Resource-bounded measure is a generalization of classical Lebesgue measure that is useful in computational complexity. The central parameter of resource-bounded measure is the resource bound ∆, which is a class of functions. When ∆ is unrestricted, i.e., contains all functions with the specified domains and codomains, resource-bounded measure coincides with classical Lebesgue measure. On the ot...

We show that BPP has p-measure zero if and only if BPP differs from EXP. The same holds when we replace BPP by any complexity class C that contains BPP and is closed under tt-reductions. The zero-one law for each of these classes C follows: Within EXP, C has either measure zero or else measure one.

Birdsong is an important signal in mate attraction and territorial defence. Quantifying the complexity of these songs can shed light on individual fitness, sexual selection behaviour. Several techniques have been used to quantify song be broadly categorized into measures sequential variations diversity. However, methods are unable account for acoustic features like frequency bandwidth variety s...