reversibility of general 1d linear cellular automata over the binary field z 2 under null boundary conditions the reversibility of cellular automata ca has long been studied but there are still many problems untouched this paper tackles the reversibility problem of the general case concerning 1d ca under null boundary conditions defined by linear rules over the binary field z 2 although transition matrix has been widely used for some special linear ca lca rules it has severe limitations its complexity depends on the number of cells and determining its reversibility becomes another unsolved tough problem for general rules by constructing deterministic finite automata dfa of the de bruijn graph presentation of ca we conclude the reversibility problem of all 1d linear rules over z 2 under null boundary conditions it turns out that any 1d lca except for some unilateral rules over z 2 under null boundary conditions can be reversible once having a proper number of cells and dfa provides an efficient way to find those numbers moreover the complexity of the dfa solution is independent of the number of cells in addition the relative low complexity of dfa can be further significantly reduced by using only a small part of it

on behavior of two dimensional cellular automata with an exceptional rule several studies a r khan p p choudhury k dihidar s mitra p sarkar vlsi architecture of a cellular automata comput math appl 33 1997 79 94 a r khan p p choudhury k dihidar r verma text compression using two dimensional cellular automata comput math appl 37 1999 115 127 k dihidar p p choudhury matrix algebraic formulae concerning some exceptional rules of two dimensional cellular automata inf sci 165 2004 91 101 have explored a new rule convention for two dimensional 2 d nearest neighborhood linear cellular automata ca with null and periodic boundary conditions a variety of applications of the rule convention have been illustrated and the vlsi architecture of cellular automata machine cam has been proposed however most of the studies address the issue of the kernel dimension of 2 d ca and many other important characteristics of ca such as garden of eden goe maximal transient length maximal cycle length etc have not been explored in this paper by exploiting matrix algebra in gf 2 the galois field with two elements we attempt to characterize the behavior of a specific rule which is not covered in existing work but accords with the same convention a necessary and sufficient condition is given to ensure that a given configuration is a goe meanwhile we propose some algorithms to determine the number of goes the maximal transient length and the maximal cycle length in a 2 d ca

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

characterisation of a particular hybrid transformation of two dimensional cellular automata abstract nowadays one dimensional 1d cellular automata ca based models and machines were demonstrated for various applications 1 7 2d ca based machines have not yet been used fruitfully mainly due to the lack of analytical insight into the behaviour of the underlying evolutionary process the set of papers 8 11 dealt with the behaviour of the uniform 2d cas in the present paper for the first time an attempt has been made to characterize a particular hybrid linear 2d ca transformation in gf 2 using matrix algebra also we deal with the synthesis problem of this particular hybrid transformation

boundary value descriptor systems well posedness reachability and observability in this paper we introduce the class of two point boundary value descriptor systems tpbvds discrete time systems described by possibly linear dynamics and a set of boundary conditions constraining the values of the system state at the two endpoints of the system s interval of definition by introducing a standard form for regular pencils we obtain a new and simple generalized cayley hamilton theorem that simplifies our investigation of well posedness green s function solutions and reachability and observability for tpbvds there are two distinct notions of reachability and observability that one can define for tpbvds associated with processes that propagate inward from and outward toward the boundaries we investigate each of these in detail obtaining among other things far simpler forms for the reachability and observability results than found previously in the literature in addition we describe several methods for the efficient solution of tpbvds one involving recursions from each end of t

emergence of universal global behavior from reversible local transitions in asynchronous systems reversible computing usually focuses on how to establish a valid equivalence between the global reversibility and local reversibility in computational systems hitherto the equivalence has been precisely developed in cellular automata combinational circuits and quantum computers but it implicitly assumes that the underlying systems are synchronously timed alternative systems include the delay insensitive di circuits and asynchronous cellular automata acas where the local operations of each component cell may be executed independently at random times despite the randomness associated with asynchronous timings equivalence between the global and local reversibility can be simply achieved in both di circuits morita 2001 and acas lee et al 2003 provided that their local operations transitions are thoroughly serialized the complete exclusion of concurrency in local behavior however will profoundly depress the parallel processing efficiency of di circuits as well as the intrinsic massive parallelism of acas this paper aims at exploring what kind of complex global behavior may arise from the concurrent operations that are invertible at local level to this end we show that di circuits composed of reversible elements can actually exhibit universal input and output behavior with the universality emerging from the concurrency in reversible local operations likewise by further embedding all circuits into the cellular space the emergence of universal global transitions from reversible local transitions can be exactly identified in an aca which due to the bijectivity of its local function has significantly lower complexity as compared to other models

generalization of cayley hamilton theorem for n d polynomial matrices the cayley hamilton theorem is extended to real polynomial matrices in n variables the known extensions of the classical cayley hamilton theorem are particular cases of the proposed extension

direct controllability and observability time domain conditions of singular systems controllability and observability criteria for singular systems using direct formulas in the time domain are introduced the method used is based on a direct expansion of the transfer function matrix via a leverrier type algorithm hence no decomposition of the state space model is needed and the criteria are implementable on a digital computer the compact form of the matrices might be helpful in other analysis as well as synthesis problems in singular systems

comments on theory and applications of cellular automata in cryptography with reply this paper argues that the cipher systems based on cellular automata ca proposed by s nandi et al 1994 are affine and are insecure a reply by s nandi and p pal chaudhuri is given the reply emphasizes the point that the regular modular cascadable structure of local neighborhood ca can be employed for building low cost cipher system hardware this cost effective engineering solution can achieve desired level of security with larger size ca

