Preview
Unable to display preview. Download preview PDF.
References
A. Arnold and M. Nivat, Formal computations of nondeterministic program schemes, Math. Syst. Theory 13(1980)219–236.
J.R. Büchi, On a decision method in restricted second order arithmetic, Proc. Cong. Logic Method and Philos. of Sci. 1960, Univ. Press, Stanford California.
R. S. Cohen and A. Y. Gold, Theory of ω-languages II: A study of various models of ω-types generation and recognition, J. Comput. Syst. Sci. 15(1977)185–208.
R. S. Cohen and A. Y. Gold, ω-computations of deterministic pushdown machines, J. Comput. Syst. Sci. 16(1978)275–300.
S. Eilenberg, Automata, Languages, and Machines, Academic Press(1974).
J. H. Gallier and K. Schimpf, Tree pushdown automata, J. Comput. Syst. Sci. 30(1985)25–40.
F. Gécseg and M. Steinby, Tree automata, Akademiai Kiado, Budapest (1984).
I. Guessarian, Pushdown tree automata, Math. Syst. Theory 16(1983) 237–264.
I. Guessarian, Algebraic semantics, Lect. Notes Comp. Sci. no. 99, Springer-Verlag, Berlin (1981).
T. Hafer and W. Thomas, Computation tree logic CTL* and path quantifiers in the theory of the binary tree, Proc. 14th ICALP, (T. Ottmann, ed.), LNCS no. 267, Springer-Verlag, Berlin(1987)269–279.
T. Hayashi and S. Miyano, Finite tree automata on infinite trees, Bull. Inform. Cybern. 21(1985)71–82.
K. Kobayashi, M. Takahashi and H. Yamasaki, Logical formulas and four subclasses of ω-regular languages, in Automata on infinite words, (M. Nivat and D. Perrin eds.), LNCS no. 192, Springer Verlag, Berlin(1984).
L. H. Landweber, Decision problem for ω-automata, Math. Syst. Theory 3(1969)376–384.
M. Linna, On ω-sets associated with context-free languages, Inf. and Control 31(1976)272–293.
D. E. Muller, Infinite sequences and finite machines, Proc. 4th IEEE on Switching Circuit Theory and Logical Design(1963)3–16.
D. Muller, A. Saoudi and P. Schupp, Alternating automata, the weak monadic theory and its complexity,13th Inter. Colloquium Automata, Languages and Programming, (L. Kott, ed.), L.N.C.S no. 226, Springer-Verlag, Berlin(1986)275–283.
T. Moriya, Topological characterisations of infinite tree languages, Theoret. Comput. Sci. 52(1987)165–171.
R. Mc Naughton, Testing and generating infinite sequences by a finite automata, Inform. and Control 9(1966)521–530.
M. Nivat et A. Saoudi, Automata on infinite trees and rational infinite tree sets, Rapport L.I.T.P no. 87–59, Univ. Paris VII, Submitted to J. Comput. Syst. Sci.
M. Nivat and A. Saoudi, Automata on infinite objects and their applications to logic programming, Univ. Paris VII, report no. 87–60(1987), to appear in Inf. and Computation.
D. Perrin, Recent results on automata and infinite words, Proc. Math. Found. of Comput. Sci. (M. P. Chytil and V. Koubek, eds.), LNCS no. 176(1984)134–148.
M. O. Rabin, Decidability of second order theories and automata on infinite trees, Trans. Amer. Math. Soc. 141(1969)1–35.
M. O. Rabin, Weakly definable relations and special automata, Math. Logic and Foundation of set theory, Y.Bar Hillel, Edit. Amsterdam North Holland (1970)1–23.
G. Rozenberg, Selective substitution grammars, Part I, Elektron. Inform. Kybernet. 13(1977)455–463.
A. Saoudi, Variétés d'automates descendants d'arbres infinis, Theoret. Comput. Sci. 43(1986)1–21.
A. Saoudi, Generalized automata on infinite trees and Muller-Mc Naughton's theorem, Univ. Paris VII, report no. 88-06(1988)
M. Takahashi, The greatest fixed points and rational omega-tree languages, Theoret. Comput. Sci. 44(1986)259–274.
J. W. Thatcher and J.B. Wright, Generalized finite automata theory with applications to a decision problem of second order logic, Math. Syst. Theory 2(1968)57–81.
W. Thomas, A Combinatorial approach to the theory of ω-automata, Inform. and Control 48(1981)261–283.
W. Thomas, A Hierarchy of sets of infinite trees, G.I Conference, L.N.C.S no. 145, (A. B. Cremers, H. P. Kriegel, eds.), Springer-Verlag, Berlin (1982)335–342.
W. Thomas, On chain logic, path logic, and first order logic over infinite trees, Proc. 2nd Symp. on Logic in Computer Sci. (1987)245–256.
K. Wagner and L. Staiger, Automatatheoretische und Automatenfreie Characterisierugen Topologischer Klasses Regular Folgmmengen, EIK 10(1974)379–392.
P. Wolper and M. Vardi, Reasoning about Fair Concurrent programs, Proc. 18th Symp. on Theory of Computing, Berkeley(1986).
A. W. Mostowski, Determinancy of Sinking Automata on Infinite trees and Inequalities between various Rabin's Pair Indices, Inform. Proc. Letters, vol. 15, no. 4(1982) 159–163.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Saoudi, A. (1989). Pushdown automata on infinite trees and omega-Kleene closure of context-free tree sets. In: Kreczmar, A., Mirkowska, G. (eds) Mathematical Foundations of Computer Science 1989. MFCS 1989. Lecture Notes in Computer Science, vol 379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51486-4_91
Download citation
DOI: https://doi.org/10.1007/3-540-51486-4_91
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51486-2
Online ISBN: 978-3-540-48176-8
eBook Packages: Springer Book Archive