Corpus ID: 2542968

Pseudorandomness for Read-Once, Constant-Depth Circuits

  title={Pseudorandomness for Read-Once, Constant-Depth Circuits},
  author={Sitan Chen and Thomas Steinke and Salil P. Vadhan},
For Boolean functions computed by read-once, depth-D circuits with unbounded fan-in over the de Morgan basis, we present an explicit pseudorandom generator with seed length ~ O(log D+1 n). The previous best seed length known for this model was ~ O(log D+4 n), obtained by Trevisan and Xue (CCC ‘13 ) for all of AC 0 (not just read-once). Our work makes use of Fourier analytic techniques for pseudorandomness introduced by Reingold, Steinke, and Vadhan (RANDOM ‘13 ) to show that the generator of… Expand
8 Citations
Near-optimal pseudorandom generators for constant-depth read-once formulas
The crux of this work is showing that after poly(log log n) independent applications of the pseudorandom restriction, the formula simplifies in the sense that every gate other than the output has only polylog n remaining children. Expand
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Motivated by the derandomization of space-bounded computation, there has been a long line of work on constructing pseudorandom generators (PRGs) against various forms of read-once branching programsExpand
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The iterated restrictions approach is used to construct an explicit PRG for read-once depth-2 AC0[⊕] formulas with optimal seed length O(log n) with near-optimal error, and a tail bound for subset-wise symmetric polynomials is extended. Expand
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It is proved that constant-width monotone branching programs of polynomial size are equivalent in power to AC circuits, and an explicit pseudorandom generator that ε-fools length n programs with seed length Õ(log(n/ε)). Expand
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In the coin problem we are asked to distinguish, with probability at least 2/3, between n i.i.d. coins which are heads with probability 1 2 + β from ones which are heads with probability 1 2 − β. WeExpand
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Bounded Independence Plus Noise


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We present an explicit pseudorandom generator for oblivious, read-once, permutation branching programs of constant width that can read their input bits in any order. The seed length is O(log2 n),Expand
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An explicit pseudorandom generator for oblivious, read-once, width-3 branching programs, which can read their input bits in any order, and has seed length O~( log^3 n ). Expand
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