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 ...
متن کاملLearning Algorithms from Natural Proofs
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)....
متن کاملUniform proofs and natural deductions
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...
متن کاملExpansion Tree Proofs and Their Conversion to Natural Deduction Proofs
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