A standard bridge between automata theory and logic is provided by the notion of characteristic formula. This paper investigates this problem for the class of event-recording automata (ERA), a subclass of timed automata in which clocks are associated with actions and that enjoys very good closure properties. We first study the problem of expressing characteristic formulae for ERA in Event-Recording Logic (ERL ), a logic introduced by Sorea to express event-based timed specifications. We prove that the construction proposed by Sorea for ERA without invariants is incorrect. More generally, we prove that timed bisimilarity cannot in general be expressed in ERL for the class of ERA , and study under which conditions on ERA it can be. Then, we introduce the logic WTμ , a new logic for event-based timed specifications closer to the timed logic ℒν that was introduced by Laroussinie, Larsen and Weise. We prove that it is strictly more expressive than ERL , and that its model-checking problem against ERA is EXPTIME -complete. Finally, we provide characteristic formulae constructions in WTμ for characterizing the general class of ERA up to timed (bi)similarity and study the complexity issues.
Mots clés : timed logic, bisimulation, event-clock automata
@article{ITA_2013__47_1_69_0,
author = {Nguena Timo, Omer Landry and Reynier, Pierre-Alain},
title = {On characteristic formulae for {Event-Recording} {Automata}},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {69--96},
publisher = {EDP-Sciences},
volume = {47},
number = {1},
year = {2013},
doi = {10.1051/ita/2012029},
mrnumber = {3072311},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ita/2012029/}
}
TY - JOUR AU - Nguena Timo, Omer Landry AU - Reynier, Pierre-Alain TI - On characteristic formulae for Event-Recording Automata JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2013 SP - 69 EP - 96 VL - 47 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2012029/ DO - 10.1051/ita/2012029 LA - en ID - ITA_2013__47_1_69_0 ER -
%0 Journal Article %A Nguena Timo, Omer Landry %A Reynier, Pierre-Alain %T On characteristic formulae for Event-Recording Automata %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2013 %P 69-96 %V 47 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2012029/ %R 10.1051/ita/2012029 %G en %F ITA_2013__47_1_69_0
Nguena Timo, Omer Landry; Reynier, Pierre-Alain. On characteristic formulae for Event-Recording Automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 47 (2013) no. 1, pp. 69-96. doi : 10.1051/ita/2012029. http://archive.numdam.org/articles/10.1051/ita/2012029/
[1] , , and , Characteristic formulae for timed automata. Theor. Inf. Appl. 34 (2000) 565-584. | Numdam | MR | Zbl
[2] and , Is your model-checker on time? On the complexity of model checking for timed modal logics. J. Log. Algebr. Program. 52-53 (2002) 7-51. | MR | Zbl
[3] and , A theory of timed automata, Theor. Comput. Sci. 126 (1994) 183-235. | MR | Zbl
[4] , and , Event-clock automata: A determinizable class of timed automata. Theor. Comput. Sci. 211 (1999) 253-273. | MR | Zbl
[5] , Definable operation in general algebras, and the theory of automata and flowcharts, in Programming Languages and Their Definition, edited by C.B. Jones. Springer. Lect. Notes Comput. Sci. 177 (1984) 30-55. | Zbl
[6] , and , Timed modal logics for real-time systems: Specification, verification and control. J. Logic Lang. Inform. 20 (2011) 169-203. | MR | Zbl
[7] , and , Alternation. J. ACM 28 (1981) 114-133. | MR | Zbl
[8] and , A linear-time model-checking algorithm for the alternation-free modal mu-calculus. Form. Method Syst. Design 2 (1993) 121-147. | MR | Zbl
[9] , A logical characterisation of event clock automata. Int. J. Found. Comput. Sci. 14 (2003) 625-640. | MR | Zbl
[10] , , and , Symbolic model-checking for real-time systems. Inf. Comput. 111 (1994) 193-244. | MR | Zbl
[11] and , CMC : A tool for compositional model-checking of real-time systems, in Proc. of IFIP TC6 WG6.1 Joint Conf. on Formal Description Techniques for Distributed Systems and Communication Protocols, FORTE XI, and Protocol Specification, Testing and Verification, PSTV XVIII (Paris, Nov. 1998), edited by S. Budkowski, A.R. Cavalli and E. Najm, Kluwer, IFIP Conference Proceedings 135 (1998) 439-456.
[12] , and , From timed automata to logic - and back, in Proc. of 20th Int. Symp. on Mathematical Foundations of Computer Science, MFCS '95 (Prague, Aug./Sept. 1995), edited by J. Wiedermann and P. Hájek, Springer. Lect. Notes Comput. Sci. 969 (1995) 529-539. | MR | Zbl
[13] , Synthesis for a Weak Real-Time Logic, Ph.D. thesis, Université Bordeaux 1 (2009).
[14] and , On characteristic formulae for event-recording automata, in Proc. of 6th Workshop on Fixed Points in Computer Science, FICS '09 (Coimbra, Sept. 2009), edited by R. Matthes and T. Uustalu. Inst. of Cybernetics, Tallinn (2009) 70-78.
[15] and , The logic of event clocks - decidability, complexity and expressiveness. J. Autom. Lang. Comb. 4 (1999) 247-286. | MR | Zbl
[16] , Bisimulation : From the origins to today, in Proc. of 19th Ann. IEEE Symp. on Logic in Computer Science, LICS '04 (Turku, July 2004). IEEE CS Press (2004) 298-302.
[17] , A decidable fixpoint logic for time-outs, in Proc. of 13th Int. Conf. on Concurrency Theory, CONCUR 2002 (Brno, Aug. 2002), edited by L. Brim, P. Jancar, M. Křetínský and A. Kučera, Springer. Lect. Notes Comput. Sci. 2421 (2002) 255-271. | MR | Zbl
[18] , Verification of Real-Time Systems through Lazy Approximations, Ph.D. thesis, Universität Ulm (2004).
[19] , Languages, automata and logic, in Handbook of Formal Languages, Beyond Words, edited by G. Rozenberg and A. Salomaa. Springer 3 (1997) 389-455. | MR | Zbl
Cité par Sources :
