The proposed cryptographic model, VHCA, is a novel approach to encryption using cellular automata. This block cipher algorithm enables encryption and decryption of a plaintext using an arrangement of radius1 CA toggle rules, expressed as a binary secret key, to encrypt blocks having 128-bits or more. While hybrid CA forward evolution is used for encryption, a deterministic preimage computation logic is used for decryption. Promising results were obtained using periodic boundary condition, which favors diffusion, in combination with multiple permutive rules that are inherently balanced functions. Evaluations of the method using statistical randomness test suites, NIST and PractRand, point to the cryptographic robustness of VHCA.
Cellular automata (CAs) are homogeneous dynamical systems discrete in time, space and state variables, with global states being updated by means of a local function acting of the neighbourhood of their constituting parts. The family of elementary CAs (ECAs) is made up by the one-dimensional binary CAs with three next-nearest neighbours. Any one-dimensional CA's local function can be represented by a De Bruijn graph, in which connected pairs of nodes represent its possible neighbourhoods and the edges connecting them, the corresponding state transitions. De Bruijn graphs are specific kinds of process graphs, which are non-deterministic finite automata that can be used to represent the CA's regular language obtained at each finite instant of time in the CA's temporal evolution. The complexity of a process graph is defined defined in terms of the number of its nodes and edges. Previous works already analysed process graphs of ECAs' temporal evolution and their complexities, as well as their growth patterns over several iterations and limit behaviour. Here, we advance on what is known in this respect for ECAs, expanding previously known complexity data on the evolution of process graphs for various rules, inferring the limit behaviour of two rules and developing a direct way of constructing the process graph associated to a specific rule at any finite number of time steps.
Urban transport is a complex and dynamic system that affects the productivity, economy, and environment of cities. Traffic congestion and parking are two major challenges that urban transport faces, as they reduce the efficiency and capacity of the road network and cause delays and pollution. In this paper, we propose a novel system for traffic modeling and parking space management in urban centers, based on Cellular Automata (CAs). The system simulates the movement of vehicles on the road and allows drivers to find and reserve parking spaces in real time. Moreover, real data from the center of Alexandroupoli City in Greece have been used as a study case for the proposed system. The system incorporates various features to make the traffic model more realistic, such as intersections, traffic lights, multi-lane, parking procedure, and vehicle sizes. The paper demonstrates how the proposed system can prevent traffic congestion and, moreover, improve parking availability in urban areas.
A cellular automaton (CA) is a bio-inspired and parallel computing paradigm, whereby how to reduce the model's complexity but without compromising its computing power is a crucial subject. A typical example is the alpha-asynchronous cellular automaton (alpha-ACA) in (Lee. et al, 2005), which has the least complexity among all CAs of the same type and is able to implement a universal Turing machine, i.e., it is Turing- complete. The reduced complexity, however, comes at a cost that makes the ACA hard to realize the full functionalities of asynchronous circuits, especially of those circuits that can process an arbitrary number of signals in parallel. Such deficiency may raise a question about the parallel computing ability of the model. Because massive parallelism is an inherent feature of a CA and constitutes the basis for simulating various complex structures, including artificial intelligent systems and life, this paper attempts to identify a further universality of the alpha-ACA beyond the Turing-completeness. To this end, an effective scheme is proposed to explicitly construct a large-scale asynchronous circuit out of a restricted set of elements, which enables the ACA to simulate a universal synchronous cellular automaton via time-space rescaling, rather than a universal Turing machine. As a result, the alpha-ACA may possibly utilize its massive parallelism into universal computations as efficiently as other synchronous CAs or bio-inspired systems.
We propose a method for constructing 9-variable cryptographic Boolean functions from the iterates of 5-variable cellular automata rules. We then analyze, for important cryptographic properties of 5variable cellular automata rules, how they are preserved after extension to 9-variable Boolean functions. For each cryptographic property, we analyze the proportion of 5-variable cellular automata rules that preserve it for each of the 48 affine equivalence classes.
We investigate connections between near-rings and cellular automata. Near-rings are the nonlinear generalisation of rings. Collections of linear cellular automata are rings, the generalisation to near-rings allows us to look at nonlinear cellular automata in an algebraic setting, providing new tools. We show that cellular automata with group structured state sets form a centralizer near-ring under composition and cell-wise addition. The property of being a unit is undecidable in certain near-rings of cellular automata, introducing a new type of undecidability into near-ring theory. Non continuous, infinite radius generalised cellular automata are investigated. The continuous near-ring of cellular automata with finite arity local functions is shown to be 2-primitive. The radical for cellular automata on a finite space group is shown to be large, in contrast to the case of torsion free space groups. The quotient near-ring is determined in this case.
