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A basic two-terminal secret key generation model is considered, where the interactive communication rate between the terminals may be limited, and in particular may not be enough to achieve the maximum key rate. We first prove a multi-letter characterization of the key-communication rate region (where the number of auxiliary random variables depends on the number of rounds of the communication), and then provide an equivalent but simpler characterization in terms of concave envelopes in the case of unlimited number of rounds. Two extreme cases are given special attention. First, in the regime of very low communication rates, the key bits per interaction bit (KBIB) is expressed with a new “symmetric strong data processing constant”, which has a concave envelope characterization analogous to that of the conventional strong data processing constant. The symmetric strong data processing constant can be upper bounded by the supremum of the maximal correlation coefficient over a set of distributions, which allows us to determine the KBIB for binary symmetric sources, and conclude, in particular, that the interactive scheme is not more efficient than the one-way scheme at least in the low communication-rate regime. Second, a new characterization of the minimum interaction rate needed for achieving the maximum key rate (MIMK) is given, and we resolve a conjecture by Tyagi regarding the MIMK for (possibly nonsymmetric) binary sources. We also propose a new conjecture for binary symmetric sources that the interactive scheme is not more efficient than the one-way scheme at any communication rate. [ABSTRACT FROM PUBLISHER]

The present paper proposed a novel approach called Wavelet based Least Significant Bit Watermarking (WLSBWM) for high authentication, security and copyright protection. Alphabet Pattern (AP) approach is used to generate shuffled image in the first stage and Pell's Cat Map (PCM) is used for providing more security and strong protection from attacks. PCM applied on each 5×5 sub images. A wavelet concept is used to reduce the dimensionality of the image until it equals to the size of the watermark image. Discrete Cosign Transform is applied in the first stage; later N level Discrete Wavelet Transform (DWT) is applied for reducing up to the size of the watermark image. The water mark image is inserted in LHn Sub band of the wavelet image using LSB concept. Simulation results show that the proposed technique produces better PSNR and similarity measure. The experimental results indicate that the present approach is more reliable and secure efficient. The robustness of the proposed scheme is evaluated against various image-processing attacks. [ABSTRACT FROM AUTHOR]

The article presents information about unicode, which are known to be the universal character set. Computers have become an indispensable part of one's life. Until recently, the outdated key character set standard, ASCII was in use. This character set has numerous limitations such as because of its constraint to include only seven of the eight bits in the byte, there is no room in ASCII to expand beyond the characters needed for the English language. Thus, in order to respond to the needs of international customer base, unicode character set is developed. The universal character set has numerous advantage because of the large number of characters that these languages share due to their common origins. These codes have found out a new way to encode languages for computer manipulation. These encoding allows over one million characters to be defined. Such codes covers not only currently used languages but also ancient languages that are studied by historians and scholars. These single character set have many advantages for all languages are particularly evident in libraries where works occur in different scripts.

Interface theories are employed in the component-based design of concurrent systems. They often emerge as combinations of Interface Automata (IA) and Modal Transition Systems (MTS), e.g., Nyman et al.'s IOMTS, Bauer et al.'s MIO, Raclet et al.'s MI or our MIA. In this paper, we generalise MI to nondeterministic interfaces, for which we properly resolve the longstanding conflict between unspecified inputs being allowed in IA but forbidden in MTS. With this solution we achieve, in contrast to related work, an associative parallel composition, a compositional preorder, a conjunction on interfaces with dissimilar alphabets supporting perspective-based specifications, and a quotienting operator for decomposing nondeterministic specifications in a single theory. In addition, we define a hiding and a restriction operator, complement conjunction with a disjunction operator and illustrate our interface theory by means of a simple example. [ABSTRACT FROM AUTHOR]

