Borel hierarchy and omega context free languages

Theoretical Computer Science

Volumn 290, Issue 3, 2003, Pages 1385-1405

  Finkel, Olivier ^a  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

Analytic sets; Borel hierarchy; Context free languages; Topological complexity

Indexed keywords

FORMAL LANGUAGES; TOPOLOGY;

ANALYTIC SETS; BOREL HIERARCHY; CONTEXT-FREE; FINITARY LANGUAGES; INFINITE TREES; RECOGNIZABLE SETS; TOPOLOGICAL COMPLEXITY; TOPOLOGICAL PROPERTIES;

CONTEXT FREE LANGUAGES;

EID: 85009165670     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(02)00042-7     Document Type: Article

References (50)

1. [1] Barua, R., The Hausdorff–Kuratowski hierarchy of ω-regular languages and a hierarchy of Muller automata. Theoret. Comput. Sci. 96 (1992), 345–360.
2. [2] Berstel, J., Transductions and context free languages, 1979, Teubner Studienbücher Informatik.
3. [3] Boasson, L., Nivat, M., Adherences of languages. J. Comput. Syst. Sci. 20:3 (1980), 285–309.
4. [4] Büchi, J.R., Weak second order arithmetic and finite automata. Z. Math. Logik Grundlag. Math. 6 (1960), 66–92.
5. [5] J.R. Büchi, On a decision method in restricted second order arithmetic, logic methodology and philosophy of science, Proc. 1960 Internat. Congr., Stanford University Press, 1962, pp. 1–11.
6. [6] J.R. Büchi, D. Siefkes, The monadic second-order theory of all countable ordinals, decidable theories 2, Springer Lecture Notes in Mathematics, Vol. 328, Springer, Berlin, 1973.
7. [7] Carton, O., Perrin, D., Chains and superchains for ω-rational sets, automata and semigroups. Internat. J. Algebra Comput. 7:7 (1997), 673–695.
8. [8] Carton, O., Perrin, D., The wagner hierarchy of ω-rational sets. Internat. J. Algebra Comput. 9:5 (1999), 597–620.
9. [9] R.S. Cohen, A.Y. Gold, Theory of ω-Languages, Parts one and two, J. Comput. Syst. Sci. 15 (2) (1977) part one 169–184, part two 185–208.
10. [10] Cohen, R.S., Gold, A.Y., ω-computations on deterministic pushdown machines. J. Comput. Syst. Sci. 3 (1978), 257–300.
11. [11] J. Duparc, La Forme Normale des Boréliens de Rang Fini, Ph.D. Thesis, Université Paris 7, 1995.
12. [12] J. Duparc, The Normal form of Borel Sets, Part 1: Borel Sets of Finite Rank, C.R. Academic Science, Paris, t. 320, Sér. 1, 1995, pp. 651–656.
13. [13] Duparc, J., Wadge hierarchy and veblen hierarchy. Part 1: Borel sets of finite rank. J. Symbolic Logic 66:1 (2001), 56–86.
14. [14] Duparc, J., Finkel, O., Ressayre, J.-P., Computer science and the fine structure of borel sets. Theoret. Comput. Sci. 257:1–2 (2001), 85–105.
15. [15] J. Duparc, A hierarchy of context free omega languages, Theoret. Comput. Sci., to appear.
16. [16] Eilenberg, S., Automata Languages and Machines, Vol. A, 1974, Academic Press, New York.
17. [17] Engelfriet, J., Hoogeboom, H.J., X-automata on ω-words. Theoret. Comput. Sci. 110:1 (1993), 1–51.
18. [18] O. Finkel, Wadge Hierarchy of Deterministic Omega Context Free Languages, in preparation.
19. [19] Finkel, O., Topological properties of omega context free languages. Theoret. Comput. Sci. 262:1–2 (2001), 669–697.
20. [20] Finkel, O., Wadge hierarchy of omega context free languages. Theoret. Comput. Sci. 269:1–2 (2001), 283–315.
21. [21] O. Finkel, Topological complexity of locally finite omega languages, Ann. Pure Appl. Logic, submitted for publication.
22. [22] Ginsburg, S., The Mathematical Theory of Context Free Languages, 1966, McGraw-Hill Book Company, New York.
