# 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.

## 14 Citations

### Ultrametric Finite Automata and Turing Machines

- Computer ScienceDevelopments 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…

### Ultrametric Algorithms and Automata

- Computer ScienceUCNC
- 2015

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…

### On the State Complexity of Ultrametric Finite Automata

- 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…

### Ultrametric Finite Automata and Their Capabilities

- Computer ScienceBalt. 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.

### Ultrametric Automata with One Head Versus Multihead Nondeterministic Automata

- Computer ScienceSOFSEM
- 2015

Advantages of ultrametric automata with one head versus multihead deterministic and nondeterministic automata are observed.

### Experiments in Complexity of Probabilistic and Ultrametric Automata

- Computer ScienceSOFSEM
- 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…

### Counting with Probabilistic and Ultrametric Finite Automata

- Computer ScienceComputing 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…

### Ultrametric Turing Machines with Limited Reversal Complexity ?

- Computer Science
- 2012

It is proved that Turing machines of this type can have advantages in reversal complexity over deterministic and probabilistic Turing machines.

### On the Hierarchy Classes of Finite Ultrametric Automata

- Computer ScienceSOFSEM
- 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.

### On a Conjecture by Christian Choffrut

- MathematicsInt. 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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