computation theory of cellular automata self organizing behaviour in cellular automata is discussed as a computational process formal language theory is used to extend dynamical systems theory descriptions of cellular automata the sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages many examples are given the sizes of the minimal grammars for these languages provide measures of the complexities of the sets this complexity is usually found to be non decreasing with time the limit sets generated by some classes of cellular automata correspond to regular languages for other classes of cellular automata they appear to correspond to more complicated languages many properties of these sets are then formally non computable it is suggested that such undecidability is common in these and other dynamical systems

on the invertible cellular automata 150 over f p in this work the reversibility problem for cellular automata with rule number 150 over the finite field f p is tackled it is shown that when null boundary conditions are stated the reversibility is independent of the state set f p and it appears when the number of cells of the cellular space satisfies some conditions furthermore the explicit expressions of the inverse cellular automata are computed

matrices a such that as 1r ra with rk i abstract we study matrices a c n n such that a s 1 r r a where r k i n and s k are nonnegative integers with k 2 such matrices are called r s 1 k potent matrices the s 0 case corresponds to matrices such that a r a r 1 with r k i n and is studied using spectral properties of the matrix r for s 1 various characterizations of the class of r s 1 k potent matrices and relationships between these matrices and other classes of matrices are presented

nondeterministic cellular automata abstract using purely topological concepts we characterize the class of nondeterministic mappings between shift spaces that give rise to nondeterministic sliding block codes we use such topological notions to investigate basic properties of surjective and reversible nondeterministic cellular automata

when and how can a cellular automaton be rewritten as a lattice gas both cellular automata ca and lattice gas automata lg provide finite algorithmic presentations for certain classes of infinite dynamical systems studied by symbolic dynamics it is customary to use the terms cellular automaton and lattice gas for a dynamic system itself as well as for its presentation the two kinds of presentation share many traits but also display profound differences on issues ranging from decidability to modeling convenience and physical implementability following a conjecture by toffoli and margolus it had been proved by kari that any invertible ca at least up to two dimensions can be rewritten as an isomorphic lg but until now it was not known whether this is possible in general for noninvertible ca which comprise almost all ca and represent the bulk of examples in theory and applications even circumstantial evidence whether in favor or against was lacking here for noninvertible ca a we prove that an lg presentation is out of the question for the vanishingly small class of surjective ones we then turn our attention to all the rest noninvertible and nonsurjective which comprise all the typical ones including conway s game of life for these b we prove by explicit construction that all the one dimensional ones are representable as lg and c we present and motivate the conjecture that this result extends to any number of dimensions the tradeoff between dissipation rate and structural complexity implied by the above results have compelling implications for the thermodynamics of computation at a microscopic scale

an adaptive secret image sharing with a new bitwise steganographic property recently numerous studies have been conducted in the area of secret image sharing and steganography the main objective of these schemes is to produce high quality tampering resistant stego images a number of these methods are based on least significant bit embedding and hence the presence of hidden data can be detected by well designed steganalysis algorithms this paper proposes a new sharing scheme for critical images so that stego images are obtained with better visual quality and at the same time the authentication ability can be adjusted to any desired level adaptive in order to achieve these objectives the construction of cellular automata is modified so that visual quality is improved although authentication bits are hidden in cover images furthermore authentication bits are computed in such a way that any tampering with one block affects more than one block for steganographic purposes least significant bit replacement is substituted with a new blockwise xor operation so that the scheme can withstand steganalysis attacks the other interesting property of the proposed method is that the size of blocks is determined dynamically therefore our approach can be adapted with secret cover images of different sizes

invertible cellular automata a review abstract in the light of recent developments in the theory of invertible cellular automata we attempt to give a unified presentation of the subject and discuss its relevance to computer science and mathematical physics

