli Fahrenberg, Kim G. Larsen, Nicolas Markey, Joël Ouaknine, and James Worrell. 2018. Model checking real-time systems. In Clarke et al. {28}, Chapter 29, 1001--1046.Google Scholar
- Thomas Brihaye, Morgane Estiévenart, and Gilles Geeraerts. 2013. On MITL and alternating timed automata. In Formal Modeling and Analysis of Timed Systems. 47--61. Google ScholarDigital Library
- Thomas Brihaye, Morgane Estiévenart, and Gilles Geeraerts. 2014. On MITL and alternating timed automata over infinite words. In Formal Modeling and Analysis of Timed Systems. 69--84. Google ScholarDigital Library
- Thomas Brihaye, Gilles Geeraerts, Hsi-Ming Ho, and Benjamin Monmege. 2017. Timed-automata-based verification of MITL over signals. In Proceedings of the 24th International Symposium on Temporal Representation and Reasoning (TIME’17). 7:1--7:19.Google Scholar
- Thomas Brihaye, Gilles Geeraerts, Hsi-Ming Ho, and Benjamin Monmege. 2017. MightyL: A compositional translation from MITL to timed automata. In Computer Aided Verification. 421--440.Google Scholar
- Janusz A. Brzozowski and Ernst Leiss. 1980. On equations for regular languages, finite automata, and sequential networks. Theor. Comput. Sci. 10, 1 (1980), 19--35.Google ScholarCross Ref
- Jerry R. Burch, Edmund M. Clarke, Kenneth L. McMillan, David L. Dill, and Lain-Jinn Hwang. 1992. Symbolic model checking: 10<sup>20</sup> states and beyond. Inf. Comput. 98, 2 (1992), 142--170. Google ScholarDigital Library
- Ashok K. Chandra and Larry J. Stockmeyer. 1976. Alternation. In Proceedings of the 17th Annual Symposium on Foundations of Computer Science. IEEE, 98--108. Google ScholarDigital Library
- Alessandro Cimatti, Marco Roveri, Simone Semprini, and Stefano Tonetta. 2006. From PSL to NBA: A modular symbolic encoding. In Proceedings of the Formal Methods in Computer Aided Design (FMCAD’06). IEEE, 125--133. Google ScholarDigital Library
- Edmund Clarke, Orna Grumberg, and Kiyoharu Hamaguchi. 1994. Another look at LTL model checking. In Proceedings of the International Conference on Computer Aided Verification. Springer, 415--427. Google ScholarDigital Library
- Edmund M. Clarke and E. Allen Emerson. 1981. Design and synthesis of synchronization skeletons using branching time temporal logic. In Workshop on Logic of Programs. Springer, 52--71. Google ScholarDigital Library
- Edmund M. Clarke, Orna Grumberg, and Doron Peled. 1999. Model Checking. MIT Press. Google ScholarDigital Library
- Edmund M. Clarke, Thomas A. Henzinger, Helmut Veith, and Roderick Bloem (Eds.). 2018. Handbook of Model Checking. Springer International Publishing. Google ScholarDigital Library
- Deepak D’Souza and R. Matteplackel. 2013. A Clock-optimal Hierarchical Monitoring Automaton Construction for MITL. Technical Report.Google Scholar
- Deepak D’Souza and Nicolas Tabareau. 2004. On timed automata with input-determined guards. In Formal Techniques, Modelling and Analysis of Timed and Fault-Tolerant Systems. Springer, 68--83.Google Scholar
- Cindy Eisner and Dana Fisman. 2018. Functional specification of hardware via temporal logic. Handbook of Model Checking (2018), 795--829.Google Scholar
- Thomas Ferrère, Oded Maler, and Dejan Ničković. 2015. Trace diagnostics using temporal implicants. In Proceedings of the International Symposium on Automated Technology for Verification and Analysis. Springer, 241--258.Google ScholarCross Ref
- Paul Gastin and Denis Oddoux. 2001. Fast LTL to Büchi automata translation. In Proceedings of the International Conference on Computer Aided Verification. Springer, 53--65. Google ScholarDigital Library
- Rob Gerth, Doron Peled, Moshe Y. Vardi, and Pierre Wolper. 1995. Simple on-the-fly automatic verification of linear temporal logic. In Protocol Specification, Testing and Verification XV. Springer, 3--18. Google ScholarDigital Library
- Dimitra Giannakopoulou and Flavio Lerda. 2002. From states to transitions: Improving translation of LTL formulae to Büchi automata. In Proceedings of the International Conference on Formal Techniques for Networked and Distributed Systems. Springer, 308--326. Google ScholarDigital Library
- Thomas A. Henzinger. 1998. It’s about time: Real-time logics reviewed. In Proceedings of the International Conference on Concurrency Theory. Springer, 439--454. Google ScholarDigital Library
- Thomas A. Henzinger, J.-F. Raskin, and P.-Y. Schobbens. 1998. The regular real-time languages. In Automata, Languages and Programming. Springer, 580--591. Google ScholarDigital Library
