On the Hierarchy Classes of Finite Ultrametric Automata

  • Rihards Krišlauks
  • Kaspars Balodis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8939)


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 + 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.


Turing Machine Ultrametric Analysis Hierarchy Class Language Class Input Word 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Rihards Krišlauks
    • 1
  • Kaspars Balodis
    • 1
  1. 1.University of Latvia Faculty of ComputingRigaLatvia

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