how to turn a second order cellular automaton into a lattice gas a new inversion scheme in second order cellular automata the signals made available to the local transition function include besides the current state of a site s neighbors also the previous state of the site itself some similarities had been noted especially in physics simulations between certain second order cellular automata and certain lattice gases here we show how to construct for any second order cellular automaton a lattice gas having isomorphic functional behavior paradoxically this isomorphism of function is achieved by compromising on the isomorphism of structure namely the group of translation symmetries of the resulting lattice gas is coarser than that of the original cellular automaton the advantage of our construction is that while invertibility in cellular automata is not directly deducible from the local map indeed it is in general undecidable in the second order case the invertibility of the cellular automaton goes hand in hand with that of the corresponding lattice gas and for lattices gases invertibility is trivially decidable on the basis of the local structure from a physical viewpoint our construction illustrates a trade off between two ways of achieving a force of a given range in a cellular automaton multiple copies of a signal are made and distributed in parallel to several sites explicitly providing the desired fanout width in a lattice gas with our construction one can let a single signal serially service a number of sites along an appropriate spacetime route the latter method is better suited to a nondissipative implementation of the dynamics

from quantum cellular automata to quantum lattice gases a natural architecture for nanoscale quantum computation is that of a quantum cellular automaton motivated by this observation we begin an investigation of exactly unitary cellular automata after proving that there can be no nontrivial homogeneous local unitary scalar cellular automaton in one dimension we weaken the homogeneity condition and show that there are nontrivial exactly unitary partitioning cellular automata we find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton this model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the dirac equation we describe two generalizations of this automaton the second of which to multiple interacting particles is the correct definition of a quantum lattice gas

garden of eden configurations for 2 d cellular automata with rule 2460n an important problem in cellular automata theory is the reversibility of a cellular automaton which is related to the existence of garden of eden configurations in cellular automata in this paper we study new local rules for two dimensional cellular automata over the ternary field z 3 the set of integers modulo three with some of their important characteristics we obtain necessary and sufficient conditions for the existence of garden of eden configurations for two dimensional ternary cellular automata also by making use of the matrix representation of two dimensional cellular automata we provide an algorithm to obtain the number of garden of eden configurations for two dimensional cellular automata defined by rule 2460n we present an application of the reversible two dimensional ternary cellular automata to cryptography

a lattice boltzmann equation for diffusion the formulation of lattice gas automata lga for given partial differential equations is not straightforward and still requires some sort of magic lattice boltzmann equation lbe models are much more flexible than lga because of the freedom in choosing equilibrium distributions with free parameters which can be set after a multiscale expansion according to certain requirements here a lbe is presented for diffusion in an arbitrary number of dimensions the model is probably the simplest lbe which can be formulated it is shown that the resulting algorithm with relaxation parameter 1 is identical to an explicit finite difference efd formulation at its stability limit underrelaxation 0 1 allows stable integration beyond the stability limit of efd the time step of the explicit lbe integration is limited by accuracy and not by stability requirements

efficient exhaustive listings of reversible one dimensional cellular automata this paper looks at an algebraic formulation of one dimensional cellular automata using the formulation connections to combinatorial structures and graph theory become clear strong results about uniqueness and isomorphism allows us to outline effective algorithms for the generation of exhaustive lists of reversible one dimensional cellular automata and to count the number of distinct examples that exist these algorithms use the orderly algorithm methods to avoid the pitfalls of brute force searches

universality of a reversible two counter machine abstract a k counter machine cm k is an automaton having k counters as an auxiliary memory it has been shown by minsky that a cm 2 can simulate any turing machine and thus it is universal in this paper we investigate the computing ability of reversible i e backward deterministic cms we first show that any irreversible cm k can be simulated by a reversible cm k 2 in this simulation however the reversible cm k 2 leaves a large number as a garbage in some counter when it halts we then show that if k more counters are added this garbage information is erased reversibly finally we prove that any reversible cm k k 1 2 3 can be simulated by a reversible cm 2 from these results computation universality of a reversible cm 2 is established

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

graph theoretical characterization of invertible cellular automata abstract a cellular automaton is defined to be invertible if its induced global rule is surjective on the set of all finite configurations it is shown that all one dimensional invertible cellular automata are obtainable from invertible nearest pair ones i e cellular automata given by a rule matrix for these an algorithm is proposed which runs in a time which is a polynomial function of the number of letters of the alphabet the result is expressed in a graph theoretical way the cellular automaton is invertible if and only if two graphs constructed by the algorithm have no edges in common it follows that if the number of letters in the alphabet is a prime the only invertible cellular automata are those for which every row or column of the rule matrix is a permutation of the alphabet for composite alphabet cardinalities several methods analytical and computational ones to obtain more complicated invertible cellular automata are proposed and used to construct examples all four letter invertible automata are constructed