- Yoram Hirshfeld and Alexander Rabinovich. 1999. Quantitative temporal logic. In Proceedings of the International Workshop on Computer Science Logic. Springer, 172--187. Google ScholarDigital Library
- Yoram Hirshfeld and Alexander Rabinovich. 2004. Logics for real time: Decidability and complexity. Fundam. Inf. 62, 1 (2004), 1--28. Google ScholarDigital Library
- Yoram Hirshfeld and Alexander Rabinovich. 2005. Timer formulas and decidable metric temporal logic. Inf. Comput. 198, 2 (2005), 148--178. Google ScholarDigital Library
- Yoram Hirshfeld and Alexander Rabinovich. 2006. An expressive temporal logic for real time. In Mathematical Foundations of Computer Science 2006. Springer, 492--504. Google ScholarDigital Library
- Yoram Hirshfeld and Alexander Rabinovich. 2006. Expressiveness of metric modalities for continuous time. In Computer Science--Theory and Applications. Springer, 211--220. Google ScholarDigital Library
- Michael Huth and Mark Ryan. 2004. Logic in Computer Science: Modelling and Reasoning About Systems. Cambridge University Press. Google ScholarDigital Library
- Yonit Kesten and Amir Pnueli. 2005. A compositional approach to CTL* verification. Theor. Comput. Sci. 331, 2--3 (2005), 397--428. Google ScholarDigital Library
- Yonit Kesten, Amir Pnueli, and Li-on Raviv. 1998. Algorithmic verification of linear temporal logic specifications. In Proceedings of the International Colloquium on Automata, Languages, and Programming. Springer, 1--16. Google ScholarDigital Library
- Roland Kindermann, Tommi A. Junttila, and Ilkka Niemelä. 2013. Bounded model checking of an MITL fragment for timed automata. In Proceedings of the 13th International Conference on Application of Concurrency to System Design (ACSD’13). 216--225. Google ScholarDigital Library
- Dileep Raghunath Kini, Shankara Narayanan Krishna, and Paritosh K. Pandya. 2011. On construction of safety signal automata for MITL{U,S} using temporal projections. In Proceedings of the 9th International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS’11). 225--239. Google ScholarDigital Library
- Ron Koymans. 1990. Specifying real-time properties with metric temporal logic. Real-time Syst. 2, 4 (1990), 255--299. Google ScholarDigital Library
- Ron Koymans, Jan Vytopil, and Willem P. de Roever. 1983. Real-time programming and asynchronous message passing. In Proceedings of the 2nd Annual ACM Symposium on Principles of Distributed Computing. ACM, 187--197. Google ScholarDigital Library
- Moez Krichen and Stavros Tripakis. 2009. Conformance testing for real-time systems. Formal Methods Syst. Des. 34, 3 (2009), 238--304. Google ScholarDigital Library
- Kim G. Larsen, Paul Pettersson, and Wang Yi. 1997. UPPAAL in a nutshell. Int. J. Softw. Tools Technol. Transf. 1, 1--2 (1997), 134--152. Google ScholarDigital Library
- Oded Maler and Dejan Nickovic. 2004. Monitoring temporal properties of continuous signals. In Proceedings of the Joint Conference on Formal Modelling and Analysis of Timed Systems and Formal Techniques in Real-Time and Fault Tolerant System (FORMATS/FTRTFT’04). 152--166.Google ScholarCross Ref
- Oded Maler, Dejan Nickovic, and Amir Pnueli. 2005. Real time temporal logic: Past, present, future. In Formal Modeling and Analysis of Timed Systems. Springer, 2--16. Google ScholarDigital Library
- Oded Maler, Dejan Nickovic, and Amir Pnueli. 2006. From MITL to timed automata. In Formal Modeling and Analysis of Timed Systems. Springer, 274--289. Google ScholarDigital Library
- Oded Maler, Dejan Nickovic, and Amir Pnueli. 2008. Checking temporal properties of discrete, timed and continuous behaviors. In Pillars of Computer Science. 475--505. Google ScholarDigital Library
- Oded Maler and Amir Pnueli. 2004. On recognizable timed languages. In Proceedings of the International Conference on Foundations of Software Science and Computation Structures. Springer, 348--362.Google ScholarCross Ref
- Zohar Manna and Amir Pnueli. 1988. The anchored version of the temporal framework. In Proceedings of the Workshop/School/Symposium of the REX Project. Springer, 201--284. Google ScholarDigital Library
- Zohar Manna and Amir Pnueli. 2012. The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer Science 8 Business Media. Google ScholarDigital Library
- Zohar Manna and Amir Pnueli. 2012. Temporal Verification of Reactive Systems: Safety. Springer Science 8 Business Media. Google ScholarDigital Library
