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- W1964795769 abstract "This paper's main result presents a 3-fold exponential algorithm that transforms a first-order formula φ together with a number d into a formula in Gaifman normal form that is equivalent to φ on the class of structures of degree at most d. For structures of polynomial growth, we even get a 2-fold exponential algorithm. These results are complemented by matching lower bounds: We show that for structures of degree 2, a 2-fold exponential blow-up in the size of formulas cannot be avoided. And for structures of degree 3, a 3-fold exponential blow-up is unavoidable. As a result of independent interest we obtain a 1-fold exponential algorithm which transforms a given first-order sentence φ of a very restricted shape into a sentence in Gaifman normal form that is equivalent to φ on all structures." @default.
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- W1964795769 date "2013-06-01" @default.
- W1964795769 modified "2023-10-14" @default.
- W1964795769 title "An Optimal Gaifman Normal Form Construction for Structures of Bounded Degree" @default.
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- W1964795769 doi "https://doi.org/10.1109/lics.2013.11" @default.
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