We lift upper and lower estimates from linear functionals to n-homogeneous polynomials and using this result show that l ∞ is finitely represented in the space of n-homogeneous poly-nomials, n ≥ 2, for any infinite dimensional Banach space. Refinements are also given. The classical Dvoretsky spherical sections theorem [5,13] states that l 2 is finitely represented in any infinite dimensional Ba...

The work is concerned with the trade-offs between the dimension and the time and space complexity of computations on nondeterministic cellular automata. We assume that the space complexity is the diameter of area in space involved in computation. It is proved, that 1). Every NCA A of dimension r, computing a predicate P with time complexity T (n) and space complexity S(n) can be simulated by r-...