- Nicolas Markey. 2003. Temporal logic with past is exponentially more succinct. EATCS Bull. 79 (2003), 122--128.Google Scholar
- Max Michel. 1984. Algebre de machines et logique temporelle. In Proceedings of the Annual Symposium on Theoretical Aspects of Computer Science. Springer, 287--298. Google ScholarDigital Library
- Max Michel. 1985. Computation of temporal operators. Logique Anal. 28, 110/111 (1985), 137--152.Google Scholar
- Satoru Miyano and Takeshi Hayashi. 1984. Alternating finite automata on ω-words. Theor. Comput. Sci. 32, 3 (1984), 321--330.Google ScholarCross Ref
- Dejan Nickovic. 2008. Checking Timed and Hybrid Properties: Theory and Applications. Ph.D. Dissertation. Université Joseph Fourier, Grenoble, France.Google Scholar
- Maurice Nivat and Dominique Perrin. 1982. Ensembles reconnaissables de mots bi-infinis. In Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing. ACM, 47--59. Google ScholarDigital Library
- Joël Ouaknine and James Worrell. 2005. On the decidability of metric temporal logic. In Logic in Computer Science. IEEE, 188--197. Google ScholarDigital Library
- Sam Owre, John M. Rushby, and Natarajan Shankar. 1992. PVS: A prototype verification system. In Proceedings of the International Conference on Automated Deduction. Springer, 748--752. Google ScholarDigital Library
- Amir Pnueli and Aleksandr Zaks. 2006. PSL model checking and run-time verification via testers. In Proceedings of the International Symposium on Formal Methods. Springer, 573--586. Google ScholarDigital Library
- Amir Pnueli and Aleksandr Zaks. 2008. On the merits of temporal testers. In 25 Years of Model Checking. Springer, 172--195. Google ScholarDigital Library
- Jean-Pierre Queille and Joseph Sifakis. 1982. Specification and verification of concurrent systems in CESAR. In Proceedings of the International Symposium on Programming. Springer, 337--351. Google ScholarDigital Library
- Jean-François Raskin and Pierre-Yves Schobbens. 1997. State clock logic: A decidable real-time logic. In Proceedings of the International Workshop on Hybrid and Real-Time Systems. Springer, 33--47. Google ScholarDigital Library
- Nima Roohi and Mahesh Viswanathan. 2018. Revisiting MITL to fix decision procedures. In Proceedings of the International Conference on Verification, Model Checking, and Abstract Interpretation. Springer, 474--494.Google ScholarCross Ref
- Fabio Somenzi and Roderick Bloem. 2000. Efficient Büchi automata from LTL formulae. In Proceedings of the International Conference on Computer Aided Verification. Springer, 248--263. Google ScholarDigital Library
- Boris A. Trakhtenbrot. 2004. Understanding basic automata theory in the continuous time setting. Fundam. Inf. 62, 1 (2004), 69--121. Google ScholarDigital Library
- Moshe Y. Vardi. 1995. Alternating automata and program verification. In Computer Science Today. Springer, 471--485.Google Scholar
- Moshe Y. Vardi and Pierre Wolper. 1986. An automata-theoretic approach to automatic program verification. In Proceedings of the 1st Symposium on Logic in Computer Science. IEEE Computer Society, 322--331.Google Scholar
- Thomas Wilke. 1994. Specifying timed state sequences in powerful decidable logics and timed automata. In Formal Techniques in Real-Time and Fault-Tolerant Systems. Springer, 694--715. Google ScholarDigital Library
Index Terms
- From Real-time Logic to Timed Automata
Recommendations
Interrupt Timed Automata: verification and expressiveness
We introduce the class of Interrupt Timed Automata (ITA), a subclass of hybrid automata well suited to the description of timed multi-task systems with interruptions in a single processor environment.
While the reachability problem is undecidable for ...
Past pushdown timed automata and safety verification
Implementation and application automataWe consider past pushdown timed automata that are discrete pushdown timed automata with past formulas as enabling conditions. Using past formulas allows a past pushdown timed automaton to access the past values of the finite state variables in the ...
Context-free timed formalisms: Robust automata and linear temporal logics
AbstractThe paper focuses on automata and linear temporal logics for real-time pushdown reactive systems bridging tractable formalisms specialized for expressing separately dense-time real-time properties and context-free properties though ...
Comments