# Universal Simulation of Automata Networks

@article{CastilloRamirez2015UniversalSO, title={Universal Simulation of Automata Networks}, author={Alonso Castillo-Ramirez and Maximilien Gadouleau}, journal={ArXiv}, year={2015}, volume={abs/1504.00169} }

Let A be a finite set and n ≥ 2. This paper introduces the concept of universal simulation in the context of semigroups of transformations of A n , also known as finite state-homogeneous automata networks. Using tools from memoryless computation, it is established that there is no universal transformation of size n that may simulate every transformation of A n , but there is such a universal transformation when the size is n + 2. A universal transformation is defined as complete if it may…

## One Citation

Technical Report Column

- Computer ScienceSIGA
- 2015

The quantitative relation between VC- dimension and two other basic parameters related to learning and teaching are studied, including the quality of sample compression schemes and of teaching sets for classes of low VC-dimension.

## References

SHOWING 1-10 OF 25 REFERENCES

A Universal Cellular Automaton in Quasi-Linear Time and its S-m-n Form

- Computer ScienceTheor. Comput. Sci.
- 1994

A quasi-linear time universal cellular automaton is described, which is capable of simulating arbitrary one-dimensional cellular automata, even two-way, and it is proved that cellular Automata form an acceptable programming system for parallel computation, thus providing an S-m-n theorem for Cellular automata.

Theory of cellular automata: A survey

- Computer Science, MathematicsTheor. Comput. Sci.
- 2005

The main goal is to provide a tutorial of CA theory to researchers in other branches of natural computing, to give a compact collection of known results with references to their proofs, and to suggest some open problems.

Computing in Permutation Groups Without Memory

- Computer Science, MathematicsChicago J. Theor. Comput. Sci.
- 2015

It is shown that binary instructions are not enough to compute all permutations without memory when the alphabet size is even, and guidelines on the implementation of memoryless computation are provided.

Mapping Computation with No Memory

- Computer ScienceUC
- 2009

The in situ trait of the programs constructed here applies to optimization of program and chip design with respect to the number of variables, since no extra writing memory is used.

Computing in Matrix Groups Without Memory

- Computer Science, MathematicsChicago J. Theor. Comput. Sci.
- 2015

The maximum complexity of a linear function when only linear instructions are allowed and which linear functions are hardest to compute when the field in question is the binary field and the number of registers is even are determined.

Algebraic theory of automata networks - an introduction

- Computer Science, MathematicsSIAM monographs on discrete mathematics and applications
- 2005

This paper presents a meta-analyses of Krohn-Rhodes theory and its applications to automata networks, aiming at determining the boundaries between state-homogeneous and asynchronous networks.

Memoryless computation: New results, constructions, and extensions

- Computer Science, MathematicsTheor. Comput. Sci.
- 2015

It is shown that combining variables, instead of simply moving them around, not only allows for memoryless programs, but also yields shorter programs and allows us to use only binary instructions, which is not sufficient in general when no memory is used.

Computation with No Memory, and Rearrangeable Multicast Networks

- Computer Science, MathematicsDiscret. Math. Theor. Comput. Sci.
- 2014

This paper surveys the computation of mappings from a set S^n to itself with "in situ programs", and details its close relation with rearrangeable multicast networks, and provides new results for both viewpoints.

Three generators for minimal writing-space computations

- Mathematics, Computer ScienceRAIRO Theor. Informatics Appl.
- 2000

In this paper, three functions are constructed such that any boolean mapping from {0,1} n to {1,0} n can be computed with a finite sequence of assignations only using the n input variables and those three functions.

Sequential computation of linear Boolean mappings

- Computer Science, MathematicsTheor. Comput. Sci.
- 2004

We prove that any linear Boolean mapping of dimension n can be computed with a double sequence of linear assignments of the n variables. The proof is effective and gives a decomposition of Boolean…