Nonuniform ACC Circuit Lower Bounds

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...

Sparse Selfreducible Sets and Nonuniform Lower Bounds

It is well-known that the class of sets that can be computed by polynomial size circuits is equal to the class of sets that are polynomial time reducible to a sparse set. It is widely believed, but unfortunately up to now unproven, that there are sets in EXP, or even in EXP that are not computable by polynomial size circuits and hence are not reducible to a sparse set. In this paper we study th...

Nonuniform Lower Bounds for Exponential Time Classes

Symmetry of Information and Nonuniform Lower Bounds

Derandomization 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...