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    First-order logic captures only AC⁰, the class of languag... — Carmelics
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    Supports→First-order logic (FO) alone is insufficient to characterize complexity classes above AC⁰, and must be extended with fixed-point or transitive closure operators to capture stronger classes.
    Supports→First-order logic (FO) cannot capture complexity classes above AC⁰ without extensions such as fixed-point or transitive closure operators.

    First-order logic captures only AC⁰, the class of languages decidable by polynomial-size circuits of constant depth.

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    Related propositions within the same area of thought.
    Adding least fixed-point operators to FO yields FO(LFP), which captures P; addin...Complexity classes such as NL and P strictly contain AC⁰.First-order logic (FO) alone is insufficient to characterize complexity classes ...First-order logic (FO) cannot capture complexity classes above AC⁰ without exten...
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    Problems such as PARITY (strings over {0,1}* containing an odd number of 1s) can...To characterize classes such as NL, P, NP, and beyond, one must extend FO with o...

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    AC^0 consists of languages decidable by polynomial-size circuits of co...88%First-order logic FO captures only the very weak complexity class AC^0...84%First-order logic (FO) cannot capture complexity classes above AC⁰ wit...83%First-order logic is undecidable, but decidable fragments of first-ord...83%

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    4 Descriptive complexity Another connection between logic and computational complexity is provided by the subject known as descriptive complexity theory. As we have seen, a problem \(X\) is taken to be ‘complex’ in the sense of computational complexity theory in proportion to how difficult it is to decide algorithmically. On the other hand, descriptive complexity takes a problem to be ‘complex’ in proportion to the logical resources which are required to describe its instances. In other words, t

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