An Evolutionary Approach to the Design of Controllable Cellular Automata Structure for Random Number Generation

Cellular Automata (CA) has been used in pseudorandom number generation over a decade. Recent studies show that two-dimensional (2-d) CA Pseudorandom Number Generators (PRNGs) may generate better random sequences than conventional one-dimensional (1-d) CA PRNGs, but they are more complex to implement in hardware than 1-d CA PRNGs. In this paper, we propose a new class of 1-d CA Controllable Cellular Automata (CCA) without much deviation from the structure simplicity of conventional 1-d CA. We give a general definition of CCA first and then introduce two types of CCA – CCA0 and CCA2. Our initial study on them shows that these two CCA PRNGs have better randomness quality than conventional 1-d CA PRNGs but their randomness is affected by their structures. To find good CCA0/CCA2 structures for pseudorandom number generation, we evolve them using the Evolutionary Multi-Objective Optimization (EMOO) techniques. Three different algorithms are presented in this paper. One makes use of an aggregation function; the other two are based on the Vector Evaluated Genetic Algorithm (VEGA). Evolution results show that these three algorithms all perform well. Applying a set of randomness tests on the evolved CCA PRNGs, we demonstrate that their randomness is better than that of 1-d CA PRNGs and can be comparable to that of two-dimensional CA PRNGs

Incremental evolution of cellular automata for random number generation

Cellular automata (CA) have been used in pseudorandom number generation for over a decade. Recent studies show that controllable CA (CCA) can generate better random sequences than conventional one-dimensional (1-d) CA and compete with two-dimensional (2-d) CA. Yet the structural complexity of CCA is higher than that of 1-d PCA. It would be good if CCA can attain good randomness quality with the least structural complexity. In this paper, we evolve PCA/CCA to their lowest complexity level using genetic algorithms (GAs). Meanwhile, the randomness quality and output efficiency of PCA/CCA are also evolved. The evolution process involves two algorithms a multi-objective genetic algorithm (MOGA) and an algorithm for incremental evolution. A set of PCA/CCA are evolved and compared in randomness, complexity, and efficiency. The results show that without any spacing, CCA could generate good random number sequences that could pass DIEHARD. And, to obtain the same randomness quality, the structural complexity of CCA is not higher than that of 1-d CA. Furthermore, the methodology developed could be used to evolve other CA or serve as a yardstick to compare different types of CA

A Family of Controllable Cellular Automata for Pseudorandom Number Generation

In this paper, we present a family of novel Pseudorandom Number Generators (PRNGs) based on Controllable Cellular Automata (CCA) ─ CCA0, CCA1, CCA2 (NCA), CCA3 (BCA), CCA4 (asymmetric NCA), CCA5, CCA6 and CCA7 PRNGs. The ENT and DIEHARD test suites are used to evaluate the randomness of these CCA PRNGs. The results show that their randomness is better than that of conventional CA and PCA PRNGs while they do not lose the structure simplicity of 1-d CA. Moreover, their randomness can be comparable to that of 2-d CA PRNGs. Furthermore, we integrate six different types of CCA PRNGs to form CCA PRNG groups to see if the randomness quality of such groups could exceed that of any individual CCA PRNG. Genetic Algorithm (GA) is used to evolve the configuration of the CCA PRNG groups. Randomness test results on the evolved CCA PRNG groups show that the randomness of the evolved groups is further improved compared with any individual CCA PRNG

The riddle of togelby

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.At the 2017 Artificial and Computational Intelligence in Games meeting at Dagstuhl, Julian Togelius asked how to make spaces where every way of filling in the details yielded a good game. This study examines the possibility of enriching search spaces so that they contain very high rates of interesting objects, specifically game elements. While we do not answer the full challenge of finding good games throughout the space, this study highlights a number of potential avenues. These include naturally rich spaces, a simple technique for modifying a representation to search only rich parts of a larger search space, and representations that are highly expressive and so exhibit highly restricted and consequently enriched search spaces. We treat the creation of plausible road systems, useful graphics, highly expressive room placement for maps, generation of cavern-like maps, and combinatorial puzzle spaces.Final Accepted Versio

Pseudorandom number generation with self programmable cellular automata

In this paper, we propose a new class of cellular automata – self programming cellular automata (SPCA) with specific application to pseudorandom number generation. By changing a cell's state transition rules in relation to factors such as its neighboring cell's states, behavioral complexity can be increased and utilized. Interplay between the state transition neighborhood and rule selection neighborhood leads to a new composite neighborhood and state transition rule that is the linear combination of two different mappings with different temporal dependencies. It is proved that when the transitional matrices for both the state transition and rule selection neighborhood are non-singular, SPCA will not exhibit non-group behavior. Good performance can be obtained using simple neighborhoods with certain CA length, transition rules etc. Certain configurations of SPCA pass all DIEHARD and ENT tests with an implementation cost lower than current reported work. Output sampling methods are also suggested to improve output efficiency by sampling the outputs of the new rule selection neighborhoods

Layered cellular automata for pseudorandom number generation

The proposed Layered Cellular Automata (L-LCA), which comprises of a main CA with L additional layers of memory registers, has simple local interconnections and high operating speed. The time-varying L-LCA transformation at each clock can be reduced to a single transformation in the set formed by the transformation matrix of a maximum length Cellular Automata (CA), and the entire transformation sequence for a single period can be obtained. The analysis for the period characteristics of state sequences is simplified by analyzing representative transformation sequences determined by the phase difference between the initial states for each layer. The L-LCA model can be extended by adding more layers of memory or through the use of a larger main CA based on widely available maximum length CA. Several L-LCA (L=1,2,3,4) with 10- to 48-bit main CA are subjected to the DIEHARD test suite and better results are obtained over other CA designs reported in the literature. The experiments are repeated using the well-known nonlinear functions and in place of the linear function used in the L-LCA. Linear complexity is significantly increased when or is used

Permutation and sampling with maximum length CA for pseudorandom number generation

In this paper, we study the effect of dynamic permutation and sampling on the randomness quality of sequences generated by cellular automata (CA). Dynamic permutation and sampling have not been explored in previous CA work and a suitable implementation is shown using a two CA model. Three different schemes that incorporate these two operations are suggested - Weighted Permutation Vector Sampling with Controlled Multiplexing, Weighted Permutation Vector Sampling with Irregular Decimation and Permutation Programmed CA Sampling. The experiment results show that the resulting sequences have varying degrees of improvement in DIEHARD results and linear complexity compared to the CA

A transformation sequencing approach to pseudorandom number generation

This paper presents a new approach to designing pseudorandom number generators based on cellular automata. Current cellular automata designs either focus on i) ensuring desirable sequence properties such as maximum length period, balanced distribution of bits and uniform distribution of n-bit tuples etc. or ii) ensuring the generated sequences pass stringent randomness tests. In this work, important design patterns are first identified from the latter approach and then incorporated into cellular automata such that the desirable sequence properties are preserved like in the former approach. Preliminary experiment results show that the new cellular automata designed have potential in passing all DIEHARD tests

Evolving cellular automata to generate nonlinear sequences with desirable properties

This paper presents a new chromosomal representation and associated genetic operators for the evolution of highly nonlinear cellular automata that generate pseudorandom number sequences with desirable properties ensured. This chromosomal representation reduces the computational complexity of genetic operators to evolve valid solutions while facilitating fitness evaluation based on the DIEHARD statistical tests