Fixpoint alternation : arithmetic, transition systems, and the binary tree
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999) no. 4-5, pp. 341-356.
@article{ITA_1999__33_4-5_341_0,
     author = {Bradfield, J. C.},
     title = {Fixpoint alternation : arithmetic, transition systems, and the binary tree},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {341--356},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {4-5},
     year = {1999},
     zbl = {0945.68126},
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     language = {en},
     url = {http://www.numdam.org/item/ITA_1999__33_4-5_341_0/}
}
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Bradfield, J. C. Fixpoint alternation : arithmetic, transition systems, and the binary tree. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999) no. 4-5, pp. 341-356. http://www.numdam.org/item/ITA_1999__33_4-5_341_0/

[1] A. Arnold, The µ-calculus alternation-depth hierarchy is strict on binary trees, this volume, p. 329. | Numdam | MR 1748659 | Zbl 0945.68118

[2] J. C. Bradfield, Verifying Temporal Properties of Systems. Birkhäuser, Boston (1991). | MR 1138724 | Zbl 0753.68065

[3] J. C. Bradfield, On the expressivity of the modal mu-calculus, C. Puech and R. Reischuk, Eds., in Proc. STACS '96. Springer, Berlin, Lecture Notes in Comput. Sci. 1046 (1996) 479-490. | MR 1462119

[4] J. C. Bradfield, The modal mu-calculus alternation hierarchy is strict. Theoret. Comput. Sci. 195 (1997) 133-153. | MR 1609327 | Zbl 0915.03017

[5] J. C. Bradfield, Simplifying the modal mu-calculus alternation hierarchy, M. Morvan, C. Meinel and D. Krob, Eds., in Proc. STACS 98. Springer, Berlin, Lecture Notes in Comput. Sci. 1373 (1998) 39-49. | MR 1650761 | Zbl 0892.03005

[6] J. C. Bradfield, Fixpoint alternation on the binary tree, Workshop on Fixpoints in Computer Science (FICS). Brno (1998).

[7] E. A. Emerson and C. S. Jutla, Tree automata, mu-calculus and determinacy, in Proc. FOCS 91 (1991).

[8] E. A. Emerson and C.-L. Lei, Efficient model checking in fragments of the propositional mu-calculus, in Proc. 1st LICS. IEEE, Los Alamitos, CA (1986) 267-278.

[9] D. Janin and I. Walukiewicz, Automata for the µ-calculus and related results, in Proc. MFCS '95. Springer, Berlin, Lecture Notes in Comput. Sci. 969 (1995) 552-562. | MR 1467281 | Zbl 1193.68163

[10] R. Kaye, Models of Peano Arithmetic. Oxford University Press, Oxford (1991). | MR 1098499 | Zbl 0744.03037

[11] D. Kozen, Results on the propositional mu-calculus. Theoret Comput. Sci. 27 (1983) 333-354. | MR 731069 | Zbl 0553.03007

[12] G. Lenzi, A hierarchy theorem for the mu-calculus, F. Meyer auf der Heide and B. Monien, Eds., in Proc. ICALP '96. Springer, Berlin, Lecture Notes in Comput. Sci. 1099 (1996) 87-109. | MR 1464442 | Zbl 1045.03516

[13] R. S. Lubarsky, µ-definable sets of integers, J. Symbolic Logic 58 (1993) 291-313. | MR 1217190 | Zbl 0776.03022

[14] D. Niwiński, On fixed point clones, L. Kott, Ed., in Proc. 13th ICALP. Springer, Berlin, Lecture Notes in Comput. Sci. 226 (1986) 464-473. | MR 864709 | Zbl 0596.68036

[15] D. Niwiński, Fixed point characterization of infinite behavior of finite state systems. Theoret. Comput. Sci. 189 (1997) 1-69. | MR 1483617 | Zbl 0893.68102

[16] C. P. Stirling, Modal and temporal logics, S. Abramsky, D. Gabbay and T. Maibaum, Eds. Oxford University Press, Handb. Log. Comput. Sci. 2 (1991) 477-563. | MR 1381700

[17] I. Walukiewicz, Monadic second order logic on tree-like structures, C. Puech and Rüdiger Reischuk, Eds., in Proc. STACS '96. Springer, Berlin, Lecture Notes in Comput. Sci. 1046 (1996) 401-414. | MR 1462113