Abstract
In this note we discuss the expressive power of μ-calculi. We concentrate on those that are extensions of propositional modal logics with a fixpoint operator. The objective is to try to match the expressive power of monadic second-order logic. We consider different kinds of models: from trees and transition systems up to traces and timed systems.
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References
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)
Alur, R., Fix, L., Henzinger, T.: Event-clock automata: A determinizable class of timed automata. Theoretical Computer Science 204 (1997)
Arnold, A., Niwiñski, D.: The Rudiments of the Mu-Calculus. Studies in Logic, vol. 146. North-Holland, Amsterdam (2001)
Ebinger, W.: Logical definability of trace languages. In: Diekert, V., Rozenberg, G. (eds.) The Book of Traces, pp. 382–390. World Scientific, Singapore (1995)
Gastin, P., Petit, A.: Infninite traces. In: Diekert, V., Rozenberg, G. (eds.) The Book of Traces, World Scientific, Singapore (1995)
Janin, D., Walukiewicz, I.: On the expressive completeness of the propositional mu-calculus with respect to monadic second order logic. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 263–277. Springer, Heidelberg (1996)
Lasota, S., Walukiewicz, I.: Alternating timed automata. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 250–265. Springer, Heidelberg (2005) (to appear)
Niwiński, D.: Fixed points vs. infinite generation. In: LICS 1988, pp. 402–409 (1988)
Shelah, S.: The monadic second order theory of order. Annals of Mathematics 102, 379–419 (1975)
Stirling, C.: Modal and Temporal Properties of Processes. Texts in Computer Science. Springer, Heidelberg (2001)
Walukiewicz, I.: Local logics for traces. Journal of Automata, Languages and Combinatorics 7(2), 259–290 (2002)
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Walukiewicz, I. (2005). How to Fix It: Using Fixpoints in Different Contexts. In: Baader, F., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32275-7_13
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DOI: https://doi.org/10.1007/978-3-540-32275-7_13
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