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The problem of classifying constacyclic codes over a finite field, both the Hamming distance and the algebraic structure, is an interesting problem in algebraic coding theory. For the repeated-root constacyclic codes of length n p s over p m , where p is a prime number and p does not divide n , the problem has been solved completely for all n ≤ 6 and partially for n = 7 , 8. In this paper, we solve the problem for n = 9 and all primes p different from 3 and 1 9. In particular, we characterize the Hamming distance of all repeated-root constacyclic codes of length 9 p s over p m . As an application, we identify all optimal and near-optimal codes with respect to the Singleton bound of these types, namely, MDS, almost-MDS, and near-MDS codes. [ABSTRACT FROM AUTHOR]

Testing modern integrated circuit (IC) is challenging with introduction of System-on Chip (SOC). Enormous test pattern count is required to authenticate the IC which inflates power consumption. Henceforth, it is mandatory to incorporate power minimization techniques at circuit design phase. Optimizing test patterns is one such effective technique that curtails test power without altering circuit design. In this paper, a new test pattern reordering algorithm is proposed based on Recurrent Neural Network. Hopfield Neural Network (HNN) constitutes an optimized solution for solving traveling salesman problem (TSP). Since, test pattern reordering can be interpreted as TSP, optimized test pattern order is attained with HNN. Energy function of this algorithm falls into local minimum, so to eradicate this issue, the algorithm is modified. Test patterns are reordered with minimal hamming distance among consecutive test patterns. The proposed algorithm is implemented in ISCAS'89 Sequential Benchmark circuits. Experimental results prove that significant reduction in transition count is accomplished with proposed algorithm without compromising fault coverage. [ABSTRACT FROM AUTHOR]

Feature extraction and matching are the basic procedures of the so-called Visual Odometer (VO), Simultaneous Localization and Mapping (SLAM) and many other image processing algorithms. Oriented features from accelerated segment test (FAST) and rotated binary robust independent elementary features (ORB) algorithm are widely used since they are computationally faster. In this paper, we proposed a method to generate a value for a feature, the value is called signature. In the matching step, we only compute Hamming distances of descriptors with the same signatures. Hence, the matching time is shortened. Compared with the original ORB algorithm, features to be matched dropped 69.63% on TUM datasets and 85.7% on VGG datasets by adopting our strategy. In addition, the precision is above 85% on both VGG and TUM datasets. We design a customized hardware architecture for ORB feature extraction and matching based on the proposed method. The hardware structure is implemented on Xilinx ZCU102 evaluation board. The clock frequency is set to 150 MHz. Our Field Programmable Gate Arrays (FPGA) system achieves 193 fps on 1 2 8 0 × 7 2 0 images with 1984 features on average and 314 fps on 6 4 0 × 4 8 0 images with 700 features on average, which is more efficient compared to the state-of-the-art works. [ABSTRACT FROM AUTHOR]

In this paper, we develop a theory for constructing cyclic codes of odd length over the ring R = ℤ 4 + u ℤ 4 + v ℤ 4 , where u 2 = v 2 = u v = v u = 0 , which plays an important role in DNA computing. A direct link between the elements of R and the 6 4 codons used in the amino acids of the living organisms is established. Then, we investigate reversible cyclic codes and reversible complement cyclic codes of odd length over R. Moreover, we give some properties of binary images of the codons under the Gray map. Finally, two examples of cyclic codes over R with their minimum Hamming distance will be studied as well. [ABSTRACT FROM AUTHOR]

Motivated by Jin–Ke–Wang's work (J. Jin, Z. T. Ke and W. Wang, Ann. Statist. 45(5) (2017) 2151–2189), this paper studies estimation of misclassification rate in the Asymptotic Rare and Weak (ARW) model. In contrast to Jin–Ke–Wang's theorem, we measure the performance of the estimator by the misclassification rate instead of Hamming distance, and extend the Gaussian noise to sub-Gaussian's. The probability estimation with convergence rate is first given under some conditions. Then we prove that condition necessary as well. A direct corollary of our estimation can be compared with Jin–Ke–Wang's theorem. It turns out that our statistical limit coincides with theirs. [ABSTRACT FROM AUTHOR]

