The main purpose of this paper is to show that, for any L(n) such that L(n)logn and [L(n)/n]0, L(n) space bounded alternating on-line Turing machines with only universal states are less powerful than ordinary L(n) space bounded alternating on-line Turing machines. Closure properties are also discussed.

This paper investigates the properties of synchronized alternating one-way multicounter machines (lsamcm's) which operate in real time (lsamcm-real's) and whose leaf-sizes are bounded by a constant or some function of the length of an input. Leaf-size reflects the number of processors which run in parallel in scanning a given input. We first consider the hieracrchies of lsamcm-real's based on the number of counters and constant leaf-sizes. We next show that lsamcm-real's are less powerful than lsamcm's which operate in linear time when the leaf-sizes of these machines are bounded by a function L(n) such that limn[L(n) log n/n]0 and L(n)2.

There have been several interesting investigations on the space functions constructed by one-dimensional or two-dimensional Turing machines. On the other hand, as far as we know, there is no investigation about the space functions constructed by three-dimensional Turing machines. In this paper, we investigate about space constructibility by three-dimensional deterministic Turing machines with cubic inputs, and show that the functions log*n and log(k)n, k1, are fully space constructible by these machines.

It has already been known that there exists an infinite hierarchy of the classes of sets of square tapes accepted by deterministic space-bounded two-dimensional Turing machines with spaces below log m. This paper shows that there exists an infinite hierarchy of the classes of sets of square tapes accepted by nondeterministic space-bounded two-dimensional Turing machines with spaces less than or equal to log m.