A continuous public goods game with variable elastic marginal profit is studied in this work both analytically and through numerical simulation a la cellular automata The implemented simulation suffers some difficulties in properly finding the Nash equilibrium in games with low elasticity, but proves to be very effective in finding the Pareto optimal solution in games with entangled players.
In this paper, we prove that there is a strongly universal cellular automaton on the heptagrid with five states under the relaxation of the assumption of rotation invariance for the rules. The result is different from that of a previous paper of the author with six states but with rotationally invariant rules. Here, the structures is more constrained than in the quoted paper with six states and rotation invariance of the rules.
Let A(Z) be a metric Cantor space of bi-infinite words and (A(Z), sigma) its corresponding full shift. Consider surjective CA (A(Z), F), (A(Z), sigma) with the Borel uniform Bernoulli measure mu. Let h(mu) (A(Z), F) and h(mu)(A(Z), sigma) denote KS-entropies of suitable CA. Denote by h(A(Z), F) the topological entropy of (A(Z), F). It is a well-known fact that for the former (lambda(+)(mu), lambda(-)(mu)) and average (I-mu(+), I-mu(-)) Lyapunov exponents of (A(Z), F), the inequalities I-mu(+) <= lambda(+)(mu), I-mu(-) <= lambda(-)(mu), h(mu) (A(Z), F) <= (I-mu(+) + I-mu(-)) center dot h(mu)(A(Z), sigma), h(A(Z), F) = (lambda(+)(mu) + lambda(-)(mu)) center dot h(mu)(A(Z), sigma) hold. Furthermore, under the above assumptions, there are examples of (A(Z), F) such that the average Lyapunov exponents provide a better upper bound for h(mu) (A(Z), F) than the former ones [P. Tisseur, Nonlinearity 13 (2000)]. In this paper we prove that under somewhat stronger assumptions, the average and former Lyapunov exponents can provide at least as excessive a real upper bound for h(mu)(A(Z), F) and h(A(Z), F), respectively, as we choose it to be.
John Pedersen proposed a way of continous transformation from one elementary cellular automaton into another one. This method grants us access to the whole new class of cellular automata with wide variety of convenient local functions; we will denote this class with P. Recently it was numerically shown that automata in P may have interesting computing capabilities. We have decided to investigate Pedersen automata, using Cantor topology, in search of some properties specific to this kind of automata. We have reached two main results: there are no isometries in P and radii of ball images are non-decreasing and bounded. We also show that similar local functions of two automata do not imply small Cantor distance between their values for equal arguments.
The life-like cellular Automata rule B34678/S3678 is a state symmetric rule with the unusual property that any area of one state in a universe of the other will transform into an area which is a chaotic mixture of both states. This area may either expand to fill the universe or shrink to an empty universe or a few small stable patterns. Larger patterns are more likely to expand than small ones. Statistical analysis of this behaviour is presented. It is noted that the chaotic mixture behaves like an extra state which is not symmetric with the others representing emergence of asymmetry.
A soft error in cellular automata (CA) is a temporal miss mapping of the local function in a cell. Because the error is temporal, caused by noise, etc, the cell works correctly in the next steps. In this paper we propose a method (or an algorithm) which converts any CA solving firing squad synchronization problem (FSSP) to new CA such that the CA recover one soft error if the error makes an undefined domain of the local function. The method first alters the local function to produce a reset state if the domain is undefined. Then the reset state propagates to left and right making any states to the soldiers. Once the reset state reaches to the left boundary, the state of the general is produced and FSSP restarts. It is proved that the reset and retry actions eventually recovers the soft error and achieves the synchronization.
In commemoration of the fifth anniversary since Nino Boccara's departure, this article offers some personal recollections and provides insight into his life and accomplishments. Detailed bibliography of his works is included together with commentary highlighting his major achievements.
In this paper, we describe a wave network for cellular automata that can generate positive integer geometric sequences {Ga1,r n}infinity (n=1) in real-time with at most r + a(1) + 2 states, where G(a1),(r) (n) = a(1)r n(-1) and r >= 2, a1 >= 1 are positive integers.
