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2017 | OriginalPaper | Buchkapitel

Timed Temporal Logics

verfasst von : Patricia Bouyer, François Laroussinie, Nicolas Markey, Joël Ouaknine, James Worrell

Erschienen in: Models, Algorithms, Logics and Tools

Verlag: Springer International Publishing

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Abstract

Since the early 1990’s, classical temporal logics have been extended with timing constraints. While temporal logics only express contraints on the order of events, their timed extensions can add quantitative constraints on delays between those events. We survey expressiveness and algorithmic results on those logics, and discuss semantic choices that may look unimportant but do have an impact on the questions we consider.

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Fußnoten
1
Zero-delay transitions are not allowed here, but could be included without affecting the presented results.
 
2
Rational bounds could be considered at the expense of scaling all constants by an appropriate factor.
 
3
That is, for every \(a \in \varSigma \), \(f_{\text {inter}}(a,\bullet ) = a_1\) and \(f_{\text {inter}}(\bullet ,a)=a_2\).
 
4
As shown in [30] this property fails without the assumption of finite variability.
 
Literatur
4.
Zurück zum Zitat Alur, R.: Techniques for automatic verification of real-time systems. Ph.D. thesis, Stanford University, Palo Alto, California, USA (1991) Alur, R.: Techniques for automatic verification of real-time systems. Ph.D. thesis, Stanford University, Palo Alto, California, USA (1991)
9.
Zurück zum Zitat Alur, R., Henzinger, T.A.: Logics and models of real time: a survey. In: Bakker, J.W., Huizing, C., Roever, W.P., Rozenberg, G. (eds.) REX 1991. LNCS, vol. 600, pp. 74–106. Springer, Heidelberg (1992). doi:10.1007/BFb0031988 CrossRef Alur, R., Henzinger, T.A.: Logics and models of real time: a survey. In: Bakker, J.W., Huizing, C., Roever, W.P., Rozenberg, G. (eds.) REX 1991. LNCS, vol. 600, pp. 74–106. Springer, Heidelberg (1992). doi:10.​1007/​BFb0031988 CrossRef
14.
Zurück zum Zitat Bouyer, P., Chevalier, F., Markey, N.: On the expressiveness of TPTL and MTL. In: Sarukkai, S., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 432–443. Springer, Heidelberg (2005). doi:10.1007/11590156_35 CrossRef Bouyer, P., Chevalier, F., Markey, N.: On the expressiveness of TPTL and MTL. In: Sarukkai, S., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 432–443. Springer, Heidelberg (2005). doi:10.​1007/​11590156_​35 CrossRef
16.
Zurück zum Zitat Brihaye, T., Estiévenart, M., Geeraerts, G., Ho, H.-M., Monmege, B., Sznajder, N.: Real-time synthesis is hard!. In: Fränzle, M., Markey, N. (eds.) FORMATS 2016. LNCS, vol. 9884, pp. 105–120. Springer, Cham (2016). doi:10.1007/978-3-319-44878-7_7 CrossRef Brihaye, T., Estiévenart, M., Geeraerts, G., Ho, H.-M., Monmege, B., Sznajder, N.: Real-time synthesis is hard!. In: Fränzle, M., Markey, N. (eds.) FORMATS 2016. LNCS, vol. 9884, pp. 105–120. Springer, Cham (2016). doi:10.​1007/​978-3-319-44878-7_​7 CrossRef
17.
Zurück zum Zitat Brihaye, T., Laroussinie, F., Markey, N., Oreiby, G.: Timed concurrent game structures. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 445–459. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74407-8_30 CrossRef Brihaye, T., Laroussinie, F., Markey, N., Oreiby, G.: Timed concurrent game structures. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 445–459. Springer, Heidelberg (2007). doi:10.​1007/​978-3-540-74407-8_​30 CrossRef
18.
Zurück zum Zitat Čerāns, K., Godskesen, J.C., Larsen, K.G.: Timed modal specification — theory and tools. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 253–267. Springer, Heidelberg (1993). doi:10.1007/3-540-56922-7_21 CrossRef Čerāns, K., Godskesen, J.C., Larsen, K.G.: Timed modal specification — theory and tools. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 253–267. Springer, Heidelberg (1993). doi:10.​1007/​3-540-56922-7_​21 CrossRef
