… complexity which, as mentioned already, we believe to be nonexistent. Rather, we propose
to evaluate the complexity of a finite sequence … it scans a given ndigit sequence S = slsZ * * * s…

… An f(n) advice sequence is a sequence of binary strings THE COMPLEXITY OF FINITE
FUNCTIONS 763 A = (al9a2,...), where \an\^f(n). For Let P / / ( n ) = {B@A:BeP {x:x#a\x\EB}. P/poly …

… and DNA sequences. We consider a given sequence as one realization of finite length of …
The other members of the ensemble are defined by appropriate surrogate sequences and …

… for finite sequences was suggested [3,4] which closely relates to their Kolmogorov complexity.
… This was motivated by the presumption that various EEG time series contain a mixture of …

… It is obvious how to express 02 and o 4 in the language of +, but in order to express o 1 and
03, we need other relations which will be introduced in a series of lemmas. These relations (…

… of the nonlinear complexity of sequences over any … complexity profile of finite length sequences
over any field, and establish a connection between Lempel–Ziv and nonlinear complexity…

… : (a) a sequence is normal if and only if there is no finite-state … 5], and (b) a sequence is
normal if and only if it is … Below we establish in a slightly more general way that no finite …

… -free Kolmogorov complexity) for every … finite state complexity on the enumeration of finite
transducers. We prove that in every sequence there are infinitely many finite state complexity …

… We study the computational complexity of solving systems of equations over a finite group.
An … Such a group defines a natural notion of complexity: for a sequence of Boolean functions { …

… We analyse the process complexity KP in the same way. If Ix I- KP(x) > Izl- KP(z) than we can
say that the sequence z withstands the random test given by KP better than x. However, the …