Suffix trees are highly regarded data structures for text indexing and string algorithms [MCreight 76, Weiner 73]. For any given string w of length n = | w | , a suffix tree for w takes O ( n ) nodes and links. It is often presented as a compacted version of a suffix trie for w , where the latter is the trie (or digital search tree) built on the suffixes of w . Here the compaction process replaces each maximal chain of unary nodes with a single arc. For this, the suffix tree requires that the labels of its arcs are substrings encoded as pointers to w (or equivalent information). On the contrary, the arcs of the suffix trie are labeled by single symbols but there can be Θ ( n 2 ) nodes and links for suffix tries in the worst case because of their unary nodes. It is an interesting question if the suffix trie can be stored using O ( n ) nodes. We present the linear-size suffix trie , which guarantees O ( n ) nodes. We use a new technique for reducing the number of unary nodes to O ( n ) , that stems from some results on antidictionaries. For instance, by using the linear-size suffix trie, we are able to check whether a pattern p of length m = | p | occurs in w in O ( m log ⁡ | Σ | ) time and we can find the longest common substring of two strings w 1 and w 2 in O ( ( | w 1 | + | w 2 | ) log ⁡ | Σ | ) time for an alphabet Σ. [ABSTRACT FROM AUTHOR]

Kubica et al. [33] and Kim et al. [29] introduced order-preserving pattern matching: for a given text the goal is to find its factors having the same ‘shape’ as a given pattern. Known results include a linear-time algorithm for this problem (in case of polynomially-bounded alphabet) and a generalization to multiple patterns. We propose an index that enables order-preserving pattern matching queries in time proportional to pattern length. The index can be constructed in O ( n log ⁡ log ⁡ n ) expected time or in O ( n log 2 ⁡ log ⁡ n / log ⁡ log ⁡ log ⁡ n ) worst-case time. It is an incomplete order-preserving suffix tree which may miss a single edge label at each branching node. For most applications such incomplete suffix trees provide the same functional power as the complete ones. We show a number of their applications, including computation of longest common factors, longest previously occurring factors and squares in a string in the order-preserving setting. We also give an O ( n log ⁡ n ) -time algorithm constructing complete order-preserving suffix trees. [ABSTRACT FROM AUTHOR]

We study the problem of indexing a text T [ 1 … n ] such that whenever a pattern P [ 1 … p ] and an interval [ α , β ] come as a query, we can report all pairs ( i , j ) of consecutive occurrences of P in T with α ≤ j − i ≤ β . We present an O ( n log ⁡ n ) space data structure with optimal O ( p + k ) query time, where k is the output size. [ABSTRACT FROM AUTHOR]

In this paper we describe a fast algorithm that creates a wavelet tree for a sequence of symbols. We show that a wavelet tree can be constructed in O ( n ⌈ log ⁡ σ / log ⁡ n ⌉ ) time where n is the number of symbols and σ is the alphabet size. [ABSTRACT FROM AUTHOR]

In this paper we extend several well-known document listing problems to the case when documents contain a substring that approximately matches the query pattern. We study the scenario when the query string can contain a wildcard symbol that matches any alphabet symbol; all documents that match a query pattern with one wildcard must be enumerated. We describe a linear space data structure that reports all documents containing a substring P in O ( | P | + σ log ⁡ log ⁡ log ⁡ n + docc ) time, where σ is the alphabet size and docc is the number of listed documents. We also describe a succinct solution for this problem, as well as a solution for an extension of this problem. Furthermore our approach enables us to obtain an O ( n σ ) -space data structure that enumerates all documents containing both a pattern P 1 and a pattern P 2 in the special case when P 1 and P 2 differ in one symbol. [ABSTRACT FROM AUTHOR]

Tablet computers and other mobile devices are widely used in education and other life activities. However, touch screen keyboards are not adapted to languages using alphabets with more letters than the English alphabet has. In this paper, we analyze the existing keyboards on such devices for various languages, influence of keyboard usability on the number of typing errors, and propose keyboard design guidelines for non-English languages. As an example, the layout for the Lithuanian language keyboard (32 native letters and 3 foreign letters) has been presented here. The described solution is not strictly related to the peculiarities of the Lithuanian language alphabet (apart from the number of letters), therefore it is suitable for other languages using a similar number of letters. [ABSTRACT FROM AUTHOR]

