One Quantifier Will Do in Existential Monadic Second-Order Logic over Pictures
نویسنده
چکیده
We show that every formula of the existential fragment of monadic second-order logic over picture models (i.e., nite, two-dimensional , coloured grids) is equivalent to one with only one existential monadic quantiier. 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 diierent (and more popular) hierarchy of quantiier alternation.
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