19.
Zurück zum Zitat Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982). doi:10.1007/BFb0025774 CrossRef Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982). doi:10.​1007/​BFb0025774 CrossRef
21.
Zurück zum Zitat Daws, C., Olivero, A., Tripakis, S., Yovine, S.: The tool Kronos. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol. 1066, pp. 208–219. Springer, Heidelberg (1996). doi:10.1007/BFb0020947 CrossRef Daws, C., Olivero, A., Tripakis, S., Yovine, S.: The tool Kronos. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol. 1066, pp. 208–219. Springer, Heidelberg (1996). doi:10.​1007/​BFb0020947 CrossRef
23.
Zurück zum Zitat Furia, C.A., Rossi, M.: On the expressiveness of MTL variants over dense time. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 163–178. Springer, Heidelberg (2007). doi:10.1007/978-3-540-75454-1_13 CrossRef Furia, C.A., Rossi, M.: On the expressiveness of MTL variants over dense time. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 163–178. Springer, Heidelberg (2007). doi:10.​1007/​978-3-540-75454-1_​13 CrossRef
24.
Zurück zum Zitat Gabbay, D.M.: Expressive functional completeness in tense logic (preliminary report). In: Mönnich, U. (ed.) SYLI, vol. 147, pp. 91–117. Springer, Heidelberg (1981). doi:10.1007/978-94-009-8384-7_4 Gabbay, D.M.: Expressive functional completeness in tense logic (preliminary report). In: Mönnich, U. (ed.) SYLI, vol. 147, pp. 91–117. Springer, Heidelberg (1981). doi:10.​1007/​978-94-009-8384-7_​4
26.
Zurück zum Zitat Godskesen, J.C., Larsen, K.G., Skou, A.: Automatic verification of real-time systems using epsilon. In: IFIP Conference Proceedings on PSTV 1994, vol. 1, pp. 323–330. Chapman & Hall (1995) Godskesen, J.C., Larsen, K.G., Skou, A.: Automatic verification of real-time systems using epsilon. In: IFIP Conference Proceedings on PSTV 1994, vol. 1, pp. 323–330. Chapman & Hall (1995)
33.
Zurück zum Zitat Jaziri, S., Larsen, K.G., Mardare, R., Xue, B.: Adequacy and complete axiomatization for timed modal logic. In: Proceedings of the 30th Conference on Mathematical Foundations of Programming Semantics (MFPS 2014), ENTCS, vol. 308, pp. 183–210. Elsevier Science Publishers (2014) Jaziri, S., Larsen, K.G., Mardare, R., Xue, B.: Adequacy and complete axiomatization for timed modal logic. In: Proceedings of the 30th Conference on Mathematical Foundations of Programming Semantics (MFPS 2014), ENTCS, vol. 308, pp. 183–210. Elsevier Science Publishers (2014)
34.
Zurück zum Zitat Kamp, J.A.W.: Tense logic and the theory of linear order. Ph.D. thesis, Computer Science Department, University of California at Los Angeles, USA (1968) Kamp, J.A.W.: Tense logic and the theory of linear order. Ph.D. thesis, Computer Science Department, University of California at Los Angeles, USA (1968)
36.
37.
Zurück zum Zitat Torre, S.L., Napoli, M.: A decidable dense branching-time temporal logic. In: Kapoor, S., Prasad, S. (eds.) FSTTCS 2000. LNCS, vol. 1974, pp. 139–150. Springer, Heidelberg (2000). doi:10.1007/3-540-44450-5_11 CrossRef Torre, S.L., Napoli, M.: A decidable dense branching-time temporal logic. In: Kapoor, S., Prasad, S. (eds.) FSTTCS 2000. LNCS, vol. 1974, pp. 139–150. Springer, Heidelberg (2000). doi:10.​1007/​3-540-44450-5_​11 CrossRef
38.
Zurück zum Zitat Laroussinie, F., Larsen, K.G.: CMC: a tool for compositional model-checking of real-time systems. In: IFIP Conference Proceedings on FORTE/PSTV 1998, vol. 135, pp. 439–456. Kluwer Academic (1998) Laroussinie, F., Larsen, K.G.: CMC: a tool for compositional model-checking of real-time systems. In: IFIP Conference Proceedings on FORTE/PSTV 1998, vol. 135, pp. 439–456. Kluwer Academic (1998)
39.
