The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time complexity of search problems concerning the function in question. Formally, given a Turing reduction from a search problem y x f  ) ( to another search prob...

495 The complexity of the Discrete Fourier Transform (OFT) is studied with respect to a new model of computation appropriate to VLSI technology. This model focuses on two key parameters, the amount of silicon area and time required to implement a OFT on a single chip. Lower bounds on area (A) and time (T) are related to the number of points (N) in the OFT: AT2 > N2/16. This inequality holds for...

In this paper we study the notion of parameterized exponential time complexity. We show that a parameterized problem can be solved in parameterized 2o(f (k))p(n) time if and only if it is solvable in time O(2δf (k)q(n)) for any constant δ > 0, where p and q are polynomials. We then illustrate how this equivalence can be used to show that special instances of parameterized NP-hard problems are a...

Parameterized Complexity in its origins was considered by many researchers to be an exotic research eld, orthogonal to the standard way of classifying problems in complexity theory. In the last years however many surprising connections between Parameterized Complexity and classical areas in complexity theory have been established. Jörg Flum and Martin Grohe survey in this column some of these i...

This paper furthers the study of quasi-linear time complexity initiated by Schnorr and Gurevich and Shelah. We show that the fundamental properties of the polynomial-time hierarchy carry over to the quasilinear-time hierarchy. Whereas all previously known versions of the Valiant-Vazirani reduction from NP to parity run in quadratic time, we give a new construction using error-correcting codes t...

In my endeavour to try and understand the main mechanisms of time perception in electroacoustic music, I explored complexity and how it can affect our experience of timescales and passing of time. This experience ultimately influences our understanding of structures and balancing of sections, our appreciation of gestural and textural development, and the interconnection of concurrent, near and ...

2. TIME-FREQUENCY REPRESENTATIONS Many functions have been proposed for estimating signal information content and complexity on the time-frequency plane, including moment-based measures such as the timebandwidth product and the Shannon and RCnyi entropies. When applied to a time-frequency representation from COhen’s class, the R h y i entropy conforms closely to t.he visually based notion of co...

We would like to thank Michelle Barnes, Craig Hiemstra and Blake LeBaron for their helpful comments. The usual disclaimer applies.

Thus, f is big O of g if f is bounded above by a constant multiple of g. Intuitively, f(n) = O(g(n)) means that f grows no faster than g as the index n grows. For example, the function f(n) = n2 is big O of the function g(n) = n3, while it is not true that g is big O of f in this case. Every function is big O of itself. The requirement that the inequality in the above definition of big O hold f...