String-Matching Cannot be Done by a Two-Head One-Way Deterministic Finite Automaton

Abstract

We show that string-matching cannot be performed by a two-head one-way deterministic finite automaton (or even by a Turing machine with two one-way input heads and o(n) storage space). Thus we answer the special case $k=2$ of the open question, due to Galil and Seiferas [GS], whether a $k$-head one-way deterministic finite automaton can perform string-matching.