Detecting Patterns Can Be Hard: Circuit Lower Bounds for the String Matching Problem

arXiv: Computational Complexity, Volume abs/1709.02034, 2017.

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Abstract:

Detecting patterns in strings and images is a fundamental and well studied problem. We study the circuit complexity of the string matching problem under two popular choices of gates: De Morgan and threshold gates. For strings of length $n$ and patterns of length $log n ll k leq n -o(n)$, we prove super polynomial lower bounds for De Morga...More

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