On the Hierarchy Classes of Finite Ultrametric Automata [chapter]

Rihards Krišlauks, Kaspars Balodis
2015 Lecture Notes in Computer Science  
This paper explores the language classes that arise with respect to the head count of a finite ultrametric automaton. First we prove that in the one-way setting there is a language that can be recognized by a one-head ultrametric finite automaton and cannot be recognized by any k-head non-deterministic finite automaton. Then we prove that in the two-way setting the class of languages recognized by ultrametric finite k-head automata is a proper subclass of the class of languages recognized by (k
more » ... + 1)-head automata. Ultrametric finite automata are similar to probabilistic and quantum automata and have only just recently been introduced by Freivalds. We introduce ultrametric Turing machines and ultrametric multi-register machines to assist in proving the results.
doi:10.1007/978-3-662-46078-8_26 fatcat:g5p6gzmbivclpionfufwsbx3xq