Let A (G) be the adjacency matrix of a graph G. Let s (v) denote the row entries of A (G) corresponding to the vertex v of G. The Hamming distance between the strings s (u) and s (v) is the number of positions in which s (u) and s (v) differ. In this paper, we study the Hamming distance between the strings generated by the adjacency matrix of subgraph complement of a graph. We also compute sum of Hamming distances between all pairs of strings generated by the adjacency matrix of G ⊕ S. [ABSTRACT FROM AUTHOR]

In this paper, we use a method inspired by the valuation theory to classify completely cyclic codes of length 3 p s over p m + u p m + u 2 p m . Then, we compute their separation parameters which was useful to compute the Hamming distance in [8]. [ABSTRACT FROM AUTHOR]

Error-correcting output coding (ECOC) is a method for constructing a multi-valued classifier using a combination of given binary classifiers. ECOC can estimate the correct category by other binary classifiers even if the output of some binary classifiers is incorrect based on the framework of the coding theory. The code word table representing the combination of these binary classifiers is important in ECOC. ECOC is known to perform well experimentally on real data. However, the complexity of the classification problem makes it difficult to analyze the classification performance in detail. For this reason, theoretical analysis of ECOC has not been conducted. In this study, if a binary classifier outputs the estimated posterior probability with errors, then this binary classifier is said to be noisy. In contrast, if a binary classifier outputs the true posterior probability, then this binary classifier is said to be noiseless. For a theoretical analysis of ECOC, we discuss the optimality for the code word table with noiseless binary classifiers and the error rate for one with noisy binary classifiers. This evaluation result shows that the Hamming distance of the code word table is an important indicator. [ABSTRACT FROM AUTHOR]

In this paper, a system based on image descriptor and Local Histogram Concatenation (LHC) for finger vein recognition is introduced. The LHC of image descriptors such as LBP, LDP CLBP cannot be inverted back to the original images, therefore they can provide good security if stored as enrolled data. On the other hand, the technique of LHC does not depict spatial information, therefore it is expected to be less sensitive to image misalignment if a measure such as the histogram difference (d X 2) is used for recognition. The use of histogram difference makes the system more robust to misalignment compared to the pixel-by-pixel-based measures such as the Hamming Distance (HD). The approach of LHC is implemented by dividing the image descriptor into non-overlapped grids, then the histogram within each grid is calculated and concatenated with the histograms of the preceding grids and finally, the concatenated histograms of each two images are compared using d X 2 measure. Two datasets, UTFVP and SDUMLA-HMT, are used for testing the performance of the system. The results have shown that the Identification Recognition Rate (IRR) is improved when LHCs of the image descriptors with (d X 2) measure are used compared to the use of only the image descriptors with HD measure. For UTFVP dataset, the IRR values were 97.44%, 95% and 98.37% when LHC and (d X 2) were used with LBP, LDP and CLBP, respectively, while these values were 89.44%, 92.63% and 92.92% when only LBP, LDP and CLBP with HD were used. For SDUMLA-HMT dataset, the IRR values of the system were 98.43%, 98.69% and 98.85% when LHC and (d X 2) were used with LBP, LDP and CLBP, respectively, while these values were 97.6%, 98.24% and 97.27% when only the image descriptors LBP, LDP and CLBP with HD were used. [ABSTRACT FROM AUTHOR]

Let A (n , d) be the size of the maximum binary code of length n and minimum Hamming distance d. A (n , d , w) is defined similarly for binary code with constant weight w. Obviously, finding the value of A (n , d) is equivalent to finding the maximum independent set of the d − 1 th-power of n -dimensional hypercube. Based on this, this paper obtains that A (3 m , 2 m) = 4 , A (m (m + 1) 2 , 2 m − 2 , m) = m + 1 , A (2 m + 1 − 2 , 2 m − 1) = 2 m + 1 , and explores the structure of the maximum code of length 2 m + 2 and minimum Hamming distance 2 m + 1 , where m is an integer. [ABSTRACT FROM AUTHOR]

Recently, Low Density Parity-Check (LDPC) codes based on Affine Permutation Matrices (APM) drew lots of attention. Compared with the Quasi-Cyclic LDPC (QC-LDPC) codes, these kinds of codes have some advantages. APM-LDPC codes obtain lower cycle-distributions, minimum hamming distance and greater girth. This paper explains the importance of cyclic distribution by comparing APM-LDPC codes with QC-LDPC codes. Then a particular form of APM-LDPC codes is proposed and researched. The new codes can low down the cycle-distribution to larger extent. In the following research, an effective method, which constructs the new codes with fixed girth, is proposed. Simulations show that the construction method is reasonable and effective. The transmission performances are better than the traditional methods, as well. Finally, the implementation and verification are carried out on FPGA. [ABSTRACT FROM AUTHOR]

