One-way sensing simple multihead finite automata with bounds on the number of times of use of sensing function in accepting computations are studied. It is shown that the languages accepted by one-way sensing simple multihead finite automata with constant sensing function bound satisfy the semilinear property, and that for one-way sensing simple multihead finite automata, m+1 times of the use of sensing function are better than m.

Let SeH{0}(k) [NSeH{0}(k)] denote the class of languages over a one-letter alphabet accepted by two-way sensing deterministic [nondeterministic] k-head finite automata. This paper shows that (i) SeH{0}(2)SeH{0}(3), and (ii) NSeH{0}(2) NSeH{0}(3). This gives an affirmative answer to an open problem in Ref. [3].

This paper investigates a relationship between accepting powers of two-way deterministic one-counter automata and one-pebble off-line deterministic Turing machines operating in space between loglog n and log n, and shows that they are incomparable.

This paper introduces a probabilistic rebound automaton (pra), and investigates its accepting power and closure property. We show that (1) the class of languages recognized by pra's with error probability less than 1/2, PRA, is incomparable with the class of context-free languages, (2) there is a language accepted by a two-way nondeterministic one counter automaton, but not in PRA, and (3) there is a language accepted by a deterministic one-marker rebound automaton, but not in PRA. We also show that PRA is not closed under concatenation and Kleene + .

This paper shows that nondeterministic sensing semi-one-way simple k-head finite automata are more powerful than nondeterministic sensing one-way simple k-head finite automata for any k2, and sensing semi-one-way simple 2-head finite automata are more powerful than semi-one-way simple 2-head finite automata, which gives an affirmative answer and a partial solution to two open problems on sensing semi-one-way simple multi-head finite automata in Ref.[3].