cellular automata as an alternative to rather than an approximation of differential equations in modeling physics abstract cellular automata are models of distributed dynamical systems whose structure is particularly well suited to ultrafast exact numerical simulation on the other hand they constitute a radical departure from the traditional partial differential equation approach to distributed dynamics here we discuss the problem of encoding the state variables and evolution laws of a physical system into this new setting and of giving suitable correspondence rules for interpreting the model s behavior

physics like models of computation abstract reversible cellular automata are computer models that embody discrete analogues of the classical physics notions of space time locality and microscopic reversibility they are offered as a step towards models of computation that are closer to fundamental physics

matrix methods and local properties of reversible one dimensional cellular automata the local behaviour of reversible one dimensional cellular automata is analysed based on perron frobenius theory it is proved by means of irreducible components that the connectivity matrices of reversible automata have a single eigenvalue equal to 1 the idempotent behaviour of such matrices is also proved by faddeev s algorithm the decomposition of these matrices into triangular factors is used to find the inverse rule for a given reversible automaton

on the size of the inverse neighborhoods for one dimensional reversible cellular automata in this paper we investigate the possible neighborhood size of the inverse automaton of some types of one dimensional reversible cellular automata considering only the case when the local function is a size two map we give a quadratic upper bound for the neighborhood size of the inverse automaton we show that this bound can be lowered in some particular cases and give an algorithm for computing these better bounds

an energy balance climate model with hysteresis abstract energy balance climate models of budyko type lead to reaction diffusion equations with slow diffusion and memory on the 2 sphere the reaction part exhibits a jump discontinuity at the snow line here we introduce a babuska duhem hysteresis in order to account for a frequent repetition of sudden and fast warming followed by much slower cooling as observed from paleoclimate proxy data existence of global solutions and of a trajectory attractor will be established for the resulting system of a parabolic differential inclusion and an ode

a class of globally controllable semilinear heat equations with superlinear terms abstract it is well known nowadays that a rather general semilinear parabolic equation governed in a bounded domain by boundary or locally distributed controls can be made globally approximately controllable in l p type spaces provided the nonlinearity is globally lipschitz however the question whether this property can possibly take place in the superlinear case in several space dimensions seems to be open the goal of this article is to describe a special class of semilinear heat equations with superlinear terms for which this property indeed holds our technique combines the asymptotic method of a y khapalov 1995 j math anal appl 194 858 882 with certain a priori estimates for the corresponding truncated spectral problem

a hierarchical classification of cellular automata abstract a central issue in the theory of cellular automata is classification a classification is a structure imposed on the space of automata which groups together cellular automata with related properties in this paper a classification based on the action of cellular automata on n step markov measures is presented this classification is hierarchical and parametric an algorithm is described which efficiently constructs all rules in a given class at a given level of the hierarchy the utility of the classification is explored in the study of the invariant statistical properties of next nearest neighbor cellular automata on two states per cell

algorithms for solving the inverse problem associated with k a k a s 1 in previous papers the authors introduced and characterized a class of matrices called k s 1 potent also they established a method to construct these matrices the purpose of this paper is to solve the associated inverse problem several algorithms are developed in order to find all involutory matrices k satisfying k a s 1 k a for a given matrix a c n n and a given natural number s the cases s 0 and s 1 are separately studied since they produce different situations in addition some examples are presented showing the numerical performance of the methods

classifying circular cellular automata we introduce a hierarchy of linear cellular automata based on their limiting behavior on spatially periodic configurations we show that it is undecidable to which class in the hierarchy a cellular automaton belongs in particular it is undecidable whether all spatially periodic configurations evolve to a fixed point furthermore there is no computable bound on the period lengths of these configurations our arguments are based on a non standard simulation of turing machines on circular cellular automata

carleman estimates for a class of degenerate parabolic operators given alpha in 0 2 and f in l 2 0 t times 0 1 we derive new carleman estimates for the degenerate parabolic problem w t x alpha w x x f where t x in 0 t times 0 1 associated to the boundary conditions w t 1 0 and w t 0 0 if 0 leq alpha 1 or x alpha w x t 0 0 if 1 leq alpha 2 the proof is based on the choice of suitable weighted functions and hardy type inequalities as a consequence for all 0 leq alpha 2 and omega subset subset 0 1 we deduce null controllability results for the degenerate one dimensional heat equation u t x alpha u x x h chi omega with the same boundary conditions as above

