Limiting negations in non-deterministic circuits

A Non-deterministic View on Non-classical Negations

Limiting Negations in Bounded-Depth Circuits: An Extension of Markov's Theorem

From a theorem of Markov, the minimum number of negation gates in a circuit sufficient to compute any collection of Boolean functions on n variable is l = ⌈log(n+1)⌉. Santha and Wilson [SIAM Journal of Computing 22(2):294–302 (1993)] showed that in some classes of bounded-depth circuits l negation gates are no longer sufficient for some explicitly defined Boolean function. In this paper, we con...

Learning Circuits with few Negations

Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and the class of all functions. We study this generalization of m...

A Note on the Power of Non-Deterministic Circuits with Gate Restrictions

We investigate the power of non-deterministic circuits over restricted sets of base gates. We note that the power of non-deterministic circuits exhibit a dichotomy, in the following sense: For weak enough bases, non-deterministic circuits are no more powerful than deterministic circuits, and for the remaining bases, non-deterministic circuits are super polynomial more efficient than determinist...

Correlation Bounds Against Monotone NC

This paper gives the first correlation bounds under product distributions (including the uniform distribution) against the class mNC of poly(n)-size O(log n)-depth monotone circuits. Our main theorem, proved using the pathset complexity framework recently introduced in [56], shows that the average-case k-CYCLE problem (on Erdős-Rényi random graphs with an appropriate edge density) is 12 + 1 pol...