parallel and sequential computation on boolean networks abstract a model of large assemblies of computing elements is provided by the concept of boolean network f 0 1 n 0 1 n then we compare different regimes of this system namely parallel and sequential computations within the framework of discrete iterations it is shown that although the asymptotic behavior of the network as characterized by the limit cycles of the iterations may differ from one sort of regime to another it may however be largely predicted as for its spatial structure we show that for all iterations some elements never change state in any limit cycle they form the stable core we introduce the notion of forcing domain of a boolean network provide an algorithm to build it and show that it is a good approximation to the stable core this thus provides a spatial characterization of the limit cycles of the different iterations a theoretical bound on the transient length is provided through the entropy of the network

idempotents in nest algebras abstract the algebraic equivalence and similarity classes of idempotents within a nest algebra alg are completely characterized we obtain necessary and sufficient conditions for two idempotents to be equivalent or similar our criterion yields examples illustrating pathology and also shows that to each equivalence class of idempotents there corresponds a dimension function from into n we complete the characterization of the algebraic equivalence classes by proving that any dimension function corresponds to an equivalence class of idempotents also to each sequence of dimension functions there corresponds a commuting sequence of idempotents a criterion is obtained for when an idempotent is similar to a subidempotent of another the mapping which sends an equivalence class or idempotent to its associated dimension function plays a role in the nest algebra theory analogous to the role played by the mapping sending a projection in a type i w algebra to its center valued trace we prove that almost commuting similar idempotents are homotopic this contrasts with the situation in certain c algebras using this we show that similar simultaneously diagonalizable idempotents are homotopic and in the continuous nest case every diagonal idempotent is homotopic to a core projection

transition phenomena in cellular automata rule space abstract we define several qualitative classes of cellular automata ca behavior based on various statistical measures and describe how the space of all cellular automata is organized as a cellular automaton is changed by varying entries in its rule table abrupt changes in qualitative behavior may occur these abrupt changes have the character of bifurcations in smooth dynamical systems or of phase transitions in statistical mechanical systems the most complex ca rules exhibit many of the characteristics of second order transitions suggesting an association between computation complexity and critical phenomena

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

digital mechanics an informational process based on reversible universal cellular automata abstract this paper is written from the perspective of a computer scientist and addressed to theoretical physicists as a consequence it may seem somewhat unusual but rest assured everything is really quite simple the point of this paper is that the study of certain phenomena from computer science suggests that there are computer systems cellular automata that may be appropriate as models for microscopic physical phenomena cellular automata are now being used to model varied physical phenomena normally modelled by wave equations fluid dynamics ising models etc we hypothesize that there will be found a single cellular automaton rule that models all of microscopic physics and models it exactly we call this field dm for digital mechanics

hunting for the fractal dimension of the kauffman model abstract the kauffman model is a random mixture of all possible cellular automata on the square lattice with nearest neighbor interactions simulations give a fractal dimension d above 1 8 compatible with the usual scaling law d d for damage spreading

annealed and quenched inhomogeneous cellular automata inca a probabilistic one dimensional cellular automaton model by domany and kinzel is mapped into an inhomogeneous cellular automaton with the boolean functions xor and and as transition rules wolfram s classification is recovered by varying the frequency of these two simple rules and by quenching or annealing the inhomogeneity in particular class 4 is related to critical behavior in directed percolation also the critical slowing down of second order phase transitions is related to a stochastic version of the classical halting problem of computation theory

a new pebble game that characterizes parallel complexity classes a new two person pebble game that models parallel computations is defined this game extends the two person pebble game defined by dymond and tompa j comput system sci 30 1985 pp 149 161 and is used to characterize two natural parallel complexity classes namely logcfl and text ac 1 the characterizations show a fundamental way in which the computations in these two classes differ this game model also unifies the proofs of some well known results of complexity theory

variances as order parameter and complexity measure for random boolean networks several order parameters have been considered to predict and characterize the transition between ordered and disordered phases in random boolean networks such as the hamming distance between replicas or the stable core which have been successfully used in this work we propose a natural and clear new order parameter the temporal variance we compute its value analytically and compare it with the results of numerical experiments finally we propose a complexity measure based on the compromise between temporal and spatial variances this new order parameter and its related complexity measure can be easily applied to other complex systems

initiation of damage in the kauffman model an alternate method is presented for initiating damage to the kauffman model a numerical study suggests that this modification increases the efficiency of generating damage clusters without changing their fractal properties