Abstract: Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match, or are compatible with, all letters in the alphabet ((full) words are just partial words without holes). The subword complexity function of a partial word over a finite alphabet assigns to each positive integer, , the number, , of distinct full words over that are compatible with factors of length of . In this paper, with the help of our so-called hole functions, we construct infinite partial words such that for any real number . In addition, these partial words have the property that there exist infinitely many non-negative integers satisfying . Combining these results with earlier ones on full words, we show that this represents a class of subword complexity functions not achievable by full words. We also construct infinite partial words with intermediate subword complexity, that is, between polynomial and exponential. [Copyright &y& Elsevier]

Regular model checking is a form of symbolic model checking for parameterized and infinite-state systems whose states can be represented as words of arbitrary length over a finite alphabet, in which regular sets of words are used to represent sets of states. We present LTL( MSO), a combination of the logics monadic second-order logic ( MSO) and LTL as a natural logic for expressing the temporal properties to be verified in regular model checking. In other words, LTL( MSO) is a natural specification language for both the system and the property under consideration. LTL( MSO) is a two-dimensional modal logic, where MSO is used for specifying properties of system states and transitions, and LTL is used for specifying temporal properties. In addition, the first-order quantification in MSO can be used to express properties parameterized on a position or process. We give a technique for model checking LTL( MSO), which is adapted from the automata-theoretic approach: a formula is translated to a buchi regular transition system with a regular set of accepting states, and regular model checking techniques are used to search for models. We have implemented the technique, and show its application to a number of parameterized algorithms from the literature. [ABSTRACT FROM AUTHOR]

Abstract: In a given word, one can count the number of occurrences of other words as a scattered subword. These counts can be “added” and/or “multiplied.” A subword history gives an instruction of what words to be counted and how these counts to be added and multiplied with other counts or integer constants, and hence, determines its unique value in a given word. Mateescu, Salomaa, and Yu asked: “is it decidable whether the value of a given subword history is non-negative in all words over a given alphabet?” (absoluteness problem). Another important problem is of whether there exists a word in which the value of a given subword history becomes 0 (equality problem). In this paper, we prove the undecidability of the equality problem and show that the equality problem is polynomial-time Karp reducible to the absoluteness problem; thus, the absoluteness problem is also undecidable. This approach solves the open problem actually under stronger conditions than supposed originally. [Copyright &y& Elsevier]

This study extends the understanding of two-element pure codes. Some characteristics of different length two-element pure codes are studied. It is shown that a language is a pure code which contains two distinct primitive words u and v with different lengths if and only if the regular expression u v of the two distinct words u and v is primitive. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we construct a new infinite class of two-character sets in and determine their automorphism groups. From this construction arise new infinite classes of two-weight codes and strongly regular graphs, and a new distance-2 ovoid of the split Cayley hexagon of order 4. [Copyright &y& Elsevier]

Abstract: We give a mass formula for self-dual codes over , where p is an odd prime. Using the mass formula, we classify such codes of lengths up to over the ring , over and over . [Copyright &y& Elsevier]

In this paper, we give an explicit p-adic expansion of (Multiple line equation(s) cannot be represented in ASCII text) as a power series in n. The coefficients are values of p-adic q-l-function for q-Euler numbers. [ABSTRACT FROM AUTHOR]

Given a string s on an alphabet Σ, a word-length k and a budget D, we want to determine the smallest number of distinct k-mers that can be left in s, if we are allowed to replace up to D letters of s. This problem has several parameters, and we discuss its complexity under all sorts of restrictions on the parameters values. We prove that some versions of the problem are polynomial, while others are NP-hard. We also introduce some Integer Programming formulations to model the NP-hard cases. [ABSTRACT FROM AUTHOR]

This paper proposes a novel and simple adaptive control algorithm for the effective delay control and resource utilization of end host multicast (EMcast) when the traffic load becomes heavy in a multigroup network with real-time flows constrained by (σ, ρ) regulators. The control algorithm is implemented at the overlay networks and provides more regulations through a novel (σ, ρ, λ) regulator at each group end host who suffers from heavy input traffic. To our knowledge, it is the first work to incorporate traffic regulators into the end host multicast to control heavy traffic output. Our further contributions include a theoretical analysis and a set of results. We prove the existence and calculate the value of the rate threshold ρ* such that for a given set of K groups, when the average rate of traffic entering the group end hosts ρ¯ > ρ*, the ratio of the worst-case multicast delay bound of the proposed (σ, ρ, λ) regulator over the traditional (σ, ρ) regulator is O((Multiple line equation(s) cannot be represented in ASCII text)) for any integer n. We also prove the efficiency of the novel algorithm and regulator in decreasing worst-case delays by conducting computer simulations. [ABSTRACT FROM AUTHOR]

