scholarly journals Simulating reversible Turing machines and cyclic tag systems by one-dimensional reversible cellular automata

2011 ◽  
Vol 412 (30) ◽  
pp. 3856-3865 ◽  
Author(s):  
Kenichi Morita
Keyword(s):  
Cellular Automata ◽  
Turing Machines ◽  
One Dimensional ◽  
Reversible Cellular Automata

scholarly journals BLOCK CIPHERS ON THE BASIS OF REVERSIBLE CELLULAR AUTOMATA

2020 ◽  
Vol 10 (1) ◽  
pp. 8-11
Author(s):  
Yuliya Tanasyuk ◽  
Petro Burdeinyi
Keyword(s):  
Cellular Automata ◽  
Block Cipher ◽  
Key Generation ◽  
One Dimensional ◽  
C Programming Language ◽  
C Programming ◽  
Shared Secret ◽  
Reversible Cellular Automata ◽  
The Given ◽  
First Time

The given paper is devoted to the software development of block cipher based on reversible one-dimensional cellular automata and the study of its statistical properties. The software implementation of the proposed encryption algorithm is performed in C# programming language in Visual Studio 2017. The paper presents specially designed approach for key generation. To ensure desired cryptographic stability, the shared secret parameters can be adjusted to contain information needed for creating substitution tables, defining reversible rules, and hiding final data. For the first time, it is suggested to create substitution tables based on iterations of a cellular automaton that is initialized by the key data.

scholarly journals Complexity-theoretic aspects of expanding cellular automata

2020 ◽  
Author(s):  
Augusto Modanese
Keyword(s):  
Cellular Automata ◽  
Polynomial Time ◽  
Time Complexity ◽  
Truth Table ◽  
Decision Problems ◽  
Turing Machines ◽  
One Dimensional ◽  
Alternative Characterization ◽  
Time Class ◽  
Theoretical Standpoint

Abstract The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between existing ones. The respective polynomial-time complexity class is shown to coincide with $${\le _{tt}^p}(\textsf {NP})$$ ≤ tt p ( NP ) , that is, the class of decision problems polynomial-time truth-table reducible to problems in $$\textsf {NP}$$ NP . An alternative characterization based on a variant of non-deterministic Turing machines is also given. In addition, corollaries on select XCA variants are proven: XCAs with multiple accept and reject states are shown to be polynomial-time equivalent to the original XCA model. Finally, XCAs with alternative acceptance conditions are considered and classified in terms of $${\le _{tt}^p}(\textsf {NP})$$ ≤ tt p ( NP ) and the Turing machine polynomial-time class $$\textsf {P}$$ P .

scholarly journals SPECTRAL PROPERTIES OF REVERSIBLE ONE-DIMENSIONAL CELLULAR AUTOMATA

2003 ◽  
Vol 14 (03) ◽  
pp. 379-395 ◽  
Author(s):  
JUAN CARLOS SECK TUOH MORA ◽  
SERGIO V. CHAPA VERGARA ◽  
GENARO JUÁREZ MARTÍNEZ ◽  
HAROLD V. McINTOSH
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Spectral Properties ◽  
Neighborhood Size ◽  
Local Behavior ◽  
One Dimensional ◽  
Single Positive ◽  
Reversible Cellular Automata ◽  
Inverse Rule

Reversible cellular automata are invertible dynamical systems characterized by discreteness, determinism and local interaction. This article studies the local behavior of reversible one-dimensional cellular automata by means of the spectral properties of their connectivity matrices. We use the transformation of every one-dimensional cellular automaton to another of neighborhood size 2 to generalize the results exposed in this paper. In particular we prove that the connectivity matrices have a single positive eigenvalue equal to 1; based on this result we also prove the idempotent behavior of these matrices. The significance of this property lies in the implementation of a matrix technique for detecting whether a one-dimensional cellular automaton is reversible or not. In particular, we present a procedure using the eigenvectors of these matrices to find the inverse rule of a given reversible one-dimensional cellular automaton. Finally illustrative examples are provided.

HOW TO SIMULATE TURING MACHINES BY INVERTIBLE ONE-DIMENSIONAL CELLULAR AUTOMATA

1995 ◽  
Vol 06 (04) ◽  
pp. 395-402 ◽  
Author(s):  
JEAN-CHRISTOPHE DUBACQ
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Turing Machine ◽  
Turing Machines ◽  
One Dimensional

The issue of testing invertibility of cellular automata has been often discussed. Constructing invertible automata is very useful for simulating invertible dynamical systems, based on local rules. The computation universality of cellular automata has long been positively resolved, and by showing that any cellular automaton could be simulated by an invertible one having a superior dimension, Toffoli proved that invertible cellular automaton of dimension d≥2 were computation-universal. Morita proved that any invertible Turing Machine could be simulated by a one-dimensional invertible cellular automaton, which proved computation-universality of invertible cellular automata. This article shows how to simulate any Turing Machine by an invertible cellular automaton with no loss of time and gives, as a corollary, an easier proof of this result.

UNCONVENTIONAL INVERTIBLE BEHAVIORS IN REVERSIBLE ONE-DIMENSIONAL CELLULAR AUTOMATA

2008 ◽  
Vol 18 (12) ◽  
pp. 3625-3632
Author(s):  
JUAN CARLOS SECK TUOH MORA ◽  
MANUEL GONZÁLEZ HERNÁNDEZ ◽  
GENARO JUÁREZ MARTÍNEZ ◽  
SERGIO V. CHAPA VERGARA ◽  
HAROLD V. McINTOSH
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Temporal Evolution ◽  
Complete Characterization ◽  
Dimensional Case ◽  
Neighborhood Size ◽  
One Dimensional ◽  
Combinatorial Properties ◽  
Reversible Cellular Automata ◽  
The One

Reversible cellular automata are discrete invertible dynamical systems determined by local interactions among their components. For the one-dimensional case, there are classical references providing a complete characterization based on combinatorial properties. Using these results and the simulation of every automaton by another with neighborhood size 2, this paper describes other types of invertible behaviors embedded in these systems different from the classical one observed in the temporal evolution. In particular, spatial reversibility and diagonal surjectivity are studied, and the generation of macrocells in the evolution space is analyzed.

scholarly journals The reversibility of one-dimensional cellular automata

2021 ◽  
Vol 22 (1) ◽  
pp. 7-15
Author(s):  
Alexey E. Zhukov
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
High Performance ◽  
Finite Automata ◽  
Finite Size ◽  
Transition Function ◽  
One Dimensional ◽  
Enumeration Problems ◽  
Reversible Cellular Automata ◽  
Binary Filter

Recently the reversible cellular automata are increasingly used to build high-performance cryptographic algorithms. The paper establishes a connection between the reversibility of homogeneous one-dimensional binary cellular automata of a finite size and the properties of a structure called binary filter with input memory and such finite automata properties as the prohibitions in automata output and loss of information. We show that finding the preimage for an arbitrary configuration of a one-dimensional cellular automaton of length L with a local transition function f is associated with reversibility of a binary filter with input memory. As a fact, the nonlinear filter with an input memory corresponding to our cellular automaton does not depend on the number of memory cells of the cellular automaton. The results obtained make it possible to reduce the complexity of solving massive enumeration problems related to the issues of reversibility of cellular automata. All the results obtained can be transferred to cellular automata with non-binary cell filling and to cellular automata of dimension greater than 1.

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