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

connectedness of the invertibles in certain nest algebras of order type ω we solve the connectedness problem for a class of nests of order type with finite dimensional atoms

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

stochastic cellular automata with gibbsian invariant measures a geometric characterization is given of a class of stochastic cellular automata whose invariant probability measures are gibbsian distributions i e markovian random fields this class whose members may be considered as the cartesian product of convex polytopes with a finite number of vertices contains all known automata of this type e g the metropolis gibbs sampler and heat bath algorithms and also a new family which is characterized by having nonreversible dynamic behavior the fact that there is a complete geometric structure instead of isolated points opens the possibility of using classical techniques such as convex programming for the design of optimal automata some examples of applications are given oriented towards the solution of image restoration problems

on the prediction of local patterns in cellular automata abstract the class of deterministic one dimensional cellular automata studied recently by wolfram are considered we represent a state of an automaton as probability distribution of patterns of a fixed size in this way information is lost but it is possible to approximate the stepwise action of the automaton by the iteration of an analytic mapping of the set of probability distributions to itself such nonlinear analytic mappings generally have nontrivial attrators and in the most interesting cases wolfram class iii these are single points the point attractors under appropriate circumstances provide good approximations to the frequencies of local patterns generated by the discrete rules from which they were derived two appropriate settings for such approximation are transient patterns generated from random starts and patterns generated in a noisy environment in the case with noise improvement is found by correction of the analytic mappings for the effects of noise examples of both types of approximation are considered

nondeterministic space is closed under complementation in this paper we show that nondeterministic space s n is closed under complementation for s n greater than or equal to log n it immediately follows that the context sensitive languages are closed under complementation thus settling a question raised by kuroda inform and control 7 1964 pp 207 233

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

attractor dominance patterns in sparsely connected boolean nets abstract an attractor dominates those states in phase space that lie in its basin of attraction this paper examines attractor dominance as a function of distance from the attractor when trajectories of sparsely connected boolean nets are aggregated suitably attractor dominance is a reasonably smooth function of distance the shape of the dominance function varies widely depending on the automaton rule in place in this paper i order the dominance functions of the rules of a family of sparsely connected boolean nets these nets are structurally generalized cellular automata two classes contain most of the variability in attractor dominance patterns within these classes two dimensions locate dominance functions and reveal changes in phase space dominance with lattice size increasing lattice size appears to move most but importantly not all dominance patterns toward the extremes shown by the three trivial rules implications of these findings are discussed

emergent properties in random complex automata abstract studies of large randomly assembled binary boolean node automata have demonstrated that such systems can spontaneously exhibit enormously ordered dynamical behavior an important approach to characterizing these behaviors has consisted of studying ensembles of automata ensemble specifications have been based on 1 choice of boolean function regulating each node in the automaton 2 random or biased mappings of the 2 n automata states into themselves 3 the numbers of inputs k per node this article briefly reviews these approaches reports new results on the expected behavior of threshold automata and automata with a particular class of biased mappings in addition it discusses emergent highly ordered dynamical behavior in random automata rich in a specific class of canalizing boolean functions due to the crystallization of powerful subautomata called forcing structures the ordered behaviors may be of importance in biological evolution in physics and in the design of adaptive automata

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

lyapunov exponents in random boolean networks a new order parameter approximation to random boolean networks rbn is introduced based on the concept of boolean derivative a statistical argument involving an annealed approximation is used allowing to measure the order parameter in terms of the statistical properties of a random matrix using the same formalism a lyapunov exponent is calculated allowing to provide the onset of damage spreading through the network and how sensitive it is to minimal perturbations finally the lyapunov exponents are obtained by means of dierent approximations through distance method and a discrete variant of the wolf s method for continuous systems c 2000 elsevier science b v all rights reserved

phase transition in an elementary probabilistic cellular automaton abstract cellular automata exhibit a large variety of dynamical behaviors from fixed point convergence and periodic motion to spatio temporal chaos by introducing probabilistic interactions and regarding the asymptotic density of non quiescent cell states as an order parameter phase transitions may be identified from a quiescent phase with 0 to a chaotic phase with non zero we consider an elementary one dimensional probabilistic cellular automaton pca with deterministic limits given by the quiescent rule 0 the rule 72 that evolves into a non trivial fixed point and the chaotic rules 18 and 90 despite the simplicity of the rules the pca shows a surprising number of transition phenomena we identify second order phase transitions from 0 to 0 with static and dynamic exponents that differ from those of directed percolation moreover we find that the non trivial fixed point rule 72 is a singular point in pca space