23. [23] Hopcroft, J.E., Ullman, J.D., Formal Languages and their Relation to Automata, 1969, Addison-Wesley Publishing Company, Reading, MA.
24. [24] Kaminsky, M., A classification of ω-regular languages. Theoret. Comput. Sci. 36 (1985), 217–229.
25. [25] Kechris, A.S., Classical Descriptive Set Theory, 1995, Springer, Berlin.
26. [26] Kuratowski, K., Topology, 1966, Academic Press, New York.
27. [27] Landweber, L.H., Decision problems for ω-automata. Math. Syst. Theory 3:4 (1969), 376–384.
28. [28] Lescow, H., Thomas, W., Logical specifications of infinite computations. de Bakker, J.W. A Decade of Concurrency, Lecture Notes on Computer Science, Vol. 803, 1994, Springer, Berlin, 583–621.
29. [29] Linna, M., On ω-sets associated with context-free languages. Inform. Control 31:3 (1976), 272–293.
30. [30] Linna, M., A decidability result for deterministic ω-context-free languages. Theoret. Comput. Sci. 4 (1977), 83–98.
31. [31] Mac Naughton, R., Testing and generating infinite sequences by a finite automaton. Inform. Control 9 (1966), 521–530.
32. [32] Moschovakis, Y.N., Descriptive Set Theory, 1980, North-Holland, Amsterdam.
33. [33] Nivat, M., Mots infinis engendrés par une grammaire algébrique. RAIRO Infor. Théor. 11 (1977), 311–327.
34. [34] Nivat, M., Sur les ensembles de mots infinis engendrés par une grammaire algébrique. RAIRO Infor. Théor. 12 (1978), 259–278.
35. [35] D. Niwinski, An Example of Non Borel Set of Infinite Trees Recognizable By a Rabin Automaton, Manuscript, University of Warsaw, 1985 (in Polish).
36. [36] D. Niwinski, Problem on ω-powers posed in the proceedings of the 1990 Workshop “Logics and recognizable sets”, Univ. Kiel, 1990.
37. [37] D. Perrin, J.-E. Pin, Infinite words, available from http://www.liafa.jussieu.fr/jep/InfiniteWords, book in preparation.
38. [38] Rogers, H., Theory of Recursive Functions and Effective Computability, 1967, McGraw-Hill, New York.
39. [39] Saoudi, A., Pushdown automata on infinite trees and nondeterministic context-free programs. Internat. J. Found. Comput. Sci. 3:1 (1992), 21–39.
40. [40] Selivanov, V., Fine hierarchy of regular ω-languages. Theoret. Comput. Sci. 191 (1998), 37–59.
41. [41] P. Simonnet, Automates et théorie descriptive, Ph.D. Thesis, Université Paris 7, March 1992.
42. [42] P. Simonnet, Automate d’ Arbres Infinis et Choix Borélien, C.R. Academic Science, Paris, t. 316, Sér. 1, 1993, pp. 97–100.
43. [43] Skurczynski, J., The borel hierarchy is infinite in the class of regular sets of trees. Theoret. Comput. Sci. 112 (1993), 413–418.
44. [44] L. Staiger, in: G. Rozenberg, A. Salomaa (Eds.), ω-Languages, Chapter of the Handbook of Formal Languages, Vol. 3, Springer, Berlin, 1997.
45. [45] L. Staiger, On ω-power languages, in new trends in formal languages, control, cooperation, and combinatorics, Lecture Notes in Computer Science, Vol. 1218, Springer, Berlin, 1997, pp. 377–393.
46. [46] Thomas, W., Automata on infinite objects. Leeuwen, J.Van, (eds.) Handbook of Theoretical Computer Science, Vol. B, 1990, Elsevier, Amsterdam, 133–191.
47. [47] W. Thomas, On the synthesis of strategies in infinite games, STACS’95, Lecture Notes in Computer Science, Vol. 900, Springer, Berlin, 1995, pp. 1–13.
48. [48] W. Thomas, Languages, automata and logic, G. Rozenberg, A. Salomaa (Eds.), Handbook of Formal Languages Theory, Vol. 3, Springer, Berlin, 1996.
49. [49] W.W. Wadge, Ph.D. Thesis, Berkeley, 1984.
50. [50] Wagner, K., On omega regular sets. Inform. Control 43 (1979), 123–177.