This paper discusses the potentiality of Cellular Automata (CAs) represented by first degree equations as source of randomness. These CAs are identified by eight constants, named as Parameters of First Degree CA. A greedy filtering technique is developed that uses existing chaotic parameters to identify the candidate CAs. Based on a theoretical strategy and experimental verification, a list of good first degree CA parameters are identified which remains as excellent source of randomness irrespective of change in number of states. Finally, we use these CAs as pseudo-random number generators.
Self-reproducing feature of cellular automata is one of the most important aim from the beginnings. In this article we show binary (2-state) infinite grid self-reproducing automata which reproduce (few copies) of the original pattern in various grids. For the three regular grids we prove their behavior based on path-counting. Similar machine also works on many semi-regular tilings. Moreover, we show that in some stage, by removing the copies and keeping only central embryo part of the pattern, it is able to reconstruct the pattern to be copied. To illustrate the self-reproduction various patterns are reproduced in various tessellations.
Quantum-dot Cellular Automata (QCA) is one of the approaches to synthesizing circuits with high density and low power dissipation to conquer pitfalls of CMOS. In QCA, the performance relies on the primitive gate count, which can be optimized by minimizing the gate count. On the other hand, proper cell layout, scalability, and reliability of the circuit can be ensured with the utilization of a regular clocking scheme. The impact of Genetic Algorithm (GA) in gate count optimization on regular clock based QCA circuits is analyzed in this research. Few multi-output boolean functions are realized using an elitism-based method considering USE and RES clocking schemes. A performance study with respect to energy consumption, QCA cost, and fault tolerance are analyzed in this work. Circuits are realized in QCADesigner. QCAPro and QCADesignerE are used for energy dissipation analysis, whereas HDLQ is used for fault tolerance analysis. The result witnessed an oscillating observation in the performance of the USE and RES clocking schemes.
This paper investigates patterns generated by some one-dimensional spatially and temporally non-uniform cellular automata. The spatially non-uniform cellular automaton is taken to be composed of finite celled blocks on the grid line where each block has a different local transition function and within any block all the cells follow same local transition function. In case of temporally non-uniform cellular automaton the entire time interval is an aggregate of blocks of time intervals. For a particular time block the cellular automaton is uniform having a particular local transition function. However, the local transition functions though same over the entire grid line differ for adjacent time blocks. The evolution patterns generated by identity, complementary, constant and shift functions and a combination of them as local transition functions are studied in this paper.
Reachability tree proves its power to characterize the elementary cel-lular automata under logic-0 constant (null) boundary condition and periodic boundary condition. A reachability tree implicitly represents the configuration space of a cellular automaton (CA). It reveals various aspects of CA, such as identification of reachable or non-reachable con -figuration, cyclic or acyclic configurations, determining reversibility or irreversibility of a given CA, and so on. This paper contributes towards the characterization of cellular automata under the open boundary con-ditions. A generalized view of reachability tree is reported, which tar -gets the different categories of open boundary condition -adiabatic boundary condition, reflexive boundary condition and constant bound-ary condition (logic-1 & logic-0). This work establishes that identical CA configuration space can be generated using cellular automata under the above mentioned boundary conditions, for a finite sized CA. This work also reports the characterization of reachability tree for CA under intermediate boundary condition which is another category of open boundary condition cellular automata.
Cellular Automata (CAs) are considered as a powerful mathematical modelling tool that is becoming more popular in scientific research and simulations. The potential of CAs to represent a broad range of physical, natural, and real-world events has grabbed the attention of researchers from a wide range of domains. Three-neighbourhood one-dimensional Cellular Automaton (CA) has a wide range of applications in a variety of disciplines, including VLSI design and testing, error-correcting codes, generation of test patterns, generation of hash functions and cryptographic encryption schemes, among others. The two-state three neighbourhood CA has been investigated in this work. A graph-based tool called the Next State RMT Transition Diagram (NSRTD) is delineated for analysing the state transition behaviour of CA with fixed points. A methodology using the NSRTD has been explored for synthesising a particular class of irreversible CA known as Single Length Cycle Two Attractor CA (TACA), having only two fixed points. Further, the proposed methodology has been extended for scalable synthesis of TACA, wherein we have considered synthesis of an (n + 1) length TACA from an existing configuration of n-length TACA and an (n +m)-length TACA from an existing configuration of n-length and m-length TACA.
