منابع مشابه
Locality from Circuit Lower Bounds
We study the locality of an extension of first-order logic that captures graph queries computable in AC, i.e., by families of polynomial-size constant-depth circuits. The extension considers first-order formulas over relational structures which may use arbitrary numerical predicates in such a way that their truth value is independent of the particular interpretation of the numerical predicates....
متن کاملBoolean Circuit Lower Bounds
The lectures are devoted to boolean circuit lower bounds. We consider circuits with gates ∧,∨,¬. Suppose L ∈ {0, 1}∗ is a language. Let Ln = L∩{0, 1}. We say that L is computed by a family of circuits C1, C2, . . . if on an input x = (x1, . . . , xn), Cn(x) is 1 when x ∈ Ln and is 0 when x / ∈ Ln. For a circuit C, we define size(C) to be the number of edges in the graph representing C, and dept...
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We present an alternate proof of the result by Kabanets and Impagliazzo (2004) that derandomizing polynomial identity testing implies circuit lower bounds. Our proof is simpler, scales better, and yields a somewhat stronger result than the original argument. ACM Classification: F.1.2, F.1.3 AMS Classification: 68Q10, 68Q15, 68Q17
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For any unsatisfiable CNF formula F that is hard to refute in the Resolution proof system, we show that a gadget-composed version of F is hard to refute in any proof system whose lines are computed by efficient communication protocols—or, equivalently, that a monotone function associated with F has large monotone circuit complexity. Our result extends to monotone real circuits, which yields new...
متن کاملDerandomization and Circuit Lower Bounds
1 Introduction Primality testing is the following problem: Given a number n in binary, decide whether n is prime. In 1977, Solovay and Strassen [SS77] proposed a new type of algorithm for testing whether a given number is a prime, the celebrated randomized Solovay-Strassen primality test. This test and similar ones proved to be very useful. This fact changed the common notion of " feasible comp...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2012
ISSN: 0097-5397,1095-7111
DOI: 10.1137/110856873