One Quantifier Will Do in Existential Monadic Second-Order Logic over Pictures
by Oliver Matz
http://www-i7.informatik.rwth-aachen.de/~matz/1WillDo.ps.Z
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Abstract:
Abstract. We show that every formula of the existential fragment of monadic second-order logic over picture models (i.e., finite, two-dimensional, coloured grids) is equivalent to one with only one existential monadic quantifier. The corresponding claim is true for the class of word models ([Tho82]) but not for the class of graphs ([Ott95]). The class of picture models is of particular interest because it has been used to show the strictness of the different (and more popular) hierarchy of quantifier alternation. 1
Citations
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| 4 | Klassifizierung von Bildsprachen mit rationalen Ausdrucken, Grammatiken und Logik-Formeln. Diploma thesis, Christian-Albrechts-Universit at – Matz - 1995 |