In the nonbinary low-density parity check (NB-LDPC) codes decoding algorithms, the iterative hard reliability based on majority logic decoding (IHRB-MLGD) algorithm has poor error correction performance. The essential reason is that the hard information is used in the initialization and iterative processes. For the problem of partial loss of information, when the reliability is assigned during initialization, the error correction performance is improved by modifying the assignment of reliability at initialization. The initialization process is determined by the probability of occurrence of the number of erroneous bits in the symbol and the Hamming distance. In addition, the IHRB-MLGD decoding algorithm uses the hard decision in the iterative decoding process. The improved algorithm adds soft decision information in the iterative process, which improves the error correction performance while only slightly increasing the decoding complexity, and improves the reliability accumulation process which makes the algorithm more stable. The simulation results indicate that the proposed algorithm has a better decoding performance than IHRB algorithm. [ABSTRACT FROM AUTHOR]

This study proposes a method to distinguish between healthy people and Parkinson's disease patients using sole pressure sensor data, neural network with weighted fuzzy membership (NEWFM), and preprocessing techniques. The preprocessing techniques include fast Fourier transform (FFT), Euclidean distance, and principal component analysis (PCA), to remove noise in the data for performance enhancement. To make the features usable as inputs for NEWFM, the Euclidean distances between the left and right sole pressure sensor data were used at the first step. In the second step, the frequency scales of the Euclidean distances extracted in the first step were divided into individual scales by the FFT using the Hamming method. In the final step, 1–15 dimensions were extracted as the features of NEWFM from the individual scales by the FFT extracted in the second step by the PCA. An accuracy of 75.90% was acquired from the eight dimensions as the inputs of NEWFM. [ABSTRACT FROM AUTHOR]

Effective resistance to intellectual property (IP) piracy, overproduction and reverse engineering are becoming more and more necessary in the integrated circuit (IC) supply chain. To protect the hardware, the obfuscation methodology hides the original function by adding a large number of redundant states. However, existing hardware obfuscation approaches have hardware overhead and efficiency of obfuscation limitations. This paper proposed a novel methodology for IP security using the minimum spanning tree finite state machine (MST-FSM) obfuscation. In the minimum spanning tree (MST) algorithm, the Hamming distance defines the cost of obfuscated states. The Kruskal algorithm optimizes the connection relationship of obfuscated states by computing the Hamming distance of the MST-FSM. The proposed MST-FSM is automatically generated and embedded in the hardware IP with the self-building program. Finally, the MST-FSM is applied on the itc99 benchmark circuits and encryption standard IP cores. Compared with other state-of-the-arts, the obfuscation potency is improved by 3.57%, and the average hardware cost is decreased by about 6.01%. [ABSTRACT FROM AUTHOR]

A closed string contains a proper factor occurring as both a prefix and a suffix but not elsewhere in the string. Closed strings were introduced by Fici (WORDS 2011) as objects of combinatorial interest. This paper addresses a new problem by extending the closed string problem to the k -closed string problem, for which a level of approximation is permitted up to a number of Hamming distance errors, set by the parameter k. We address the problem of deciding whether or not a given string of length n over an integer alphabet is k -closed and additionally specifying the border resulting in the string being k -closed. Specifically, we present an 𝒪 (k n) -time and 𝒪 (n) -space algorithm to achieve this along with the pseudocode of an implementation and proof-of-concept experimental results. [ABSTRACT FROM AUTHOR]

We use two main techniques, namely, residuation and separators of points, to show that the Hilbert function of a certain fat point set supported on a grid complete intersection is the same as the Hilbert function of a reduced set of points called a partial intersection. As an application, we answer a question of Tohǎneanu and Van Tuyl which relates the minimum Hamming distance of a special linear code and the minimum socle degree of the associated fat point set. [ABSTRACT FROM AUTHOR]

Fuzzy set theory and fuzzy logic have been successfully developed in engineering and mathematics. However, these concepts have found great acceptance in social sciences in recent years since they provide an answer to those problems in the real world that cannot be modeled using classical mathematics. In this paper, we propose a new methodology for accounting science based on fuzzy triangular numbers. The methodology uses Hamming distance between fuzzy triangular numbers and arithmetic operations to evaluate corporate governance of multinational public stock corporations (PSCs) in the telecommunications sector. [ABSTRACT FROM AUTHOR]

