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• W1572916600 abstract "There are many ways to define complexity in logic. In finite model theory, it is the complexity of describing properties, whereas in proof complexity it is the complexity of proving properties in a proof system. Here we consider several notions of complexity in logic, the connections among them, and their relationship with computational complexity. In particular, we show how the complexity of logics in the setting of finite model theory is used to obtain results in bounded arithmetic, stating which functions are provably total in certain weak systems of arithmetic. For example, the transitive closure function (testing reachability between two given points in a directed graph) is definable using only NL-concepts (where NL is non-deterministic log-space complexity class), and its totality is provable within NL-reasoning." @default.
• W1572916600 created "2016-06-24" @default.
• W1572916600 creator A5003773985 @default.
• W1572916600 date "2008-06-10" @default.
• W1572916600 modified "2023-10-08" @default.
• W1572916600 title "Many Facets of Complexity in Logic" @default.
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• W1572916600 doi "https://doi.org/10.1007/978-3-540-69407-6_35" @default.
• W1572916600 hasPublicationYear "2008" @default.
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