Abstract
This paper studies logical definability of tree languages (sets of finite trees). The logical systems we consider are located between first-order logic and monadic second-order logic. We obtain results which clarify the expressive power of first-order logic extended by “modulo counting quantifiers”.
The present work was supported by EBRA Working Group 3166” Algebraic and Syntactic Methods in Computer Science (ASMICS)”.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J.R.Büchi, Weak second-order arithmetik and finite automata, Z. math. Logik Grundlagen Math., 6, 1960, pp. 66–92.
J.Doner, Tree acceptors and some of their applications, J. of Comp. and System Sci., 4, 1970, pp. 406–451.
A.Ehrenfeucht, An application of games to the completeness problem for formalized theories, Fund. Math., 49, 1961, pp. 129–141.
C.C.Elgot, Decision problems of finite automata design and related arithmetics, Trans. Amer. Math. Soc., 98, 1961, pp. 21–52.
F.Gecség and M.Steinby, ”Tree Automata”, Akadémiai Kiadó, Budapest, 1984.
U.Heuter, First-order properties of trees, star-free expressions and aperiodicity, RAIRO Informatique Théor. Appl., 25, 1991, pp. 125–145.
U.Heuter, Zur Klassifizierung regulärer Baumsprachen, Dissertation, RWTH Aachen, 1989.
R.McNaughton and S.Papert, ”Counter-free Automata”, M.I.T.-Press, Cambridge, Mass., 1971.
A.R.Meyer, A note on star-free events, J. Assoc. Comput. Mach., 16, 1969, pp. 220–225.
J.D.Monk, ”Mathematical Logic”, Springer Verlag, New York Heidelberg Berlin.
M.Nivat and A.Podelski, Tree monoids and recognizability of sets of finite trees, LITP Report 87-43, Université Paris VII, 1987.
D.Niwiński, Modular quantifiers in antichain logic of trees, manuscript, 1990.
J.G.Rosenstein, ”Linear orderings”, Academic Press, New York, 1982.
M.P.Schützenberger, On monoids having only trivial subgroups, Inform. Contr., 8, 1965, pp. 190–194.
H.Straubing, D.Thérien and W.Thomas, Regular languages defined with generalized quantifiers, Proc. 15th ICALP, T. Lepistö, A. Salomaa Eds., LNCS 317, 1988, pp. 561–575.
W.Thomas, Classifying regular events in symbolic logic, J. of Comp. and System Sci., 25, 1982, pp. 360–376.
W.Thomas, Logical aspects in the study of tree languages, Ninth Colloquium on Trees in Algebra and Programming, B. Courcelle Ed., Cambridge Univ. Press, 1984, pp. 31–51.
J.W.Thatcher and J.B.Wright, Generalized finite automata with an application to a decision problem of second-order logic, Math. Syst. Theory, 2, 1968, pp.57–82.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Potthoff, A. (1992). Modulo counting quantifiers over finite trees. In: Raoult, J.C. (eds) CAAP '92. CAAP 1992. Lecture Notes in Computer Science, vol 581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55251-0_15
Download citation
DOI: https://doi.org/10.1007/3-540-55251-0_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55251-2
Online ISBN: 978-3-540-46799-1
eBook Packages: Springer Book Archive