References

  1. L. Alberucci & A. Facchini (2009): The modal μ-calculus over restricted classes of transition systems. Journal of Symbolic Logic 74(4), pp. 1367–1400, doi:10.2178/jsl/1254748696.
  2. H. R. Andersen (1994): A Polyadic Modal μ-Calculus. Technical Report ID-TR: 1994-195. Dept. of Computer Science, Technical University of Denmark, Copenhagen, doi:10.1.1.42.1859.
  3. A. Arnold (1999): The modal μ-calculus alternation hierarchy is strict on binary trees. RAIRO - Theoretical Informatics and Applications 33, pp. 329–339, doi:10.1051/ita:1999121.
  4. J. Bradfield & C. Stirling (2001): Modal logics and μ-calculi: an introduction. In: J. Bergstra, A. Ponse & S. Smolka: Handbook of Process Algebra. Elsevier, pp. 293–330, doi:10.1016/B978-044482830-9/50022-9.
  5. J. Bradfield & C. Stirling (2007): Modal mu-calculi. In: P. Blackburn, J. van Benthem & F. Wolter: Handbook of Modal Logic: Studies in Logic and Practical Reasoning Volume 3. Elsevier, pp. 721–756, doi:10.1016/S1570-2464(07)80015-2.
  6. J. C. Bradfield (1996): The Modal μ-calculus Alternation Hierarchy Is Strict. In: Proc. 7th Conf. on Concurrency Theory, CONCUR'96, LNCS 1119. Springer, pp. 233–246, doi:10.1007/3-540-61604-7_58.
  7. J. C. Bradfield (1999): Fixpoint Alternation: Arithmetic, Transition Systems, and the Binary Tree. RAIRO - Theoretical Informatics and Applications 33(4/5), pp. 341–356, doi:10.1051/ita:1999122.
  8. G. D'Agostino & Giacomo Lenzi (2010): On the μ-calculus over transitive and finite transitive frames. Theoretical Computer Science 411(50), pp. 4273–4290, doi:10.1016/j.tcs.2010.09.002.
  9. E. A. Emerson & C. L. Lei (1986): Efficient Model Checking in Fragments of the Propositional μ–Calculus. In: Symposion on Logic in Computer Science. IEEE, Washington, D.C., USA, pp. 267–278.
  10. M. Grohe (1996): Arity hierarchies. Annals of Pure and Applied Logic 82(2), pp. 103–163, doi:10.1016/0168-0072(95)00072-0.
  11. J. Gutierrez, F. Klaedtke & M. Lange (2014): The μ-Calculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity. Theoretical Computer Science 560(3), pp. 292–306, doi:10.1016/j.tcs.2014.03.027.
  12. N. Immerman (1986): Relational Queries Computable in Polynomial Time. Information and Control 68(1–3), pp. 86–104, doi:10.1016/S0019-9958(86)80029-8.
  13. B. Knaster (1928): Un théorèm sur les fonctions d'ensembles. Annals Soc. Pol. Math 6, pp. 133–134.
  14. D. Kozen (1982): Results on the Propositional μ-Calculus. In: Proc. 9th Int. Coll. on Automata, Languages and Programming, ICALP'82, LNCS 140. Springer, pp. 348–359, doi:10.1007/BFb0012782.
  15. M. Lange & E. Lozes (2012): Model Checking the Higher-Dimensional Modal μ-Calculus. In: Proc. 8th Workshop on Fixpoints in Computer Science, FICS'12, Electr. Proc. in Theor. Comp. Sc. 77, pp. 39–46, doi:10.4204/EPTCS.77.
  16. M. Lange, E. Lozes & M. Vargas Guzmán (2014): Model-Checking Process Equivalences. Theoretical Computer Science 560, pp. 326–347, doi:10.1016/j.tcs.2014.08.020.
  17. G. Lenzi (1996): A Hierarchy Theorem for the μ-Calculus. In: Proc. 23rd Int. Coll. on Automata, Languages and Programming, ICALP'96, LNCS 1099. Springer, pp. 87–97, doi:10.1007/3-540-61440-0_119.
  18. D. Niwiński (1988): Fixed Points vs. Infinite Generation. In: Proc. 3rd Ann. Symp. on Logic in Computer Science, LICS'88. IEEE Computer Society, pp. 402–409.
  19. M. Otto (1999): Bisimulation-invariant PTIME and higher-dimensional μ-calculus. Theor. Comput. Sci. 224(1–2), pp. 237–265, doi:10.1016/S0304-3975(98)00314-4.
  20. C. Stirling (1995): Local Model Checking Games. In: Proc. 6th Conf. on Concurrency Theory, CONCUR'95, LNCS 962. Springer, pp. 1–11, doi:10.1007/3-540-60218-6_1.
  21. C. Stirling (1996): Games and Modal μ-Calculus. In: T. Margaria & B. Steffen: Proc. 2nd Int. Workshop on Tools and Algorithms for the Construction and Analysis of Systems, TACAS'96, LNCS 1055. Springer, pp. 298–312, doi:10.1007/3-540-61042-1_51.
  22. A. Tarski (1955): A Lattice-theoretical Fixpoint Theorem and its Application. Pacific Journal of Mathematics 5, pp. 285–309, doi:10.2140/pjm.1955.5.285.
  23. M. Y. Vardi (1982): The Complexity of Relational Query Languages (Extended Abstract). In: Proc. 14th Symp. on Theory of Computing, STOC'82. ACM, San Francisco, CA, USA, pp. 137–146, doi:10.1145/800070.
  24. I. Walukiewicz (2002): Monadic second-order logic on tree-like structures. Theor. Comput. Sci 275(1-2), pp. 311–346, doi:10.1016/S0304-3975(01)00185-2.

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