circuit definitions of nondeterministic complexity classes we consider restictions on boolean circuits and use them to obtain new uniform circuit characterizations of nondeterministic space and time classes we also obtain characterizations of counting classes based on nondeterministic time bounded computations on the arithmetic circuit model it is shown how the notion of semiunboundedness unifies the definitions of many natural complexity classes

positive and negative proofs for circuits and branching programs we extend the operator in a natural way and derive new types of counting complexity classes while in the case of c classes where c could be some circuit based class like nc 1 only proofs for acceptance of some input are being counted one can also count proofs for rejection the zap c complexity classes we propose here implement this idea we show that in certain cases zap c lies between c and gap c which could help understanding the relationship between c and gap c in particular we consider zap nc 1 and polynomial size branching programs of bounded and unbounded width finally we argue about negative proofs in turing machines and how those relate to open questions

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

statistical mechanics of probabilistic cellular automata we investigate the behavior of discrete time probabilistic cellular automata pca which are markov processes on spin configurations on ad dimensional lattice from a rigorous statistical mechanics point of view in particular we exploit whenever possible the correspondence between stationary measures on the space time histories of pcas on d and translation invariant gibbs states for a related hamiltonian on d 1 this leads to a simple large deviation formula for the space time histories of the pca and a proof that in a high temperature regime the stationary states of the pca are gibbsian we also obtain results about entropy fluctuations and correlation inequalities and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high noise regime we discuss phase transitions in the low noise or low temperature regime and review toom s proof of nonergodicity of a certain class of pcas

long range effects in an elementary cellular automaton we present evidence that one of the elementary one dimensional cellular automata in the sense of wolfram rule 22 in wolfram s notation involves very complex long range effects similar to a critical phenomenon this is in contrast to superficial evidence that would suggest that this rule leads to fairly simple behavior

dynamics of a globally coupled oscillator array abstract we study a set of n globally coupled ordinary differential equations of the form encountered in circuit analysis of superconducting josephson junction arrays particular attention is paid to two kinds of simple time periodic behavior known as in phase and splay phase states some results valid for general n as well as further results for n 2 and n are presented a recurring theme is the appearance of very weak dynamics near the periodic states the implications for josephson junction arrays are discussed

the computational complexity of generating random fractals we examine a number of models that generate random fractals the models are studied using the tools of computational complexity theory from the perspective of parallel computation diffusion limited aggregation and several widely used algorithms for equilibrating the ising model are shown to be highly sequential it is unlikely they can be simulated efficiently in parallel this is in contrast to mandelbrot percolation which can be simulated in constant parallel time our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory in addition the results may serve as a guide to simulation physics

global properties of cellular automata cellular automata are discrete mathematical systems that generate diverse often complicated behavior using simple deterministic rules analysis of the local structure of these rules makes possible a description of the global properties of the associated automata a class of cellular automata that generate infinitely many aperiodic temporal sequences is defined as is the set of rules for which inverses exist necessary and sufficient conditions are derived characterizing the classes of nearest neighbor rules for which arbitrary finite initial conditions i evolve to a homogeneous state ii generate at least one constant temporal sequence

boolean dynamics of networks with scale free topology the dynamics of boolean networks with scale free topology are studied the existence of a phase transition from ordered to chaotic dynamics governed by the value of the scale free exponent of the network is shown analytically by analyzing the overlap between two distinct trajectories the phase diagram shows that the phase transition occurs for values of the scale free exponent in the open interval 2 2 5 since the boolean networks under study are directed graphs the scale free topology of the input connections and that of the output connections are studied separately ultimately these two topologies are shown to be equivalent a numerical study of the attractor structure of the configuration space reveals that this structure is similar in both networks with scale free topologies and networks with homogeneous random topologies however an important result of this work is that the fine tuning usually required to achieve stability in the dynamics of networks with homogeneous random topologies is no longer necessary when the network topology is scale free finally based on the results presented in this work it is hypothesized that the scale free topology favors the evolution and adaptation of network functioning from a biological perspective

