Fooling a two Way Automaton or one Pushdown Store is better than one Counter for two Way Machines

Abstract We define a language L and show that it cannot be recognized by any two way deterministic counter machine. It is done by fooling any given such machine; i.e. showing that if it accepts L ' ⊇ L , then L ' − L ≠ O . For this purpose, an argument stronger than the well-known crossing sequence argument needs to be introduced. Since L is accepted by a two-way deterministic pushdown automation, we consequently show that one pushdown stack is more powerful than one counter for deterministic two way machines.