continuity of information transport in surjective cellular automata we introduce a local version of the shannon entropy in order to describe information transport in spatially extended dynamical systems and to explore to what extent information can be viewed as a local quantity using an appropriately defined information current this quantity is shown to obey a local conservation law in the case of one dimensional reversible cellular automata with arbitrary initial measures the result is also shown to apply to one dimensional surjective cellular automata in the case of shift invariant measures bounds on the information flow are also shown

relaxation properties of elementary reversible cellular automata abstract the relaxation properties of a number of elementary reversible cellular automata are studied different rules have different types of relaxation behavior possible relationships between the thermodynamic behavior and phase space structure are discussed

inverse rules of eca with rule number 150 the explicit expressions of local transition functions of the inverse cellular automata of elementary cellular automata with rule number 150 and periodic boundary conditions are given the procedure to obtain such local transition functions is based on the algebraic properties of elementary cellular automata

a random np complete problem for inversion of 2d cellular automata in this paper we prove the co rnp completeness rnp random np of the following decision problem given a 2 dimensional cellular automaton a is a reversible when restricted to finite configurations extending a given row in order to prove this result we introduce a polynomial reduction from problems concerning finite tilings into problems concerning cellular automata then we add to tile sets and cellular automata two probability functions and we prove that these problems are not only co np complete but co rnp complete too

approximate controllability for nonlinear degenerate parabolic problems with bilinear control abstract in this paper we study the global approximate multiplicative controllability for nonlinear degenerate parabolic cauchy neumann problems first we obtain embedding results for weighted sobolev spaces that have proved decisive in reaching well posedness for nonlinear degenerate problems then we show that the above systems can be steered in l 2 from any nonzero nonnegative initial state into any neighborhood of any desirable nonnegative target state by bilinear piecewise static controls moreover we extend the above result relaxing the sign constraint on the initial data

controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term a qualitative approach in this paper we are concerned with the global nonnegative approximate controllability property of a rather general semilinear heat equation with superlinear term governed in a bounded domain omega subset r n by a multiplicative bilinear control in the reaction term like v u x t where v is the control we show that any nonnegative target state in l 2 omega can approximately be reached from any nonnegative nonzero initial state by applying at most three static bilinear l infty omega controls subsequently in time this result is further applied to discuss the controllability properties of the nonhomogeneous version of this problem with bilinear term like v u x t theta x where theta is given our approach is based on an asymptotic technique allowing us to distinguish and make use of the pure diffusion and or pure reaction parts of the dynamics of the system at hand while suppressing the effect of a general nonlinear term

interior degenerate singular parabolic equations in nondivergence form well posedness and carleman estimates abstract we consider non smooth general degenerate singular parabolic equations in non divergence form with degeneracy and singularity occurring in the interior of the spatial domain in presence of dirichlet or neumann boundary conditions in particular we consider well posedness of the problem and then we prove carleman estimates for the associated adjoint problem

a multisecret sharing scheme for color images based on cellular automata in this work a new multisecret sharing scheme for secret color images among a set of users is proposed the protocol allows that each participant in the scheme to share a secret color image with the rest of participants in such a way that all of them can recover all the secret color images only if the whole set of participants pools their shadows the proposed scheme is based on the use of bidimensional reversible cellular automata with memory the security of the scheme is studied and it is proved that the protocol is ideal and perfect and that it resists the most important statistical attacks

predecessors of cellular automata states ii pre images of finite sequences abstract graph theoretic techniques are used to derive algorithms which determine all pre images of any given finite sequence s under one dimensional cellular automata rules defined over z 2 it is also shown that for a given rule q the number of pre images of any finite sequence is determined by an algebraic form in the components of q this extends results of jen on the enumeration of pre images we also show that the set of k site rules for which a given sequence s has no pre images is determined by the solution set of a non linear diophantine equation