In this paper, we define the new idea of triangular cubic hesitant fuzzy number (TCHFN). We discuss some basic operational laws of triangular cubic hesitant fuzzy number and hamming distance of TCHFNs. We introduce the new concept of triangular cubic hesitant TOPSIS method. Furthermore, we extend the classical cubic hesitant the technique for order of preference by similarity to ideal solution (TOPSIS) method to solve the Multi-Criteria decision-making (MCDM) method based on triangular cubic hesitant TOPSIS method. The new ranking method for TCHFNs is used to rank the alternatives. Finally, an illustrative example is given to verify and demonstrate the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we define a new idea of trapezoidal neutrosophic cubic hesitant fuzzy number based on migraine diseases. We define and the migraine diseases on trapezoidal neutrosophic cubic hesitant fuzzy number and operational laws of trapezoidal neutrosophic cubic hesitant fuzzy number and hamming distance of TrNCHFNs. The new concept of trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method is introduced. Furthermore, we extend MCDM method based on the trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method. Finally, an illustrative example is given to verify and demonstrate the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we describe the new idea of trapezoidal linguistic uncertain cubic fuzzy number. We discuss some basic operational laws of trapezoidal linguistic uncertain cubic fuzzy number and hamming distance of TrLUCFNs. We introduce the new concept of trapezoidal linguistic uncertain cubic fuzzy TOPSIS method. Furthermore, we extend the classical trapezoidal linguistic uncertain cubic fuzzy TOPSIS method to solve the MCDM method based on trapezoidal linguistic uncertain cubic fuzzy TOPSIS method. The new ranking method for TrLUCFNs is used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a novel feature extraction method based on an improved color local binary pattern (LBP) is proposed for color face recognition. Firstly, in a given neighborhood of every pixel, we choose some sampling points from three color channels simultaneously and the numbers of the sampling points from every channel may be different. Secondly, we use a new rule to select the threshold which does not always locate in the geometrical center of the given neighborhood. Thirdly, in order to excavate the potential of the proposed sampling method, we use the k -uniform LBP to obtain the binary code of each pixel. In addition, we embed the Hamming distance into our method for improving the recognition rate of the proposed method. For evaluating the performance of our method, we implement the proposed method and several related methods on five public face databases: FERET, CMU-PIE, Georgia, FEI and Asian databases. Experimental results show that our method possesses higher recognition rates and lower computational cost than other related color face recognition methods. [ABSTRACT FROM AUTHOR]

Two isometry groups of combinatorial codes are described: the group of isometries, that is, the group of Hamming isometries from a code to itself and the group of monomial isometries, which is the group of those isometries of a code to itself that extend to monomial maps. Unlike the case of classical linear codes, where these groups are the same, it is shown that for combinatorial codes the groups can be arbitrarily different. In particular, there exist codes with the richest possible group of isometries and the trivial group of monomial isometries. In the paper, the two groups are characterized and codes with predefined isometry groups are constructed. [ABSTRACT FROM AUTHOR]

Approximate Nearest Neighbor (ANN) search is a challenging problem with the explosive high-dimensional large-scale data in recent years. The promising technique for ANN search include hashing methods which generate compact binary codes by designing effective hash functions. However, lack of an optimal regularization is the key limitation of most of the existing hash functions. To this end, a new method called Adaptive Hashing with Sparse Modification (AHSM) is proposed. In AHSM, codes consist of vertices on the hypercube and the projection matrix is divided into two separate matrices. Data is rotated through a orthogonal matrix first and modified by a sparse matrix. Here the sparse matrix needs to be learned as a regularization item of hash function which is used to avoid overfitting and reduce quantization distortion. Totally, AHSM has two advantages: improvement of the accuracy without any time cost increasement. Furthermore, we extend AHSM to a supervised version, called Supervised Adaptive Hashing with Sparse Modification (SAHSM), by introducing Canonical Correlation Analysis (CCA) to the original data. Experiments show that the AHSM method stably surpasses several state-of-the-art hashing methods on four data sets. And at the same time, we compare three unsupervised hashing methods with their corresponding supervised version (including SAHSM) on three data sets with labels known. Similarly, SAHSM outperforms other methods on most of the hash bits. [ABSTRACT FROM AUTHOR]

