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.
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Matz, O. (1998). One quantifier will do in existential monadic second-order logic over pictures. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055826
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DOI: https://doi.org/10.1007/BFb0055826
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