relations between k s 1 potent matrices and different classes of complex matrices in this paper k s 1 potent matrices are considered a matrix a cn n is called k s 1 potent when kas 1k a where k is an involutory matrix and s 1 2 3 specifically k s 1 potent matrices are analyzed considering their relations to different classes of complex matrices these classes of matrices are s 1 generalized projectors k hermitian matrices normal matrices and matrices b cn n anti commuting with k or such that kb is involutory hermitian or normal in addition some new relations for k generalized centrosymmetric matrices have been derived

two dimensional cellular automata a largely phenomenological study of two dimensional cellular automata is reported qualitative classes of behavior similar to those in one dimensional cellular automata are found growth from simple seeds in two dimensiona cellular automata can produce patterns with complicated boundaries characterized by a variety of growth dimensions evolution from disordered states can give domains with boundaries that execute effectively continuous motions some global properties of cellular automata can be described by entropies and lyapunov exponents others are undecidable

reversible cellular automata with memory two dimensional patterns from a single site seed standard cellular automata ca are ahistoric memoryless i e the new state of a cell depends on its neighborhood configuration only at the preceding time step historic memory of all past iterations can be incorporated into ca by featuring each cell by a weighted mean of all its past states in this paper a new kind of reversible ca which incorporates memory is introduced in a two dimensional scenario

representations of geometrical and topological quantities in cellular automata abstract this paper addresses the problem of finding novel representations of analogs of physical field variables in cellular automata several examples illustrate how this might be done 1 a manifestly covariant vector law for diffusion 2 a model for potential energy and exact one forms 3 a counting algorithm using a winding number density and 4 fields which support topological charges in order to combine the advantages of cellular automata and continuum analysis it is necessary to have representations which involve more than one cell

theory of cellular automata a survey this article surveys some theoretical aspects of cellular automata ca research in particular we discuss classical and new results on reversibility conservation laws limit sets decidability questions universality and topological dynamics of ca the selection of topics is by no means comprehensive and reflects the research interests of the author 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

characterizations of k s 1 potent matrices and applications abstract recently situations where a matrix coincides with some of its powers have been studied this kind of matrices is related to the generalized inverse matrices on the other hand it is possible to introduce another class of matrices that involve an involutory matrix generalizing the well known idempotent matrix widely useful in many applications in this paper we introduce a new kind of matrices called k s 1 potent as an extension of the aforementioned ones first different properties of k s 1 potent matrices have been developed later the main result developed in this paper is the characterization of this kind of matrices from a spectral point of view in terms of powers of the matrix by means of the group inverse and via a block representation of a matrix of index 1 finally an application of the above results to study linear combinations of k s 1 potent matrices is derived

local structure theory for cellular automata abstract the mean field theory for cellular automata wolfram and schulman and seiden is generalized to the local structure theory the local structure theory is a sequence of finitely parameterized models of the statistical features of a cellular automaton s evolution the n th model in the sequence takes into account correlations in terms of the probability of blocks of n states a class of measures the n block measures is introduced the local structure operator of order n maps n block measures to n block measures in a manner which reflects the cellular automaton map on blocks of states the fixed points of the map on measures approximate the invariant measures of the cellular automaton the ability of the local structure theory to model evolution from uncorrelated initial distributions is studied the theory gives exact results in simple cases in more complex cases monte carlo numerical experiments suggest that an accurate statistical portrait of cellular automaton evolution is obtained the invariant measures of a cellular automaton and the stability of these measures may be obtained from the local structure theory the local structure theory appears to be a powerful method for characterization and classification of cellular automata nearest neighbor cellular automata with two states per cell are studied using this method

algorithms for k s 1 potent matrix constructions in this paper we deal with k s 1 potent matrices these matrices generalize all the following classes of matrices k potent matrices periodic matrices idempotent matrices involutory matrices centrosymmetric matrices mirrorsymmetric matrices circulant matrices among others several applications of these classes of matrices can be found in the literature we develop algorithms in order to compute k s 1 potent matrices and k s 1 potent linear combinations of k s 1 potent matrices in addition some examples are presented in order to show the numerical performance of the method