connecting invertible analytic toeplitz operators in g t p abstract we prove that there exists an orthonormal basis f for classical hardy space h 2 such that each invertible analytic toeplitz operator could be connected to the identity via a norm continuous path of invertible elements of the lower triangular operators with respect to f

effects of small world topology on the critical boundary for boolean networks abstract due to their complexity real dynamic systems are widely regarded as operating on the boundary between order and chaos therefore it is of great interest to determine analytical expressions for this boundary for random boolean networks model a well known critical value of bias is established as p crit 1 2 1 1 2 k where k is the mean connectivity recent research shows however that this expression may need to be modified in this paper we shall focus on the effects of topology deviation from the random network assumption since the topologies of many real networks are neither pure random nor fully regular boolean networks a modification of the critical boundary condition is given with parameters of the degree distribution in the setting of more realistic networks modeled with small world features

mutual information functions versus correlation functions this paper studies one application of mutual information to symbolic sequences the mutual information functionm d this function is compared with the more frequently used correlation function d an exact relation betweenm d and d is derived for binary sequences for sequences with more than two symbols no such general relation exists in particular d 0 may or may not lead tom d 0 this linear but not general independence between symbols separated by a distance is studied for ternary sequences also included is the estimation of the finite size effect on calculating mutual information finally the concept of symbolic noise is discussed

relaxation and limit cycles in a global version of the quenched kauffman model abstract a combinatorial method is used to investigate all possible cellular automata defined on a finite set of w global configurations relaxation time is defined as the number of steps before entering a fixed point or a cycle for given w we derive an analytical formula for the distribution of relaxation times t pw t w ww 1 k 0w t 1 wk k the same distribution is proved to be valid for the length of limit cycles the results have some relevance to the quenched kauffman model

is there a sharp phase transition for deterministic cellular automata abstract previous work has suggested that there is a kind of phase transition between deterministic automata exhibiting periodic behavior and those exhibiting chaotic behavior however unlike the usual phase transitions of physics this transition takes place over a range of values of the parameter rather than at a specific value the present paper asks whether the transition can be made sharp either by taking the limit of an infinitely large rule table or by changing the parameter in terms of which the space of automata is explored we find strong evidence that for the class of automata we consider the transition does become sharp in the limit of an infinite number of symbols the size of the neighborhood being held fixed our work also suggests an alternative parameter in terms of which it is likely that the transition will become fairly sharp even if one does not increase the number of symbols in the course of our analysis we find that mean field theory which is our main tool gives surprisingly good predictions of the statistical properties of the class of automata we consider

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

kauffman boolean model in undirected scale free networks we investigate analytically and numerically the critical line in undirected random boolean networks with arbitrary degree distributions including the scale free topology of connections p k ensuremath sim k ensuremath ensuremath gamma we explain that the unattainability of the critical line in numerical simulations of classical random graphs is due to percolation phenomena we suggest that recent findings of discrepancy between simulations and theory in directed random boolean networks might have the same reason we also show that in infinite scale free networks the transition between frozen and chaotic phases occurs for 3l ensuremath gamma l3 5 since most critical phenomena in scale free networks reveal their nontrivial character for ensuremath gamma l3 the position of the critical line in the kauffman model seems to be an important exception to the rule

non cancellative boolean circuits a generalization of monotone boolean circuits cancellations are known to be helpful in efficient algebraic computation of polynomials over fields we define a notion of cancellation in boolean circuits and define boolean circuits that do not use cancellation to be non cancellative non cancellative boolean circuits are a natural generalization of monotone boolean circuits we show that in the absence of cancellation boolean circuits require super polynomial size to compute the determinant interpreted over gf 2 this non monotone boolean function is known to be in p in the spirit of monotone complexity classes we define complexity classes based on non cancellative boolean circuits we show that when the boolean circuit model is restricted by withholding cancellation p and popular classes within p are restricted as well but classes np and above remain unchanged

