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Abstract: We show that the monadic second-order quantifier alternation hierarchy over finite directed graphs and over finite two-dimensional grids is infinite. For this purpose we investigate sets of grids where the width is a function in the height. The infiniteness of the hierarchy is then witnessed by n-fold exponential functions for increasing integers n. 1 Introduction The subject of this paper is monadic second-order logic over graphs. In this logic, one can quantify over vertices and sets of... (Update)
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BibTeX entry: (Update)
O. Matz and W. Thomas. The monadic quantifier alternation hierarchy over graphs is infinite. In Twelfth Annual IEEE Symposium on Logic in Computer Science, pages 236--244, Warsaw, Poland, 1997. IEEE. http://citeseer.ist.psu.edu/article/matz98monadic.html More
@inproceedings{ matz97monadic,
author = "O. Matz and W. Thomas",
title = "The Monadic Quantifier Alternation Hierarchy over Graphs is Infinite",
booktitle = "Proc. 12th Annual {IEEE} Symposium on Logic in Computer Science({LICS}'97)",
address = "Warsaw, Poland",
pages = "236--244",
year = "1997",
url = "citeseer.ist.psu.edu/article/matz98monadic.html" }
Citations (may not include all citations):294 Finite Model Theory (context) - Ebbinghaus, Flum - 1995
100 Weak second-order arithmetic and finite automata (context) - Buchi - 1960
55 Classifying regular events in symbolic logic (context) - Thomas - 1982
43 Zeitschrift fur Mathematische Logik und Grundlagen der Mathe.. (context) - Fagin, spectra - 1975
37 Decision problems of finite automata design and related arit.. (context) - Elgot - 1961
35 Information and Computation (context) - Fagin, Stockmeyer et al. - 1995
32 Two-dimensional languages - Giammarresi, Restivo - 1996
11 Recognizable picture languages and domino tiling (context) - Latteux, Simplot - 1994
8 Monadic second-order logic and recognizability by tiling sys.. (context) - Giammarresi, Restivo et al. - 1996
8 Note on the number of monadic quantifiers in monadic \Sigma (context) - Otto - 1995
7 alternation in second order logic (context) - Makowsky, Pnueli - 1994
5 Problem proposed in Oberwolfach Meeting 1995; published in: .. (context) - Fagin - 1995
5 Klassifizierung von Bildsprachen mit rationalen Ausdrucken (context) - Matz - 1995
5 Two-dimensional languages and recognizable functions (context) - Giammarresi - 1994
4 The expressive power of transitive closure and 2-way multihe.. - Bargury, Makowsky - 1992
3 Languages that capture complexity classes (context) - Immermann - 1988
3 private communication (context) - Ajtai, Fagin et al. - 1996
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