منابع مشابه
Boolean 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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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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The effect of severely tightening the uniformity of Boolean circuit families is investigated. The impact on NC and its subclasses is shown to depend on the characterization chosen for the class, while classes such as P appear to be more robust. Tightly uniform subclasses of NC whose separation may be within reach of current techniques emerge.
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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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In this work, we are interested in non-trivial upper bounds on the spectral norm of binary matrices M from {−1, 1}N×N . It is known that the distributed Boolean function represented by M is hard to compute in various restricted models of computation if the spectral norm is bounded from above by N1−ε, where ε > 0 denotes a fixed constant. For instance, the size of a two-layer threshold circuit (...
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ژورنال
عنوان ژورنال: computational complexity
سال: 2014
ISSN: 1016-3328,1420-8954
DOI: 10.1007/s00037-014-0087-y