non commutative arithmetic circuits depth reduction and size lower bounds abstract we investigate the phenomenon of depth reduction in commutative and non commutative arithmetic circuits we prove that in the commutative setting uniform semi unbounded arithmetic circuits of logarithmic depth are as powerful as uniform arithmetic circuits of polynomial degree and unrestricted depth earlier proofs did not work in the uniform setting this also provides a unified proof of the circuit characterizations of the class logcfl and its counting variant logcfl we show that ac1 has no more power than arithmetic circuits of polynomial size and degree no log log n improving the trivial bound of no log n connections are drawn between tc1 and arithmetic circuits of polynomial size and degree then we consider non commutative computation we show that over the algebra max concat arithmetic circuits of polynomial size and polynomial degree can be reduced to o log2 n depth and even to o log n depth if unbounded fanin gates are allowed this establishes that optlogcfl is in ac1 this is the first depth reduction result for arithmetic circuits over a non commutative semiring and it complements the lower bounds of kosaraju and nisan showing that depth reduction cannot be done in the general non commutative setting we define new notions called short left paths and short right paths and we show that these notions provide a characterization of the classes of arithmetic circuits for which optimal depth reduction is possible this class also can be characterized using the auxpda model finally we characterize the languages generated by efficient circuits over the semiring 2 union concat in terms of simple one way machines and we investigate and extend earlier lower bounds on non commutative circuits

time evolution of damage in the ising model the time evolution of the damage in the ising model with the heat bath and glauber dynamics has been investigated with the damage spreading method the damage density d t and the average distance r t of damaged sites from the origin have been measured numerically from the simulational data the scaling forms have been established as d t tx r t t1z and d t r t df and the corresponding exponents x z and df have been estimated

the arveson frequency response and systems theory a frequency domain theory which is applicable to all linear systems and a class of non linear systems is formulated in a hilbert resolution space setting our approach is predicated on an analytic characterization of certain non selfadjoint operator algebras due to arveson although originally used as an analytic tool arveson in fact formulated an operator valued frequency response function for the elements of these algebras which in particular include the causal operators defined on a hilbert resolution space the resultant arveson frequency response afr is well defined for all linear and non linear systems on a hilbert resolution space and in the linear case it is characterized by an analyticity theory which is identical to that of the classical time invariant frequency response concept moreover it yields computationally viable formulae for the most widely studied classes of linear systems including the time varying abcd systems finally the classical frequency response concepts and their ti

scaling laws in critical random boolean networks with general in and out degree distributions we evaluate analytically and numerically the size of the frozen core and various scaling laws for critical boolean networks that have a power law in and or out degree distribution to this purpose we generalize an efficient method that has previously been used for conventional random boolean networks and for networks with power law in degree distributions with this generalization we can also deal with power law out degree distributions when the power law exponent is between 2 and 3 the second moment of the distribution diverges with network size and the scaling exponent of the nonfrozen nodes depends on the degree distribution exponent furthermore the exponent depends also on the dependence of the cutoff of the degree distribution on the system size altogether we obtain an impressive number of different scaling laws depending on the type of cutoff as well as on the exponents of the in and out degree distributions we confirm our scaling arguments and analytical considerations by numerical investigations

invertible behavior in elementary cellular automata with memory elementary cellular automata ecas have been studied for their ability to generate complex global behavior despite their simplicity one variation of ecas is obtained by adding memory to each cell in a neighborhood this process generates a provisional configuration in which the application of an evolution rule establishes the dynamics of the system this version is known as an eca with memory ecam most previous work on ecams analyzed the complex behavior taking chaotic ecas however the present paper investigates reversible ecams as obtained from reversible and permutative ecas these ecas have at least one ancestor for every configuration thus the correct permutation of states may specify the memory function to obtain reversible ecams for permutative ecas which are often irreversible we demonstrate that the use of a quiescent state and the correct manipulation of de bruijn blocks produce reversible ecams

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

the modular structure of kauffman networks this is the second paper of a series of two about the structural properties that influence the asymptotic dynamics of random boolean networks here we study the functionally independent clusters in which the relevant elements introduced and studied in our first paper 3 are subdivided we show that the phase transition in random boolean networks can also be described as a percolation transition the statistical properties of the clusters of relevant elements that we call modules give an insight on the scaling behavior of the attractors of the critical networks that according to kauffman have a biological analogy as a model of genetic regulatory systems

evolution by damage spreading in kauffman model in kauffman s boolean automata model on the square lattice the darwinian fitness of survival can be defined as the fraction of elements which do not change from one iteration to the next biological mutations are simulated by filpping one bit in the rule of one site selection of the fitter mutant then optimizes the whole lattice completely this optimization is particularly effective near the critical point of the transition to chaos but is in itself not a critical phenomenon also a two dimensional spin glass can be optimized in this way

