We completely characterise the complexity in the decision tree model of computing composite relations of the form h = g(f^1,...,f^n), where each relation f^i is boolean-valued. Immediate corollaries include a direct sum theorem for decision tree complexity and a tight characterisation of the decision tree complexity of iterated boolean functions.
Decision Tree Complexity versus Block Sensitivity and Degree
Relations between the decision tree complexity and various other complexity measures of Boolean functions is a thriving topic of research in computational complexity . It is known that decision tree complexity is bounded above by the cube of block sensitivity, and the cube of polynomial degree. However, the widest separation between decision tree complexity and each of block sensitivity and degree that is witnessed by known Boolean functions is quadratic. In this work, we investigate the tightness of the existing cubic upper bounds. We improve the cubic upper bounds for many interesting classe…
Inapproximability of sufficient reasons for decision trees
Centro Nacional de Inteligencia Artificial（国家人工智能中心）；Instituto de Ingeniería Matemática y Computacional, Universidad Católica de Chile（智利天主教大学数学与计算工程学院）；Instituto Milenio Fundamentos de los Datos（千禧年数据基础研究所）
