Abstract
We give an algebraic characterization of the regular languages defined by sentences with both modular and first-order quantifiers that use only two vari- ables.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. Baziramwabo, P. McKenzie and D. Thérien, “Modular Temporal Logic”, Proc. 1999 IEEE Conference on Logic in Computer Science (LICS), Trento, Italy, July 1999.
D. Beauquier and J. E. Pin, “Factors of Words”;, Proc. 16th ICALP, Springer Lecture Notes in Computer Science 372 (1989) 6379.
S. Eilenberg, Automata, Languages and Machines, vol. B, Academic Press, New York, 1976.
K. Etessami, M. Vardi, and T. Wilke, “First-Order Logic with Two Variables and Unary Temporal Logic”, Proceedings, 12th IEEE Symposium on Logic in Computer Science, 228–235 (1996).
N. Immerman and D. Kozen, “Definability with a Bounded Number of Bound Variables”, Information and Computation, 83, 121–139 (1989).
J. Kamp, Tense Logic and the Theory of Linear Order, Ph. D. thesis, UCLA (1968).
R. McNaughton and S. Papert, Counter-Free Automata, MIT Press, Cambridge, Massachusetts, 1971.
S. Margolis, M. Sapir, and P. Weil, “Closed Subgroups in Pro-V Topologies and the Extension Problem for Inverse Automata”, preprint.
J. E. Pin, Varieties of Formal Languages, Plenum, London, 1986.
J. E. Pin and P. Weil, “Polynomial Closure and Unambiguous Product”, Theory Comput. Systems 30 (1997) 383–422.
J. Rhodes and B. Tilson, “The Kernel of Monoid Morphisms”, J. Pure and Applied Algebra 62 (1989) 227–268.
L. Ribes and P. Zaleskii, “The pro-p topology of a free group and algorithmic problems in semigroups”, International Journal of Algebra and Computation 4 (1994) 359–374.
P. Stiffler, “Extensions of the Fundamental Theorem of Finite Semigroups”, Advances in Mathematics, 11 159–209 (1973).
H. Straubing, Finite Automata, Formal Languages, and Circuit Complexity, Birkhäuser, Boston, 1994.
H. Straubing, “Families of recognizable sets corresponding to certain varieties of finite monoids”, Journal of Pure and Applied Algebra 15 (1979), 305–318.
H. Straubing, D. Théerien, and W. Thomas, “Regular Languages Defined by Generalized Quantifiers”, Information and Computation 118 289–301 (1995).
D. Thérien and T. Wilke, “Over Words, Two Variables are as Powerful as One Quantifier Alternation,” Proc. 30th ACM Symposium on the Theory of Computing 256–263 (1998).
T. Wilke, “Classifying Discrete Temporal Properties”, Habilitationsschrift, University of Kiel, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Straubing, H., Thérien, D. (2001). Regular Languages Defined by Generalized First-Order Formulas with a Bounded Number of Bound Variables. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_48
Download citation
DOI: https://doi.org/10.1007/3-540-44693-1_48
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41695-1
Online ISBN: 978-3-540-44693-4
eBook Packages: Springer Book Archive