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• W3097875562 abstract "Kuske and Schweikardt introduced the very expressive first-order counting logic FOC(P) to model database queries with counting operations. They showed that there is an efficient model-checking algorithm on graphs with bounded degree, while Grohe and Schweikardt showed that probably no such algorithm exists for trees of bounded depth. We analyze the fragment FO({>0}) of this logic. While we remove for example subtraction and comparison between two non-atomic counting terms, this logic remains quite expressive: We allow nested counting and comparison between counting terms and arbitrarily large numbers. Our main result is an approximation scheme of the model-checking problem for FO({>0}) that runs in linear fpt time on structures with bounded expansion. This scheme either gives the correct answer or says I do not know. The latter answer may only be given if small perturbations in the number-symbols of the formula could make it both satisfied and unsatisfied. This is complemented by showing that exactly solving the model-checking problem for FO({>0}) is already hard on trees of bounded depth and just slightly increasing the expressiveness of FO({>0}) makes even approximation hard on trees." @default.
• W3097875562 created "2020-11-09" @default.
• W3097875562 creator A5059825938 @default.
• W3097875562 creator A5062653045 @default.
• W3097875562 date "2020-10-28" @default.
• W3097875562 modified "2023-09-27" @default.
• W3097875562 title "Approximate Evaluation of First-Order Counting Queries" @default.
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• W3097875562 hasPublicationYear "2020" @default.
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