Generalizing the notion of automatic complexity of individual words due to Shallit and Wang,
we define the automatic complexity A (E) of an equivalence relation E on a finite set S of …

For a finite word w of length n we define and study the Kolmogorov structure function hw for
nondeterministic automatic complexity. We prove upper bounds on hw that appear to be …

For a finite word w of length n and a class of finite automata\mathcal A, we study the
Kolmogorov structure function h_w for automatic complexity restricted to\mathcal A. We …

We consider options that pay the complexity deficiency of a sequence of up and down ticks
of a stock upon exercise. We study the price of European and American versions of this …

We show that two possible definitions of the Kolmogorov structure function for
nondeterministic automatic complexity for a binary word x do not coincide. These definitions …