secret image sharing based on cellular automata and steganography recently lin and tsai secret image sharing with steganography and authentication the journal of systems and software 73 2004 405 414 and yang et al improvements of image sharing with steganography and authentication the journal of systems and software 80 2007 1070 1076 proposed secret image sharing schemes combining steganography and authentication based on shamir s polynomials the schemes divide a secret image into some shadows which are then embedded in cover images in order to produce stego images for distributing among participants to achieve better authentication ability chang et al sharing secrets in stego images with authentication pattern recognition 41 2008 3130 3137 proposed in 2008 an improved scheme which enhances the visual quality of the stego images as well and the probability of successful verification for a fake stego block is 1 16 in this paper we employ linear cellular automata digital signatures and hash functions to propose a novel t n threshold image sharing scheme with steganographic properties in which a double authentication mechanism is introduced which can detect tampering with probability 255 256 employing cellular automata instead of shamir s polynomials not only improves computational complexity from o nlog 2n to o n but obviates the need to modify pixels of cover images unnecessarily compared to previous methods c lin w tsai secret image sharing with steganography and authentication the journal of systems and software 73 2004 405 414 c yang t chen k yu c wang improvements of image sharing with steganography and authentication the journal of systems and software 80 2007 1070 1076 c chang y hsieh c lin sharing secrets in stego images with authentication pattern recognition 41 2008 3130 3137 we use fewer number of bits in each pixel of cover images for embedding data so that a better visual quality is guaranteed we further present some experimental results

statistical mechanics of surjective cellular automata reversible cellular automata are seen as microscopic physical models and their states of macroscopic equilibrium are described using invariant probability measures we establish a connection between the invariance of gibbs measures and the conservation of additive quantities in surjective cellular automata namely we show that the simplex of shift invariant gibbs measures associated to a hamiltonian is invariant under a surjective cellular automaton if and only if the cellular automaton conserves the hamiltonian a special case is the well known invariance of the uniform bernoulli measure under surjective cellular automata which corresponds to the conservation of the trivial hamiltonian as an application we obtain results indicating the lack of non trivial gibbs or markov invariant measures for sufficiently chaotic cellular automata we discuss the relevance of the randomization property of algebraic cellular automata to the problem of approach to macroscopic equilibrium and pose several open questions as an aside a shift invariant pre image of a gibbs measure under a pre injective factor map between shifts of finite type turns out to be always a gibbs measure we provide a sufficient condition under which the image of a gibbs measure under a pre injective factor map is not a gibbs measure we point out a potential application of pre injective factor maps as a tool in the study of phase transitions in statistical mechanical models

invariant in cellular automata for a subclass of the set of reversible cellular automata the author gives the form of an exact time invariant quantity which can be seen as a kind of energy with the ergodic assumption this is a model of two interacting ising spin systems

reversible boolean networks ii phase transitions oscillations and local structures we continue our consideration of a class of models describing the reversible dynamics of n boolean variables each with k inputs we investigate in detail the behavior of the hamming distance as well as of the distribution of orbit lengths as n and k are varied we present numerical evidence for a phase transition in the behavior of the hamming distance at a critical value kc 1 62 and also an analytic theory that yields the exact bounds 1 5 k c 2 we also discuss the large oscillations that we observe in the hamming distance for k k c as a function of time as well as in the distribution of cycle lengths as a function of cycle length for moderate k both greater than and less than kc we propose that local structures or subsets of spins whose dynamics are not fully coupled to the other spins in the system play a crucial role in generating these oscillations the simplest of these structures are linear chains called linkages and rings called circuits we discuss the properties of the linkages in some detail and sketch the properties of circuits we argue that the observed oscillation phenomena can be largely understood in terms of these local structures 2001 published by elsevier science b v

resolution scalable image coding with reversible cellular automata in a resolution scalable image coding algorithm a multiresolution representation of the data is often obtained using a linear filter bank reversible cellular automata have been recently proposed as simpler nonlinear filter banks that produce a similar representation the original image is decomposed into four subbands such that one of them retains most of the features of the original image at a reduced scale in this paper we discuss the utilization of reversible cellular automata and arithmetic coding for scalable compression of binary and grayscale images in the binary case the proposed algorithm that uses simple local rules compares well with the jbig compression standard in particular for images where the foreground is made of a simple connected region for complex images more efficient local rules based upon the lifting principle have been designed they provide compression performances very close to or even better than jbig depending upon the image characteristics in the grayscale case and in particular for smooth images such as depth maps the proposed algorithm outperforms both the jbig and the jpeg2000 standards under most coding conditions

