One-way multihead deterministic finite automata

SummaryIt is shown that the family of languages recognized by one-way k head deterministic finite state automata ℒ(1 DFA(k)) and the family of languages recognized by one-way k head deterministic sensing finite state automata ℒ(1DSeFA(k)) are not closed under concatenation, Kleene star and reversal for k≧2. These results are obtained as consequences of a theorem giving a sufficient condition for a language L in order not to be in ℒ(1DSeFA(k)). Several further results above the classes ℒ(1DFA(k)) and ℒ(1DSeFA(k)) are simple consequences of this theorem.