Zurück zum Zitat Laroussinie, F., Larsen, K.G., Weise, C.: From timed automata to logic — and back. In: Wiedermann, J., Hájek, P. (eds.) MFCS 1995. LNCS, vol. 969, pp. 529–539. Springer, Heidelberg (1995). doi:10.1007/3-540-60246-1_158 CrossRef Laroussinie, F., Larsen, K.G., Weise, C.: From timed automata to logic — and back. In: Wiedermann, J., Hájek, P. (eds.) MFCS 1995. LNCS, vol. 969, pp. 529–539. Springer, Heidelberg (1995). doi:10.​1007/​3-540-60246-1_​158 CrossRef
43.
Zurück zum Zitat Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30206-3_12 CrossRef Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004). doi:10.​1007/​978-3-540-30206-3_​12 CrossRef
44.
Zurück zum Zitat Milner, R.: Communication and Concurrency, Prentice Hall International Series in Computer Science. Prentice Hall Int., Upper Saddle River (1989)MATH Milner, R.: Communication and Concurrency, Prentice Hall International Series in Computer Science. Prentice Hall Int., Upper Saddle River (1989)MATH
45.
47.
Zurück zum Zitat Ouaknine, J., Worrell, J.: On metric temporal logic and faulty turing machines. In: Aceto, L., Ingólfsdóttir, A. (eds.) FoSSaCS 2006. LNCS, vol. 3921, pp. 217–230. Springer, Heidelberg (2006). doi:10.1007/11690634_15 CrossRef Ouaknine, J., Worrell, J.: On metric temporal logic and faulty turing machines. In: Aceto, L., Ingólfsdóttir, A. (eds.) FoSSaCS 2006. LNCS, vol. 3921, pp. 217–230. Springer, Heidelberg (2006). doi:10.​1007/​11690634_​15 CrossRef
48.
Zurück zum Zitat Ouaknine, J., Worrell, J.: Safety metric temporal logic is fully decidable. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 411–425. Springer, Heidelberg (2006). doi:10.1007/11691372_27 CrossRef Ouaknine, J., Worrell, J.: Safety metric temporal logic is fully decidable. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 411–425. Springer, Heidelberg (2006). doi:10.​1007/​11691372_​27 CrossRef
49.
Zurück zum Zitat Pandya, P.K., Shah, S.S.: On expressive powers of timed logics: comparing boundedness, non-punctuality, and deterministic freezing. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 60–75. Springer, Heidelberg (2011). doi:10.1007/978-3-642-23217-6_5 CrossRef Pandya, P.K., Shah, S.S.: On expressive powers of timed logics: comparing boundedness, non-punctuality, and deterministic freezing. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 60–75. Springer, Heidelberg (2011). doi:10.​1007/​978-3-642-23217-6_​5 CrossRef
51.
Zurück zum Zitat Queille, J.P., Sifakis, J.: Specification and verification of concurrent systems in CESAR. In: Dezani-Ciancaglini, M., Montanari, U. (eds.) Programming 1982. LNCS, vol. 137, pp. 337–351. Springer, Heidelberg (1982). doi:10.1007/3-540-11494-7_22 CrossRef Queille, J.P., Sifakis, J.: Specification and verification of concurrent systems in CESAR. In: Dezani-Ciancaglini, M., Montanari, U. (eds.) Programming 1982. LNCS, vol. 137, pp. 337–351. Springer, Heidelberg (1982). doi:10.​1007/​3-540-11494-7_​22 CrossRef
52.
Zurück zum Zitat Raskin, J.-F.: Logics, automata and classical theories for deciding real time. Thèse de doctorat, FUNDP, Namur, Belgium (1999) Raskin, J.-F.: Logics, automata and classical theories for deciding real time. Thèse de doctorat, FUNDP, Namur, Belgium (1999)
54.
Zurück zum Zitat Yi, W.: CCS + time = an interleaving model for real time systems. In: Albert, J.L., Monien, B., Artalejo, M.R. (eds.) ICALP 1991. LNCS, vol. 510, pp. 217–228. Springer, Heidelberg (1991). doi:10.1007/3-540-54233-7_136 CrossRef Yi, W.: CCS + time = an interleaving model for real time systems. In: Albert, J.L., Monien, B., Artalejo, M.R. (eds.) ICALP 1991. LNCS, vol. 510, pp. 217–228. Springer, Heidelberg (1991). doi:10.​1007/​3-540-54233-7_​136 CrossRef
Metadaten
Titel
Timed Temporal Logics
verfasst von
Patricia Bouyer
François Laroussinie
Nicolas Markey
Joël Ouaknine
James Worrell
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-63121-9_11