This paper investigates the closure properties of multi-inkdot nondeterministic Turing machines with sublogarithmic space. We show that the class of sets accepted by the Turing machines is not closed under concatenation with regular set, Kleene closure, length-preserving homomorphism, and intersection.

A cooperating system of finite automata (CS-FA) has more than one finite automata (FA's) and an input tape. These FA's operate independently on the input tape and can communicate with each other on the same cell of the input tape. For each k ≥ 1, let L[CS-1DFA(k)] (L[CS-1UFA(k)]) be the class of sets accepted by CS-FA's with k one-way deterministic finite automata (alternating finite automata with only universal states). We show that L[CS-1DFA(k+1)] - L[CS-1UFA(k)] ≠ ∅ and L[CS-1UFA(2)] - ∪1≤k<∞L[CS-1DFA(k)] ≠ ∅.

It was unknown whether there exists a language accepted by a two-way nondeterministic one counter automaton, but not accepted by any nondeterministic rebound automaton. This paper solves this problem, and shows that there exists such a language.

This paper investigates the closure properties of 1-inkdot nondeterministic Turing machines and 1-inkdot alternating Turing machines with only universal states which have sublogarithmic space. We show for example that the classes of sets accepted by these Turing machines are not closed under length-preserving homomorphism, concatenation with regular set, Kleene closure, and complementation.

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.