Extended finite automata are finite state automata equipped with the additional ability to apply an operation on the currently remaining input word, depending on the current state. Hybrid extended finite automata can choose from a finite set of such operations. In this paper, five word operations are taken into consideration which always yield letter-equivalent results, namely reversal and shift operations. The computational power of those machines is investigated, locating the corresponding families of languages in the Chomsky hierarchy. Furthermore, different types of hybrid extended finite automata, defined by the set of operations they are allowed to apply, are compared with each other, demonstrating that there exist dependencies and independencies between the input manipulating operations. [ABSTRACT FROM AUTHOR]

The factor oracle is a relatively new data structure for the set of factors of a string. It has been introduced by Allauzen, Crochemore, and Raffinot in 1999. It may recognize non-factors (hence the name "oracle") but its implementational simplicity and experimental behaviour are stunning; factor oracle based string matching has been conjectured optimal on average. However, its structure is not well understood. We take important steps in clarifying its structure by explaining how it can be obtained as a quotient of the trie of the set of factors. When seen this way, all known properties of the factor oracle become simple observations. Also, we introduce a framework where various oracles can be compared. The factor oracle is better than several natural ones obtained from the trie of the set of factors, the suffix and the factor automata, respectively. [ABSTRACT FROM AUTHOR]

We consider forgetting automata, i.e., linear bounded automata which can only use the operations "move", "erase" (rewrite with a blank symbol) and "delete" (remove completely). A classification of the families of languages corresponding to the possible combinations of operations has been given in [1], here we address some of the problems left open. Furthermore the unary case is being investigated. [ABSTRACT FROM AUTHOR]

Rational relations are a powerful model used in many domains such as natural language processing. In this article, we propose a new model of finite state automata: multi-tape automata with symbol classes and identity or non-identity constraints. This model generalizes classical multi-tape automata, as well as automata and transducers with extended alphabet. We define this model in terms of a constraint satisfaction problem and discuss a problem occurring when handling the projection operation. Finally, we describe its implementation and results of a performance test. [ABSTRACT FROM AUTHOR]

We investigate the open question asking whether there exist independent systems of three equations over three unknowns admitting non-periodic solutions, formulated in 1983 by Culik II and Karhumäki. In particular, we give a negative answer to this question for a large class of systems. More specifically, the question remains open only for a well specified class of systems. We also investigate systems of two equations over three unknowns for which we give necessary and sufficient conditions for admitting at most quasi-periodic solutions, i.e., solutions where the images of two unknowns are powers of a common word. In doing so, we also give a number of examples showing that these conditions represent a boundary point between systems admitting purely non-periodic solutions and those admitting at most quasi-periodic ones. [ABSTRACT FROM AUTHOR]

Using the fact that the Parikh matrix mapping is not an injective mapping, the paper investigates some properties of the set of the binary words having the same Parikh matrix; these words are called "amiable" Some results concerning the conditions when the equivalence classes of amiable words have more than one element, a characterization theorem concerning a graph associated to an equivalence class of amiable words, and some basic properties of a rank distance defined on these classes are the main subjects considered here. [ABSTRACT FROM AUTHOR]

The online squarefree recognition problem is to detect the first occurrence of a square in a string whose characters are provided as input one at a time. We present an efficient algorithm to solve this problem for strings over arbitrarily ordered alphabets in O(n log n) time, where n is the ending position of the first square. We also note that the same technique yields an O(n·(|Σn|+log n))-time algorithm for general alphabets, where |Σn| is the number of different symbols in the first n positions of the input string. (This is faster than the previously fastest method for general alphabets when |Σn| = o(log2 n).) Finally, we present a simple algorithm for a dynamic version of the problem over general alphabets in which we are initially given a squarefree string, followed by a series of updates, and the objective is to determine after each update if the resulting string is still squarefree. [ABSTRACT FROM AUTHOR]