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

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

on the effect of memory in one dimensional k 4 automata on networks the effect of implementing memory in cells of one dimensional ca and on nodes of various types of automata on networks with increasing degrees of random rewiring is studied in this article paying particular attention to the case of four inputs as a rule memory induces a moderation in the rate of changing nodes and in the damage spreading albeit in the latter case memory turns out to be ineffective in the control of the damage as the wiring network moves away from the ordered structure that features proper one dimensional ca this article complements the previous work done in the two dimensional context

boolean derivatives on cellular automata abstract boolean derivatives are applied to cellular automata they extract the linear part of arbitrary rules and provide an intrinsic classification derivatives are applied to tracing complexity growth and to lattice gases a complete table of derivatives is given for one dimensional elementary cellular automata

a taxonomy of problems with fast parallel algorithms the class nc consists of problems solvable very fast in time polynomial in log n in parallel with a feasible polynomial number of processors many natural problems in nc are known in this paper an attempt is made to identify important subclasses of nc and give interesting examples in each subclass the notion of nc 1 reducibility is introduced and used throughout problem r is nc 1 reducible to problem s if r can be solved with uniform log depth circuits using oracles for s problems complete with respect to this reducibility are given for many of the subclasses of nc a general technique the parallel greedy algorithm is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in nc 2 solvable by uniform boolean circuits of depth o log 2 n and polynomial size the class logcfl is given a new characterization in terms of circuit families the class det of problems reducible to integer determinants is defined and many examples given a new problem complete for deterministic polynomial time is given namely finding the lexicographically first maximal clique in a graph this paper is a revised version of s a cook 1983 in proceedings 1983 intl found comut sci conf lecture notes in computer science vol 158 pp 78 93 springer verlag berlin new york

on the dynamics of random boolean networks with scale free outgoing connections abstract in the classical model of random boolean networks rbn the number of incoming connections is the same for every node while the distribution of outgoing links is poissonian these rbn are known to display two major dynamical behaviours depending upon the value of some model parameters an ordered and a chaotic regime we introduce a modification of the classical way of building a rbn which maintains the property that all the nodes have the same number of incoming links but which gives rise to a scale free distribution of outgoing connections because of this modification the dynamical properties are deeply modified the number of attractors is much smaller than in classical rbn their length and the duration of the transients are shorter moreover the number of different attractors is almost independent of the network size over almost three orders of magnitudes while in classical rbn this number grows with the size of the network these results are based upon a detailed study of networks where each node has two input connections a limited study of networks with three input connections per node shows that also in this case the number of attractors is almost independent of the network size

damage spreading in non frustrated phase of a triangular antiferromagnet abstract we investigate a first order phase transition from a non magnetic phase to a non frustrated phase of a two dimensional triangular lattice with antiferromagnetic bonds a cellular automaton is defined which chooses a magnetic state of subsequent lattice sites where an interphase boundary arrives as to minimise the local energy the ground state magnetic state is found to be unstable with respect to the point defects of magnetic structure

cellular automata in fuzzy backgrounds abstract the main purpose of this work is to understand some limitations introduced by the classical definitions of cellular automata ca to this end we have defined a new model of cas fuzzy ca s which allows the observation of interesting chaotic properties of elementary cas to date neither a formal nor a precise definition of chaos in cas exists we believe that the proposed model provides a sharper tool to detect which properties can be associated to a chaotic behavior we also define a measure rule entropy which gives information about the ca s dynamics solely on the basis of the rule table and provides theoretical explanations to some of the empirical observations

pp is closed under truth table reductions beigel reingold and spielman j comput system sci 50 191 202 1995 showed that pp is closed under intersection and a variety of special cases of polynomial time truth table closure we extend their techniques to show that pp is closed under general polynomial time truth table reductions we also show that pp is closed under constant round truth table reductions

an order parameter for networks of automata an exact polynomial equation is given for the size of the stable core of networks of automata with random connections when the connectivity k of a network equals 1 2 3 4 or 5 this equation is exactly solvable it is found that the size of the stable core is an order parameter for a phase transition well known from kauffman s model a new derivation of critical parameter values follows the phase structure is found to be independent of the updating scheme used in the dynamical law for the network

