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ALOGTIME and a conjecture of S.A. Cook

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Abstract

Usingsequential, machine-independent characterization of theparallel complexity classesAC k andNC k, we establish the following conjecture of S.A. Cook. There is a free variable equational logicALV with the property thatif f, g are function symbols forALOGTIME computable functions for which “f=g” is provable inALV, then there are polynomial size Frege proofs for the infinite family {|f=g| n m :n, m∈ℕ} of propositional tautologies. Here, the propositional formula |f=g| n m expresses the equality off andg on inputs of length at mostn, provided that the function values are of length at mostm. We establish a related result with constant formula-depth polynomial size Frege proofs for a systemAV related to uniformAC 0 functions.

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Authors and Affiliations

  1. Department of Computer Science, Boston College, 02167, Chestnut Hill, MA, USA

    Peter Clote

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  1. Peter Clote
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Additional information

Part of this research supported by NSF Grant # DCR-860615. Extended abstract of this paper appeared in theIEEE Proc. of Logic in Computer Science, Philadelphia (June 1990).

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Clote, P. ALOGTIME and a conjecture of S.A. Cook. Ann Math Artif Intell 6, 57–106 (1992). https://doi.org/10.1007/BF01531023

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