For certain problems (for example, computing repetitions and repeats, data compression applications) it is not necessary that the suffixes of a string represented in a suffix tree or suffix array should occur in lexicographical order (lexorder). It thus becomes of interest to study possible alternate orderings of the suffixes in these data structures, that may be easier to construct or more efficient to use. In this paper we consider the "reconstruction" of a suffix array based on a given reordering of the alphabet, and we describe simple time- and space-efficient algorithms that accomplish it. [ABSTRACT FROM AUTHOR]

Various code constructions use expander graphs to improve the error resilience. Often the use of expanding graphs comes at the expense of the alphabet size. In this correspondence, we show that by replacing the balanced expanding graphs used in the above constructions with unbalanced dispersers the alphabet size can be dramatically improved. [ABSTRACT FROM AUTHOR]

We determine the entropy rate of patterns of certain random processes including all finite-entropy stationary processes. For independent and identically distributed (i.i.d.) processes, we also bound the speed at which the per-symbol pattern entropy converges to this rate, and show that patterns satisfy an asymptotic equipartition property. To derive some of these results we upper bound the probability that the nth variable in a random process differs from all preceding ones. [ABSTRACT FROM AUTHOR]

Let Φm ⊆ C be the set of all mth roots of unity, m ∊ IN. A balanced code over Φm is a block code over the alphabet Φm such that each code word is balanced; that is, the complex sum of its components (or weight) is equal to 0. Let Bm (n) be the set of all balanced words of length n over Φm. In this correspondence, it is shown that when m is a prime number, the set Bm(n) is not empty if, and only if, m divides n. In this case, the minimum redundancy for a balanced code over Φm of length n is = ρ(Bm(n)) = n - ∟logm∣Bm(n)∣⅃ ≈ [(m - 1)/2]logm(2πn) - m/2. On the other hand, it is shown that when m = 4, the set B4 (n) is not empty if, and only if, n is even, and in this case, the minimum redundancy for a balanced code over Φ4 of length n is ρ(B4(n)) = n - ∟log4∣B4(n)∣⅃ ≈ log4 n + 0.326. Further, this correspondence completely solves the problem of designing efficient coding methods for balanced codes over Φm, when m = 4. In fact, it reduces the problem of designing efficient coding schemes for balanced codes over Φ4 to the design of efficient balanced codes over the usual bipolar alphabet Φ4 = {-1, +1}. [ABSTRACT FROM AUTHOR]

We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern overlaps introduced in this paper, which is a subgraph of the de Bruijn graph and which we prove to be Hamiltonian. In other cases we reduce a problem under consideration to known facts on unavoidable sets of words. We also give a relation between our problem and the extensively studied universal cycles and prove that there exists a universal cycle for word patterns of any length over any alphabet. The Stirling numbers of the second kind and the Mobius function appear in our results. [ABSTRACT FROM AUTHOR]

In this paper the authors propose a method for high-accuracy recognition of large character sets using a new combination of a statistical method and neural networks. In their method, a hierarchical structure that has several neural networks arranged in a line after the statistical method is used. First, recognition using a statistical method is performed, and this represents the final result if the top candidate does not belong to a predefined set of similar characters. If it does, then the input character is discriminated in a neural network which designates the top candidate by determining the similar characters. The results are output as final results. The basic idea of this method is the functional division of a statistical method and neural networks, and the use of a neural network as determined by a statistical method. The results of recognizing 3201 character types including JIS-1 Kanji showed an improvement in the correct recognition rate due to the combined use of a statistical method and neural networks, thereby demonstrating the validity of the authors' approach. © 2005 Wiley Periodicals, Inc. Syst Comp Jpn, 36(9): 97–107, 2005; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/scj.20330 [ABSTRACT FROM AUTHOR]

