Quantum Certificate Complexity

Given a Boolean function f, we study two natural generalizations of the certificate complexity C(f): the randomized certificate complexity RC(f) and the quantum certificate complexity QC(f). Using Ambainis' adversary method, we exactly characterize QC(f) as the square root of RC(f). We then use this result to prove the new relation R0(f) = O(Q2(f)^2 Q0(f) log n) for total f, where R0, Q2, and Q0 are zero-error randomized, bounded-error quantum, and zero-error quantum query complexities respectively. Finally we give asymptotic gaps between the measures, including a total f for which C(f) is superquadratic in QC(f), and a symmetric partial f for which QC(f) = O(1) yet Q2(f) = Omega(n/log n).Comment: 9 page

Properties of complexity measures for PRAMs and WRAMs

AbstractThe computation of Boolean functions by parallel computers with shared memory (PRAMs and WRAMs) is considered. In particular, complexity measures for parallel computers like critical and sensitive complexity are compared with other complexity measures for Boolean functions like branching program depth and length of prime implicants and clauses.The relations between these complexity measures and their asymptotic behaviour are investigated for the classes of Boolean functions, monotone functions and symmetric functions