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

relay based identification of a class of nonminimum phase siso processes a set of general expressions is derived from a single symmetrical relay feedback test for identification of a class of process transfer functions using these expressions the parameters of open loop stable nonminimum phase transfer function models may be obtained from simple measurements made on the limit cycle for comparison the conventional describing function based identification formulae are presented fourier series based curve fitting with the options of nonlinear least squares method and trust region algorithm is used to measure limit cycle parameters in the presence of measurement noise examples are given to illustrate the value of the proposed method

generalization of cayley hamilton theorem for multivariate rational matrices the two equivalent generalizations of the famous cayley hamilton theorem for multivariate rational matrices over any number field are proposed which are also generalizations of the nine known generalized cayley hamilton theorems restricting our results to a smaller range leads to the two equivalent generalized cayley hamilton theorems for multivariate polynomial matrices over any number field one of which is more efficient in some cases than a known result

structure and reversibility of 2d hexagonal cellular automata cellular automata are used to model dynamical phenomena by focusing on their local behavior which depends on the neighboring cells in order to express their global behavior the geometrical structure of the models suggests the algebraic structure of cellular automata after modeling the dynamical phenomena it is sometimes an important problem to be able to move backwards in order to understand it better this is only possible if cellular automata is reversible in this paper 2d finite cellular automata defined by local rules based on hexagonal cell structure are studied rule matrix of the hexagonal finite cellular automaton is obtained the rank of rule matrices representing the 2d hexagonal finite cellular automata via an algorithm is computed it is a well known fact that determining the reversibility of a 2d cellular automata is a very difficult problem in general here the reversibility problem of this family of 2d hexagonal cellular automata is also resolved completely

computation of the transfer function matrix and its laurent expansion of generalized two dimensional systems an algorithm is developed for the computation of the transfer function matrix of a two dimensional system which is given in its generalized form the algorithm is a recursion in terms of the original system matrix and does not require the inversion of a two variable polynomial matrix an algorithm for the evaluation of the laurent expansion of the inverse of a two variable polynomial matrix is also presented

brief paper a generalized relay identification method for time delay and non minimum phase processes a generalized relay identification method is proposed in this paper for time delay and non minimum phase processes a distinct merit of the proposed method is that the process gain can be uniformly derived from a single run of the relay test independent of the relay type being unbiased or biased an analytical relay response expression is derived for assessing the process response under an unbiased or biased relay test a frequency response algorithm is also derived for estimating the multiple frequency response points of the process by categorizing cases of the model parameters to be identified the corresponding identification algorithms are developed using fitting conditions established for the process response at the oscillation frequency based on the improved estimation of multiple frequency response points a recursive least squares identification algorithm is then proposed for obtaining further enhanced fitting accuracy over a user specified frequency range e g the low frequency range often concerned in practical controller tuning illustrative examples from the recent literature are given to demonstrate the effectiveness and merits of the proposed algorithms

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

on computing the entropy of cellular automata we study the topological entropy of a particular class of dynamical systems cellular automata the topological entropy of a dynamical system x f is a measure of the complexity of the dynamics of f over the space x the problem of computing or even approximating the topological entropy of a given cellular automata is algorithmically undecidable ergodic theory dynamical systems 12 1992 255 in this paper we show how to compute the entropy of two important classes of cellular automata namely linear and positively expansive cellular automata in particular we prove a closed formula for the topological entropy of d dimensional d 1 linear cellular automata over the ring zm m 2 and we provide an algorithm for computing the topological entropy of positively expansive cellular automata

on the directional entropy of z2 actions generated by additive cellular automata abstract we show that for an additive one dimensional cellular automaton ca z 2 action on the space of all doubly infinite sequences with values in a finite set z a 0 1 2 a 1 determined by an additive automaton rule f x n k x n k i k k i x n i mod a and a invariant uniform bernoulli measure the directional entropy is h v 2 k 2 log a for v k 1 k 2 z 2 where k 2 k 1 and i z a we also calculate the measure theoretic entropy for additive ca z n actions generated by some additive one dimensional cellular automata and shift transformation and we show that uniform bernoulli measure is a maximal measure for additive ca z n actions

transfer function matrix of singular systems a formula is given which allows the determination of the transfer function matrix of linear multivariable singular systems i e systems of the form e dot x ax bu with e singular directly in terms of the matrices of the state space description and the characteristic polynomial without inverting a polynomial matrix an alternative closed form expression for the transfer function matrix in terms of the pencil a se is also given

