Magnus G. Find, Mika Goos, Matti Jarvisalo, Petteri Kaski, Miko Koivisto, Janne Korhonen
Given a boolean n x n matrix A we consider arithmetic circuits for computing the transformation x 7! Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative integers), and non-monotone XOR-circuits (addition modulo 2). Our focus is on separating OR-circuits from the two other models in terms of circuit complexity: (1) We show how to obtain matrices that admit OR-circuits of size O(n), but require SUM-circuits of size (n^(3/2)/log^2n). (2) We consider the task of rewriting a given OR-circuit as a XOR-circuit and prove that any subquadratic-time algorithm for this task violates the strong exponential time hypothesis.
, Goos, M.
, Jarvisalo, M.
, Kaski, P.
, Koivisto, M.
and Korhonen, J.
Separating OR, SUM, and XOR Circuits, Journal of Computer and System Sciences, [online], https://doi.org/10.1016/j.jcss.2016.01.001
(Accessed December 4, 2023)