We study linearized systems of equations in characteristic of the form where is a square matrix and . We present algorithms for calculating their solutions and for determining the minimum distance of their solution spaces. In the case when has entries in , the finite field of elements, we explore the relationships between the minimal and characteristic polynomials of and the above mentioned features of the solution space. In order to extend and generalize these findings to the case when has entries in an arbitrary field of characteristic , we obtain generalizations of the characteristic polynomial of a matrix and the Cayley-Hamilton theorem to square linearized systems. [ABSTRACT FROM AUTHOR]

Motivated by a generalization of the football pool problem, we introduce additive cyclic codes over mixed alphabets of the form where , for distinct primes . We study their algebraic properties, generating sets, and duals. Additionally, we give examples of additive cyclic codes over the alphabet that have best-known or optimal parameters. [ABSTRACT FROM AUTHOR]

Accurate and fast target image recognition is an important function of applications such as remote sensing imaging and medical imaging. However, an operator such as speeded up robust feature (SURF) cannot be accurately matched in the recognition process of a target image. This led us to propose the use of a method capable of matching identification, i.e. binary robust invariant scalable keypoints (BRISK) operators, in combination with SURF operators. The proposed algorithm combines the accuracy of SURF operators and the rapidity of BRISK operators to obtain a quick and accurate way of matching. The initial matching of image feature extraction for targets is performed using the SURF-BRISK algorithm, and similarity measurements of feature matching are performed for the feature points of initial matching using the Hamming distance. Then, secondary fine matching is performed using the M-estimator Sample and Consensus (MSAC) algorithm to eliminate mismatched point pairs in order to achieve recognition of target images. Then, the three-dimensional coordinates of the work piece are obtained by using a binocular stereo vision system to provide location coordinates for the robots to grasp the work pieces accurately. In the experiment, stereo vision matching is conducted for targets obtained using the SURF-BRISK algorithm, and the location coordinates of targets are passed to the robot controller. The experimental results show that if the special geometric distortion is neglected, this method can be adapted for accurate positioning of the target; hence, it can identify the target in complex environments, access the location coordinates of the target, and achieve accurate robotic grasping of the work piece in real time. [ABSTRACT FROM AUTHOR]

In this paper, a novel algorithm for approximate string matching (ASM) is proposed. The novelty resides in the fact that, unlike most other methods, the proposed algorithm is not based on the Hamming or Levenshtein distances, but instead computes a score for each symbol in the search text based on a consensus measure. Those symbols with sufficiently high scores will likely correspond to approximate instances of the pattern string. To demonstrate the usefulness of the proposed method, it has been applied to the detection of QRS complexes in electrocardiographic signals with competitive results when compared against the classic Pan-Tompkins (PT) algorithm. The proposed method outperformed PT in 72% of the test cases, with no extra computational cost. [ABSTRACT FROM AUTHOR]

Let , where and . In this paper, minimum generating sets of cyclic codes over are given. A necessary and sufficient condition for cyclic codes over to be -free is obtained and a BCH-type bound on the minimum Hamming distance for them is also given. [ABSTRACT FROM AUTHOR]

In this paper, based on the Steane's enlargement construction, three classes of non-binary quantum codes are constructed from classical repeated-root cyclic codes of length 2ps over 픽q with odd characteristic p. The exact minimum distances of these quantum codes are determined. This construction yields a quantum MDS code with parameters [[2p, 2p - 4, 3]]p and two good quantum codes with parameters [[2p, 2p - 7, 4]]p and [[2p, 2p - 10, 5]]p. [ABSTRACT FROM AUTHOR]

Evolutionary studies have been of prime importance to life scientists since ancient times. The advancements in technology has made it possible to make available the massive amounts of genomic data. The abundance of genomic data poses new challenges for biologists, computer scientists and mathematicians to develop approaches for discovery of new relationships in data and evolutionary networks. In this work, nucleotide sequences are converted into binary sequences to explore the network among different species. A new approach based on binary sequences has been proposed to reconstruct the accurate phylogenetic network. The algorithm developed is validated by comparing the results with those obtained by already existing method of network construction. A program is also coded in C language on the Intel Core i3 Dell inspiron machine to obtain the evolutionary network. The new approach developed also provides the fast solutions as there is no need of aligning the sequences. [ABSTRACT FROM AUTHOR]

