Advantages of Ultrametric Counter Automata

Ultrametric algorithms are similar to probabilistic algorithms but they describe the degree of indeterminism by p-adic numbers instead of real numbers. No wonder that only very few examples of advantages for ultrametric algorithms over probabilistic ones have been published up to now, and all they are slightly artificial. This paper considers ultrametric and probabilistic one-counter automata with two one-way input tapes. A language is found which is recognizable by ultrametric but not by probabilistic automata of this type.