On two-way multihead automata

Abstract

For each positive integer n , let ℒ N ( n ) be the class of sets accepted by a family of automata of type N , each with a read-only input with endmarkers and n two-way input heads. The following result, which is applicable to most types of two-way multihead devices, is proved: If for each positive integer n , there is some integer M n > n such that ℒ N ( n ) is properly contained in ℒ N ( M n ), then ℒ N ( n ) is properly contained in ℒ N ( n + c N ) for each n , where c N =1 or 2, depending on the type of the device. As a consequence, it is shown that deterministic two-way finite automata with n +2 heads are strictly more powerful than deterministic two-way finite automata with n heads for each positive integer n . It is also shown that the class of sets accepted by deterministic (nondeterministic) two-way pushdown automata with n heads is properly included in the class of sets accepted by deterministic (nondeterministic) two-way pushdown automata with n +1 heads.