Fixpoint alternation : arithmetic, transition systems, and the binary tree

J. C. Bradfield

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (1999)

  • Volume: 33, Issue: 4-5, page 341-356
  • ISSN: 0988-3754

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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 33.4-5 (1999): 341-356. <http://eudml.org/doc/92608>.

@article{Bradfield1999,
author = {Bradfield, J. C.},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {modal mu-calculus alternation hierarchy},
language = {eng},
number = {4-5},
pages = {341-356},
publisher = {EDP-Sciences},
title = {Fixpoint alternation : arithmetic, transition systems, and the binary tree},
url = {http://eudml.org/doc/92608},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Bradfield, J. C.
TI - Fixpoint alternation : arithmetic, transition systems, and the binary tree
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 1999
PB - EDP-Sciences
VL - 33
IS - 4-5
SP - 341
EP - 356
LA - eng
KW - modal mu-calculus alternation hierarchy
UR - http://eudml.org/doc/92608
ER -

References

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  1. [1] A. Arnold, The µ-calculus alternation-depth hierarchy is strict on binary trees, this volume, p. 329. Zbl0945.68118MR1748659
  2. [2] J. C. Bradfield, Verifying Temporal Properties of Systems. Birkhäuser, Boston (1991). Zbl0753.68065MR1138724
  3. [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. MR1462119
  4. [4] J. C. Bradfield, The modal mu-calculus alternation hierarchy is strict. Theoret. Comput. Sci. 195 (1997) 133-153. Zbl0915.03017MR1609327
  5. [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. Zbl0892.03005MR1650761
  6. [6] J. C. Bradfield, Fixpoint alternation on the binary tree, Workshop on Fixpoints in Computer Science (FICS). Brno (1998). 
  7. [7] E. A. Emerson and C. S. Jutla, Tree automata, mu-calculus and determinacy, in Proc. FOCS 91 (1991). 
  8. [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. [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. Zbl1193.68163MR1467281
  10. [10] R. Kaye, Models of Peano Arithmetic. Oxford University Press, Oxford (1991). Zbl0744.03037MR1098499
  11. [11] D. Kozen, Results on the propositional mu-calculus. Theoret Comput. Sci. 27 (1983) 333-354. Zbl0553.03007MR731069
  12. [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. Zbl1045.03516MR1464442
  13. [13] R. S. Lubarsky, µ-definable sets of integers, J. Symbolic Logic 58 (1993) 291-313. Zbl0776.03022MR1217190
  14. [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. Zbl0596.68036MR864709
  15. [15] D. Niwiński, Fixed point characterization of infinite behavior of finite state systems. Theoret. Comput. Sci. 189 (1997) 1-69. Zbl0893.68102MR1483617
  16. [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. MR1381700
  17. [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. MR1462113

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