We propose a new way of characterizing the complexity of online problems. Instead of measuring the degradation of the output quality caused by the ignorance of the future we choose to quantify the amount of additional global information needed for an online algorithm to solve the problem optimally. In our model, the algorithm cooperates with an oracle that can see the whole input. We define the advice complexity of the problem to be the minimal number of bits (normalized per input request, and...

This paper discusses $n$-island finite automata whose transition graphs can be expressed as $n$-member sequences of islands $i_1,i_2,\cdots ,i_n$, where there is a bridge leaving $i_j$ and entering $i_{j+1}$ for each $1\le j\le n-1$. It concentrates its attention on even computation defined as any sequence of moves during which these automata make the same number of moves in each of the islands. Under the assumption that these automata work only in an evenly computational way, the paper proves its main result stating that $n$-island finite automata...