multi value cellular automaton models and metastable states in a congested phase in this paper a family of multi value cellular automaton ca associated with traffic flow is presented the family is obtained by extending the rule 184 ca which is an ultradiscrete analogue to the burgers equation ca models in the family show both metastable states and stop and go waves which are often observed in real traffic flow metastable states in the models exist not only on a prominent part of a free phase but also in a congested phase

garden of eden states in traffic models we investigate the allowed configurations in the stationary state of the cellular automaton model for single lane traffic it is found that certain states in the configuration space cannot be reached if one uses parallel dynamics these so called garden of eden goe states do not exist for random sequential dynamics and are responsible for the strong short ranged correlations found in parallel dynamics by eliminating the goe states we obtain a simple and effective approximative description of the model for the exact solution is recovered for this elimination leads to much higher values of the flux compared to the mean field result which are in good agreement with monte carlo simulations

text compression using two dimensional cellular automata abstract this paper presents an elegant mathematical model using simple matrix algebra for characterising the behaviour of two dimensional nearest neighbourhood linear cellular automata with periodic boundary conditions based on this mathematical model the vlsi architecture of a cellular automata machine cam has been proposed for text compression experimental results of comparisons with adaptive huffman coding scheme also presented

vlsi architecture of a cellular automata machine abstract in the past cellular automata based models and machines 1 have been proposed for simulation of physical systems without any analytical insight into the behaviour of the underlying simulation machine this paper makes a significant departure from this traditional approach an elegant mathematical model using simple matrix algebra is reported in this paper for characterizing the behaviour of two dimensional nearest neighbourhood linear cellular automata with null and periodic boundary conditions based on this mathematical model a vlsi architecture of a cellular automata machine cam has been proposed interesting applications of cam in the fields of image analysis and fractal image generation are also reported

inversion of 2d cellular automata some complexity results abstract in this paper we prove the co np completeness of the following decision problem given a two dimensional cellular automaton a even with von neumann neighborhood is a injective when restricted to finite configurations not greater than its length in order to prove this result we introduce two decision problems concerning respectively turing machines and tilings that we prove np complete then we present a transformation of problems concerning tilings into problems concerning cellular automata

leverrier s algorithm for singular systems an algorithm is presented which allows the computation of the transfer function of a singular system from its state space description without inverting a polynomial matrix this algorithm is an extension of the leverrier algorithm for the more general case of singular systems and it reduces the computational cost

further remarks on the cayley hamilton theorem and leverrier s method for the matrix pencil se a some results for matrix pencils are extended to the singular case se a a singular leverrier s relation cayley hamilton theorem and newton s formula are given a finite series expansion for se a 1 is given in terms of the generalized tschirnhausen polynomials

technical communique relay feedback method under large static disturbances none of the previous relay feedback methods can provide a desired cyclic steady state in the case of large static disturbances of which the magnitude is bigger than the magnitude of the relay the proposed relay feedback method overcomes this limitation by placing a relay before a proportional integral pi controller of which the integral part plays an important role in rejecting the large static disturbances this is very attractive from a practical point of view because we do not need to define deviation variables in order to apply the proposed relay test furthermore the proposed method can provide the frequency data of the process for a pre specified phase angle by adjusting the integral gain

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

on the generalized cayley hamilton theorem the cayley hamilton theorem is extended to the case where two a and b n times n matrices are involved results similar to the regular case are presented the results are useful for problems that concern the analysis as well as the synthesis of singular systems for the definition of a function of two matrices f a b and in various other problems in linear algebra

the generalized cayley hamilton theorem for standard pencils abstract the cayley hamilton theorem is extended from the case of one matrix to that of two matrices the developed theorem is suitable for the standard form pencil se a let s det se a r 0 n a r s r then we show that r 0 n a r a r e n r 0 such a neat result which is very similar to the original theorem also is due to some nice properties of the standard pair e a for example e and a commute and share the same eigenspaces

fast switches in relay feedback systems relays are common in automatic control systems even linear systems with relay feedback are however far from fully understood new results are given about the behavior of these systems via a state space approach it is proved that there exist multiple fast switches if and only if the sign of the first nonvanishing markov parameter of the linear system is positive fast switches are shown to occur as part of stable limit cycles an analysis is developed for these limit cycles that illustrates how they can be predicted

generalized cayley hamilton theorem for polynomial matrices with arbitrary degree we give an alternative more convenient expression of the well known cayley hamilton theorem when polynomial matrices of arbitrary degree are involved based on the results of a recently developed algorithm fragulis et al 1991 for the computation of the inverse of a polynomial matrix certain relationships among the coefficient matrices of the given polynomial matrix are obtained we also propose two ways of finding the powers of a polynomial matrix one in terms of its coefficient matrices and the other making use of the generalized cayley hamilton theorem these methods are of closed form and are easily implementable in a digital computer