clustering coding switching hierarchical ordering and control in a network of chaotic elements abstract a network of chaotic elements is investigated with the use of globally coupled maps a simple coding of many attractors with clustering is shown through the coding the attractors are organized so that their change exhibits bifurcation like phenomena a precision dependent tree is constructed which leads to the similarity of our attractor with those of spin glasses hierarchical dynamics is constructed on the tree which leads to the dynamical change of trees and the temporal change of effective degrees of freedom by a simple input on a site we can switch among attractors and tune the strength of chaos a threshold on a cluster size is found beyond which a peculiar posi nega switch occurs possible application to biological information processing is discussed with the emphasis on the fuzzy switch chaotic search and hierarchical code categorization

skew circuits of small width abstract a celebrated result of barrington 1985 proved that polynomial size width 5 branching programs bp are equivalent in power to a restricted form of branching programs polynomial sized width 5 permutation branching programs pbp which in turn capture all of nc 1 on the other hand it is known that width 3 pbps require exponential size to compute the and function no such lower bound is known for width 4 pbps however it is widely conjectured that width 4 pbps will not capture all of nc 1 in this work we study the power of bounded width branching programs by comparing them with bounded width skew circuits it is well known that branching programs of bounded width have the same power as skew circuit of bounded width the naive approach converts a bp of width w to a skew circuit of width w 2 we improve this bound and show that bp of width w 5 can be converted to a skew circuit of width 7 this also implies that skew circuits of bounded width are equal in power to skew circuits of width 7 for the other way we prove that for any w 2 a skew circuit of width w can be converted into an equivalent branching program of width w we prove that width 2 skew circuits are not universal while width 3 skew circuits are universal and that any polynomial sized cnf or dnf is computable by width 3 skew circuits of polynomial size it is known that parity does not have small cnfs or dnfs it is easy to see that parity has width 4 skew circuits we prove that a width 3 skew circuit computing parity requires exponential size this gives an exponential separation between the power of width 3 skew circuits and width 4 skew circuits

lyapunov analysis and information flow in coupled map lattices abstract lyapunov analysis for the coupled map lattices is presented the co moving lyapunov exponent is calculated which is related with the propagation of the disturbance in space the propagation speed agrees with the zero crossing point of the co moving lyapunov exponent the co moving mutual information flow is introduced which shows the selective transmission of the information at some speed lyapunov spectra and vectors are calculated spatial structures of the vectors are investigated possible analogy with the anderson localization problem is discussed

phase transitions in an elementary probabilistic cellular automaton with memory abstract standard cellular automata ca are ahistoric memoryless i e the new state of a cell depends on the neighborhood configuration only at the preceding time step this article considers an extension to the standard framework of ca by implementing memory capabilities in cells thus in ca with memory while the update rules of the ca remain unaltered historic memory of all past iterations is retained by featuring each cell by a summary of all its past states a study is conducted of the effect of historic memory on a given side of the hypercube of elementary probabilistic ca which shows interesting phase transition phenomena

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

phenomenology of nonlocal cellular automata dynamical systems with nonlocal connections have potential applications to economic and biological systems this paper studies the dynamics of nonlocal cellular automata in particular all two state three input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings although it is observed that sometimes a rule can have different dynamical behaviors with different wirings the nonlocal cellular automata rule space is studied using a mean field parametrization which is ideal for the situation of random wiring nonlocal cellular automata can be considered as computers carrying out computation at the level of each component their computational abilities are studied from the point of view of whether they contain many basic logical gates in particular i ask the question of whether a three input cellular automaton rule contains the three fundamental logical gates two input rules and and or and one input rule not a particularly interesting edge of chaos nonlocal cellular automaton the rule 184 is studied in detail it is a system of coupled selectors or multiplexers it is also part of the fredkin s gate a proposed fundamental gate for conservative computations this rule exhibits irregular fluctuations of density large coherent structures and long transient times

parameter characterization of two dimensional cellular automata rule space cellular automata ca are discrete dynamical systems formed by a great number of identical and simple components with local connectivity it has been proved that the problem of forecasting the dynamical behavior of ca is undecidable based upon parameterizations of ca rule space several approximations have been investigated the majority of these studies are focused on the one dimensional ca the present work generalizes for the two dimensional space the definition of three parameters previously published in the one dimensional context sensitivity neighborhood dominance and activity propagation as an example of the application of such generalized parameters some simulations about the computational task known as the density classification task are reported