The most important families of nonlinear codes are systematic. A brute-force check is the only known method to compute their weight distribution and distance distribution. On the other hand, it outputs also all closest word pairs in the code. In the black-box complexity model, the check is optimal among closest-pair algorithms. In this paper, we provide a Gröbner basis technique to compute the weight/distance distribution of any systematic nonlinear code. Also our technique outputs all closest pairs. Unlike the check, our method can be extended to work on code families. [ABSTRACT FROM AUTHOR]

Subcube embeddability of the hypercube can be enhanced by introducing an additional dimension. A set of new dimensions, characterized by the Hamming distance between the pairs of nodes it connects, is introduced using a measure defined as the magnitude of a dimension. An enumeration of subcubes of various size is presented for a dimension parameterized by its magnitude. It is shown that the maximum number of subcubes for a Qn can only be attained when the magnitude of dimension is n-1 or n. It is further shown that the latter two dimensions can optimally increase the number of subcubes among all possible choices. [ABSTRACT FROM AUTHOR]

Soft set, as a parametrized family of subsets of a crisp universal set, has more ability to handle uncertain information. In this paper, we propose two types of similarity measure between soft sets and made a comparative study of these two techniques. Also we have shown an application of this similarity measure of soft sets. [ABSTRACT FROM AUTHOR]

One popular approach to prediction of binding motifs of transcription factors is to model the problem as to search for a group of l-mers (motifs), for some l > 0, one from each of the provided promoter regions of a group of co-expressed genes, that exhibit high information content when aligned without gaps. In our current work, we assume that these desired l-mers have evolved from a common ancestor, each of which has mutations in at most k-positions from the common ancestor, where k is substantially smaller than l. This implies that these l-mers should belong to the k-neighborhood of their common ancestor, measured in terms of Hamming distance. If the ancestor is given, then the problem for finding these l-mers becomes trivial. Unfortunately, the problem of identifying the unknown ancestor is probably as hard as the problem of predicting the motifs themselves. Our goal is to identify a set of l-mers that slightly violate the k-neighborhood of a putative ancestor, but capture all the desired motifs, which will lead to an efficient way for identification of the desired motifs. The main contributions of this paper are in four aspects: (a) we have derived nontrivial lower and upper bounds of information content for a set of l-mers that differ from an unknown ancestor in no more than k positions; (b) we have defined a new distance between two sequences and a k-pseudo-neighborhood, based on the new distance, that contains the k-neighborhood, defined by Hamming distance, of the to-be-defined ancestor; (c) we have developed an algorithm to minimize the sum of all the distances between a predicted ancestor motif and a group of l-mers from the provided promoter regions, using the new distance; and (d) we have tested PROMOCO and compared its prediction results performance with two other prediction programs. The algorithm, implemented as a computer software program PROMOCO, has been used to find all conserved motifs in a set of provided promoter sequences. Our preliminary application of PROMOCO shows that it achieves better or comparable prediction results, when compared to popular programs for identification of cis regulatory binding motifs. A limitation of the algorithm is that it does not work well when the size of the set of provided promoter sequences is too small or when desired motifs appear in only small portion of the given sequences. [ABSTRACT FROM AUTHOR]

A border of a string is a prefix of the string that is simultaneously its suffix. It is one of the basic stringology keystones used as a part of many algorithms in pattern matching, molecular biology, computer-assisted music analysis and others. The paper offers the automata-theoretical description of Iliopoulos's ALL_BORDERS algorithm. The algorithm finds all borders of a string with don't care symbols. We show that ALL_BORDERS algorithm is an implementation of a finite state transducer of specific form. We describe how such a transducer can be constructed and what should be the input string like. The described transducer finds a set of lengths of all borders. Last but not least, we define approximate borders and show how to find all approximate borders of a string when we concern Hamming distance definition. Our solution of this problem is based on transducers again. This allows us to use analogy with automata-based pattern matching methods. Finally we discuss conditions under which the same principle can be used for other distance measures. [ABSTRACT FROM AUTHOR]

In this paper, the individual is represented by a Bit-String based on the Penna model. The infection information is also denoted by a Bit-String including 0 and 1. The degree of getting an infection is rested with the matching degree between the Bit-String of the individual and the Bit-String of infection information. Thus, we define the Hamming Distance with age. The infection rules among individuals is described by Cellular Automata on the lattice with L * L. We discuss the existence and extinction for a certain infection on the process of evolution. [ABSTRACT FROM AUTHOR]