Abstract
In the context of real-time systems, Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent and widely used extensions of Linear Temporal Logic. In this paper, we examine the possibility of using MTL and TPTL to specify properties about classes of non-monotonic data languages over the natural numbers. Words in this class may model the behaviour of, e.g., one-counter machines. We proved, however, that the satisfiability problem for many reasonably expressive fragments of MTL and TPTL is undecidable, and thus the use of these logics is rather limited. On the positive side we prove that satisfiability for the existential fragment of TPTL is NP-complete.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alur, R., Henzinger, T.A.: Real-time logics: Complexity and expressiveness. Inf. Comput. 104(1), 35–77 (1993)
Alur, R., Henzinger, T.A.: A really temporal logic. J. ACM 41(1), 181–204 (1994)
Bojanczyk, M., David, C., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data words. ACM Trans. Comput. Log. 12(4), 27 (2011)
Bollig, B.: An automaton over data words that captures EMSO logic. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 171–186. Springer, Heidelberg (2011)
Bollig, B., Cyriac, A., Gastin, P., Narayan Kumar, K.: Model checking languages of data words. In: Birkedal, L. (ed.) FOSSACS 2012. LNCS, vol. 7213, pp. 391–405. Springer, Heidelberg (2012)
Bouyer, P.: A logical characterization of data languages. Inf. Process. Lett. 84(2), 75–85 (2002)
Bouyer, P., Chevalier, F., Markey, N.: On the expressiveness of TPTL and MTL. Inf. Comput. 208(2), 97–116 (2010)
Carapelle, C., Feng, S., Fernandez Gil, O., Quaas, K.: Ehrenfeucht-Fraïssé games for TPTL and MTL over data words, http://arxiv.org/abs/1311.6250
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, Second Edition, 2nd edn. The MIT Press and McGraw-Hill Book Company (2001)
Demri, S., Lazic, R.: LTL with the freeze quantifier and register automata. ACM Trans. Comput. Log. 10(3) (2009)
Demri, S., Lazić, R.S., Sangnier, A.: Model checking Freeze LTL over one-counter automata. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 490–504. Springer, Heidelberg (2008)
Figueira, D., Segoufin, L.: Future-looking logics on data words and trees. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 331–343. Springer, Heidelberg (2009)
Jaffar, J., Maher, M.J., Stuckey, P.J., Yap, R.H.C.: Beyond finite domains. In: Borning, A. (ed.) PPCP 1994. LNCS, vol. 874, pp. 86–94. Springer, Heidelberg (1994)
Minsky, M.L.: Recursive unsolvability of Post’s problem of “tag” and other topics in theory of Turing machines. Annals of Mathematics 74(3), 437–455 (1961)
Ouaknine, J., Worrell, J.B.: 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)
Ouaknine, J., Worrell, J.: On the decidability and complexity of metric temporal logic over finite words. Logical Methods in Computer Science 3(1) (2007)
Quaas, K.: Model checking metric temporal logic over automata with one counter. In: Dediu, A.-H., Martín-Vide, C., Truthe, B. (eds.) LATA 2013. LNCS, vol. 7810, pp. 468–479. Springer, Heidelberg (2013)
Segoufin, L.: Automata and logics for words and trees over an infinite alphabet. In: Ésik, Z. (ed.) CSL 2006. LNCS, vol. 4207, pp. 41–57. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Carapelle, C., Feng, S., Fernández Gil, O., Quaas, K. (2014). Satisfiability for MTL and TPTL over Non-monotonic Data Words. In: Dediu, AH., Martín-Vide, C., Sierra-Rodríguez, JL., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2014. Lecture Notes in Computer Science, vol 8370. Springer, Cham. https://doi.org/10.1007/978-3-319-04921-2_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-04921-2_20
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04920-5
Online ISBN: 978-3-319-04921-2
eBook Packages: Computer ScienceComputer Science (R0)