The Monadic Quantifier Alternation Hierarchy over Grids and Pictures
نویسنده
چکیده
The subject of this paper is monadic second-order logic over two-dimensional grids. We give a game-theoretical proof for the strictness of the monadic second-order quan-tiier alternation hierarchy over grids. Additionally, we can show that monadic second-order logic over coloured grids is expressive enough to deene complete problems for each level of the polynomial time hierarchy.
منابع مشابه
One Quantifier Will Do in Existential Monadic Second-Order Logic over Pictures
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 ...
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