Natural Proofs
نویسندگان
چکیده
منابع مشابه
Natural proofs
The ultimate goal we have is separating classes (or proving they are equal if they are). But our success so far seems to be limited: We know a (quite) tight time hierarchy, a tight space hierarchy, non-deterministic hierarchies, and some other (weaker) hierarchies. However, we are unable to even prove that LOG 6= P#P or that BPP 6= NEXP. In this lecture we seek some justification to this state ...
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Based on Håstad’s (1986) circuit lower bounds, Linial, Mansour, and Nisan (1993) gave a quasipolytime learning algorithm for AC0 (constant-depth circuits with AND, OR, and NOT gates), in the PAC model over the uniform distribution. It was an open question to get a learning algorithm (of any kind) for the class of AC0[p] circuits (constant-depth, with AND, OR, NOT, and MODp gates for a prime p)....
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Using some routine properties ([zu], [po]) of the Prawitz translation φ from (sequent calculus) derivations to (natural) deductions, and restricting ourselves to the language of first-order hereditary Harrop formulae, we show (i) that φ maps the simple uniform derivations of Miller et al onto the set of deductions in expanded normal form; and (ii) that φ identifies two such derivations iff they...
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We present a new form of Herbrand's theorem which is centered around structures called expansion trees. Such trees contains substitution formulas and selected (critical) variables at various non-terminal nodes. These trees encode a shallow formula and a deep formula the latter containing the formulas which label the terminal nodes of the expansion tree. If a certain relation among the selected ...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1997
ISSN: 0022-0000
DOI: 10.1006/jcss.1997.1494