Unprovability of lower bounds on circuit size in certain fragments of bounded arithmetic
نویسندگان
چکیده
منابع مشابه
Unprovability of Lower Bounds on Circuit Size in Certain Fragments of Bounded Arithmetic
We show that if strong pseudorandom generators exist then the statement “α encodes a circuit of size n(log ∗ n) for SATISFIABILITY” is not refutable in S2 2(α). For refutation in S1 2(α), this is proven under the weaker assumption of the existence of generators secure against the attack by small depth circuits, and for another system which is strong enough to prove exponential lower bounds for ...
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We prove that TNC1 , the true universal first-order theory in the language containing names for all uniform NC algorithms, cannot prove that for sufficiently large n, SAT is not computable by circuits of size n where k ≥ 1, c ≥ 4 unless each function f ∈ SIZE(n) can be approximated by formulas {Fn}n=1 of subexponential size 2 2/c) with subexponenital advantage: Px∈{0,1}n [Fn(x) = f(x)] ≥ 1/2 + ...
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ژورنال
عنوان ژورنال: Izvestiya: Mathematics
سال: 1995
ISSN: 1064-5632,1468-4810
DOI: 10.1070/im1995v059n01abeh000009