Unconventional Finite Automata and Algorithms

We investigate several unconventional models of finite automata and algorithms. We show that two-way alternating automata can be smaller than fast bounded-error probabilistic automata. We introduce ultrametric finite automata which use p-adic numbers to describe the branching process of the computation. We examine the size complexity of all the abovementioned automata for the counting problem. We also examine two-way frequency finite automata. We define ultrametric query algorithms and examine ultrametric query complexity for Boolean functions. We generalize the notion of frequency computation by requiring some structure for the correct outputs.