The last step of the Information Retrieval process is to display the found documents to the user. However, some difficulties might occur at that point. English texts are usually written in the ASCII standard. Unlike the English language, many languages have different character sets, and do not have one standard. This plurality of standards causes problems, especially in a web environment, where one may download a document with an unknown standard. This paper suggests a purely automatic way of finding the standard which was used by the document writer based on the statistical letters distribution in the language. We developed a vector-space-based method that creates frequencies vectors for each letter of the language and then matches a new document's vectors to the pre-computed templates. The algorithm was applied on various types of corpora in Hebrew, Russian and English, and provides an efficient solution to the stated problem in most cases. [ABSTRACT FROM AUTHOR]

Given a positive integer n and a finite alphabet Σ, a word w over Σ is said to guarantee minimum image if, for every homomorphism φ from the free monoid Σ[*] over £ into the monoid of all transformations of an n-element set, the range of the transformation wφ has the minimum cardinality among the ranges of all transformations of the form vφ where v runs over Σ[*]. Although the existence of words guaranteeing minimum image is pretty obvious, the problem of their explicit description is very far from being trivial. Sauer and Stone in 1991 gave a recursive construction for such a word w but the length of their word was doubly exponential (as a function of n). We first show that some known results of automata theory immediately lead to an alternative construction that yields a simpler word that guarantees minimum image: it has exponential length, more precisely, its length is O(|Σ|1/6[sup(n³-n)]. Then with some more effort, we find a word guaranteeing minimum image similar to that of Sauer and Stone but of length O(Σ½[sup(n²-n)]). On the other hand, we prove that the length of any word guaranteeing minimum image cannot be less than |Σ|[supn-1]. [ABSTRACT FROM AUTHOR]

The paper investigates inequalities between the numbers of different (scattered) subword occurrences. The Parikh matrix recently introduced is an efficient tool. We give various characterizations for Parikh matrices. Of special interest is the case where the matrix determines the word uniquely. We investigate such matrix unambiguous words. The considerations are extended to concern languages. Several open problems and problem areas are indicated. [ABSTRACT FROM AUTHOR]

In 1976, Dekking showed that there exists an infinite binary word that contains neither squares yy with |y| ≥ 4 nor cubes xxx. We show that 'cube' can be replaced by any fractional power > 5/2. We also consider the analogous problem where '4' is replaced by any integer. This results in an interesting and subtle hierarchy. [ABSTRACT FROM AUTHOR]

Episturmian words, which include the Arnoux-Rauzy sequences, are infinite words on a finite alphabet generalizing the Sturmian words and sharing many of their same properties. This was studied in previous papers. Here we gain a deeper insight into these properties. This leads in particular to consider numerations systems similar to the Ostrowski ones and to give a matrix formula for computing the number of representations of an integer in such a system. We also obtain a complete answer to the question: if an episturmian word is morphic, which shifts of it, if any, also are morphic? [ABSTRACT FROM AUTHOR]

A simplified alpha-numeric phonetic alphabet is proposed. It uses digits, standard keyboard symbols, and upper- and lowercase letters to give a computer-compatible unambiguous single-character phonetic writing of English. Such a phonetic spelling, in conjunction with a pronouncing dictionary giving standardized pronunciation of English worth in this phonetic alphabet, together with appropriate computer compilers and speech synthesizers and recognition systems, would facilitate man-machine oral communication and expand the use of talking and listening computers. This phonetic text is considerably shorter than standard English, can be written on any typewriter or computer terminal, and is easily learned in a short time. Rules and characteristics of this language are given, and it is compared to other phonetic alphabets. [ABSTRACT FROM AUTHOR]

Although there is a simple and fast method to separate and classify letter in lateral printed string by regarding a valley of the projection of the original image as a gap of letters, this method cannot be applied to cases where adjacent letters are connected or large clutter is involved. This paper proposes a method which separates and recognizes each letter even in such cases as described in the foregoing, using a three-layered BP model with feedback connections. The recognition experiments using the proposed method were carried out with lateral strings of five printed letter (capital A to E) binarized through s CCD camera. The results show that the method is superior to conventional methods when applied to a letter string recognition system used in the process of factory automation. [ABSTRACT FROM AUTHOR]