# Ultrametric automata and Turing machines

@inproceedings{Freivalds2012UltrametricAA,
title={Ultrametric automata and Turing machines},
author={Rusins Freivalds},
booktitle={Turing-100},
year={2012}
}
We introduce a notion of ultrametric automata and Turing machines using p-adic numbers to describe random branching of the process of computation. These automata have properties similar to the properties of probabilistic automata but complexity of probabilistic automata and complexity of ultrametric automata can differ very much.
• R. Freivalds
• Computer Science
Developments in Language Theory
• 2013
We introduce a notion of ultrametric automata and Turing machines using p-adic numbers to describe random branching of the process of computation. These automata have properties similar to the
We introduce a notion of ultrametric automata and Turing machines using p-adic numbers to describe random branching of the process of computation. These automata have properties similar to the
• Computer Science
• 2012
We introduce a notion of ultrametric finite automata using p-adic numbers to describe random branching of the process of computation. These automata have properties similar to the properties of
• Computer Science
Balt. J. Mod. Comput.
• 2016
A survey is presented on ultrametric automata and their language recognition capabilities and can have small number of states when classical automata require much more states.
• Computer Science
SOFSEM
• 2015
• Computer Science
SOFSEM
• 2015
We try to compare the complexity of deterministic, nondeterministic, probabilistic and ultrametric finite automata for the same language. We do not claim to have final upper and lower bounds. Rather
• K. Balodis
• Computer Science
Computing with New Resources
• 2014
We investigate the state complexity of probabilistic and ultrametric finite automata for the problem of counting, i.e. recognizing the one-word unary language $$C_n=\left\{ 1^n \right\}$$. We also
• Computer Science
• 2012
It is proved that Turing machines of this type can have advantages in reversal complexity over deterministic and probabilistic Turing machines.
• Computer Science
SOFSEM
• 2015
It is proved that in the one-way setting there is a language that can be recognized by a one-head ultrametric finite automaton and cannot be recognizing by any k-head non-deterministic finite automata.
• Mathematics
Int. J. Found. Comput. Sci.
• 2017
This work investigates the same question for different automata models and obtains new upper and lower bounds for some of them including alternating, ultrametric, quantum, and affine finite automata.

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We discuss ultrametric pseudodifferential operators and wavelets and applications to models of interbasin kinetics. We show, that, using the language of ultrametric pseudodifferential operators, it
The problem of determining the prime numbers p for which a given number a is a primitive root, modulo JP, is mentioned, for the partieular case a — 10, by Gauss in the section of the Disquisitiones
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