On the Expressiveness of MTL with Past Operators
We compare the expressiveness of variants of Metric Temporal Logic (MTL) obtained by adding the past operators ‘S’ and ‘S I ’. We consider these variants under the “pointwise” and “continuous” interpretations over both finite and infinite models. Among other results, we show that for each of these variants the continuous version is strictly more expressive than the pointwise version. We also prove a counter-freeness result for MTL which helps to carry over some results from  for the case of infinite models to the case of finite models.
KeywordsTemporal Logic Stability Point Regular Language Past Operator Periodic Sequence
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- 2.Alur, R., Henzinger, T.A.: Real-time Logics: Complexity and Expressiveness. In: LICS, pp. 390–401. IEEE Computer Society, Los Alamitos (1990)Google Scholar
- 4.D’Souza, D., Prabhakar, P.: On the expressiveness of MTL in the pointwise and continuous semantics. In: Formal Methods Letters, Software Tools for Technology Transfer (to appear)Google Scholar
- 5.Kamp, J.A.W.: Tense Logic and the Theory of Linear Order. PhD thesis, University of California, Los Angeles, California (1968)Google Scholar
- 7.McNaughton, R., Papert, S.A.: Counter-Free Automata (M.I.T. research monograph no. 65). MIT Press, Cambridge (1971)Google Scholar
- 8.Ouaknine, J., Worrell, J.: On the Decidability of Metric Temporal Logic. In: LICS, pp. 188–197. IEEE Computer Society, Los Alamitos (2005)Google Scholar
- 10.Prabhakar, P., D’Souza, D.: On the expressiveness of MTL with past operators. Technical Report IISc-CSA-TR-2006-5, Indian Institute of Science, Bangalore 560012, India (May 2006), URL: http://archive.csa.iisc.ernet.in/TR/2006/5/