on reversibility of cellular automata with periodic boundary conditions reversibility of one dimensional cellular automata with periodic boundary conditions is discussed it is shown that there exist exactly 16 reversible elementary cellular automaton rules for infinitely many cell sizes by means of a correspondence between elementary cellular automaton and the de bruijn graph in addition a sufficient condition for reversibility of three valued and two neighbour cellular automaton is given

additive cellular automata and global injectivity abstract we employ algebraic methods to investigate the global injectivity of additive cellular automata when the state alphabet is a finite commutative ring the set of local rules of such additive cellular automata in d 1 dimensions itself forms a ring the invertible elements in this ring correspond to the globally injective additive cellular automata we indicate how one determines the invertible elements and thus the globally injectibe cellular automata in particular we show that in contrast to the general situation the global injectivity of additive cellular automata in d 1 dimensions is decidable construction of local rules for the inverse cellular automata is illustrated through examples a strict upper bound on the radius of the inverse cellular automata is obtained in the special case of linear cellular automata with state alphabet the ring of integers modulo m we count the globally injective cellular automata of up to a given radius we show that in one dimension a non globally injective additive cellular automaton is either not injective on spatially periodic configurations of any period n n or the set of n 0 such that the cellular automation is injective on spatially periodic configurations of period n has positive density in n

the complexity of reversible cellular automata we study the orbits of reversible one dimensional cellular automata it is shown that the turing degree structure of the orbits of these automata is the same as for general cellular automata in particular there are reversible cellular automata whose orbits have arbitrary recursively enumerable degree

nonconstructible blocks in 1d cellular automata minimal generators and natural systems the paper concerns minimal nonconstructible blocks of cellular automata i e minimal combinations of cell states that never appear in the evolution of an automaton using our previous work on the construction of predecessors of given configurations we analyse with numerical experiments the sets of nonconstructible blocks for one dimensional 1d cellular automata with binary and ternary neighbourhoods and binary cell states and compare our results with the classification made by voorhees we also analyse the relationship of the voorhees classes to the static parameter gl on applying our algorithm to cellular automata models of natural systems we provide common sense interpretations of unreachable states of some biological distributed processes

calculation of critical properties for the anisotropic two layer ising model on the kagome lattice cellular automata approach abstract the critical point k c of the two layer ising model on the kagome lattice has been calculated with a high precision using the probabilistic cellular automata with the glauber algorithm the critical point is calculated for different values of the inter and intra layer couplings k 1 k 2 k 3 k z where k 1 k 2 and k 3 are the nearest neighbor interactions within each layer in the 1 2 and 3 directions respectively and k z is the intralayer coupling a general ansatz equation for the critical point is given as a function of the inter and intra layer interactions k 3 k 1 k 2 k 1 and k z k 1 for the one and two layer ising models on the kagome lattice

cellular automaton fluids 1 basic theory continuum equations are derived for the large scale behavior of a class of cellular automaton models for fluids the cellular automata are discrete analogues of molecular dynamics in which particles with discrete velocities populate the links of a fixed array of sites kinetic equations for microscopic particle distributions are constructed hydrodynamic equations are then derived using the chapman enskog expansion slightly modified navier stokes equations are obtained in two and three dimensions with certain lattices viscosities and other transport coefficients are calculated using the boltzmann transport equation approximation some corrections to the equations of motion for cellular automaton fluids beyond the navier stokes order are given

a verifiable multi secret sharing scheme based on cellular automata in this paper we propose a verifiable t n threshold multi secret sharing scheme based on one dimensional cellular automata where the number of secrets is not restricted by n or t we show that our scheme can be used to solve an open problem proposed recently in alvarez et al 2008 g alvarez l hernandez encinas a martin del rey a multisecret sharing scheme for color images based on cellular automata information sciences 178 2008 4382 4395

spectral study of r s 1 k and r s 1 k potent matrices abstract the r s 1 k and r s 1 k potent matrices have been studied in several recent papers we continue these investigations from a spectral point of view specifically a spectral study of r s 1 k potent matrices is developed using characterizations involving an associated matrix pencil a r the corresponding spectral study for r s 1 k potent matrices involves the pencil a r in order to present some properties the relevance of the projector i a a where a is the group inverse of a is highlighted in addition some applications and numerical examples are given particularly involving pauli matrices and the quaternions