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. 
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14 Citations
Highly Influential Citations
4
Background Citations
7
Methods Citations
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14 Citations

Ultrametric Finite Automata and Turing Machines

  • 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…

Ultrametric Algorithms and Automata

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

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

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

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

Experiments in Complexity of Probabilistic and Ultrametric Automata

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

  • 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…

Ultrametric Turing Machines with Limited Reversal Complexity ?

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

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

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.

References

SHOWING 1-10 OF 25 REFERENCES

Non-Constructive Methods for Finite Probabilistic Automata

  • R. Freivalds
  • Computer Science, Mathematics
    Int. J. Found. Comput. Sci.
  • 2007
Finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton, and these results imply a similar result for quantum finite automata.

Algorithmic Number Theory

  • W. Bosma
  • Mathematics, Computer Science
    Lecture Notes in Computer Science
  • 2000
Ajtai’s worstcase/average-case connections for the shortest vector problem, similar results for the closest vector problem and short basis problem, NP-hardness and non-NP- hardness, transference theorems between primal and dual lattices, and application to secure cryptography are discussed.

Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models

I. Measurements and Numbers. II. Fundamentals. III. Non-Archimedean Analysis. IV. The Ultrametric Hilbert Space Description of Quantum Measurements with a Finite Exactness. V. Non-Kolmogorov…

P-adic analysis and mathematical physics

P-adic numbers p-adic analysis non-Archimedean geometry distribution theory pseudo differential operators and spectral theory p-adic quantum mechanics and representation theory quantum field theory…

Ultrametric Analysis and Interbasin Kinetics

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…

On Artin's conjecture.

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…

Quantum Computing

p-adic Numbers, p-adic Analysis, and Zeta-Functions

P-adic numbers p-adic interpolation of the reimann zeta-function p-adic power series rationality of the zeta-function of a set of equations over a finite field (Part contents).

P-Adic Numbers: An Introduction

1 Aperitif.- 1 Aperitif.- 1.1 Hensel's Analogy.- 1.2 Solving Congruences Modulopn.- 1.3 Other Examples.- 2 Foundations.- 2.1 Absolute Values on a Field.- 2.2 Basic Properties.- 2.3 Topology.- 2.4…

On Artin's Conjecture for Primitive Roots

Various generalizations of the Artin’s Conjecture for primitive roots are considered. It is proven that for at least half of the primes p, the first log p primes generate a primitive root. A uniform…