Circuit and Decision Tree Complexity of Some Number Theoretic Problems

Open problems in number theoretic complexity, II

On the Complexity of Certain Algebraic and Number Theoretic Problems

Some Decision Problems of Enormous Complexity

We present some new decision and comparison problems of unusually high computational complexity. Most of the problems are strictly combinatorial in nature; others involve basic logical notions. Their complexities range from iterated exponential time completeness to ∈0 time completeness to θ(Ω,0) time completeness to θ(Ωω,,0) time completeness. These three ordinals are well known ordinals from p...

Some Number Theoretic Results

This note consists of two rather separate topics . In §1 we generalize a topic from combinatorial number theory to get an order of magnitude for the number of elements in a maximal set of residues (mod p) such that sums of different numbers of elements from this set are distinct. We show that the correct order is ep'" 3 although we are unable to establish the correct value for the constant c . ...

Graph-theoretic Arguments in Circuit Complexity