Position Of String Research Articles

Tight comparison bounds for the string prefix-matching problem

In the string prefix-matching problem one is interested in finding the longest prefix of a pattern string of length m that occurs starting at each position of a text string of length n. This is a natural generalization of the string matching problem where only occurences of the whole pattern are sought. The Knuth-Morris-Pratt string matching algorithm can be easily adapted to solve the string prefix-matching problem without making additional comparisons. In this paper we study the exact complexity of the string prefix-matching problem in the deterministic sequential comparison model. Our bounds do not account for comparisons made in a pattern preprocessing step. The following results are presented: 1. (1) A family of linear-time string prefix-matching algorithms that make at most ⌊( (2m−1) m )n⌋ comparisons. 2. (2) A tight lower bound of ⌊(( 2m−1) m )n⌋ comparisons for any string prefix-matching algorithm that has to match the pattern ‘ ab m −1’. We also consider the special case when the pattern and the text strings are the same string and all comparisons are accounted. This problem, which we call the string self-prefix problem, is similar to the failure function that is computed in the pattern preprocessing of the Knut-Morris-Pratt string matching algorithm and used in several other comparison efficient algorithms. By using the lower bound for the string prefix-matching problem we are able to show: 3. (3) A lower bound of 2m−⌊2 m ⌋ comparisons for the self-prefix problem.

A probabilistic analysis of a pattern matching problem

The study and comparison of strings of symbols from a finite or an infinite alphabet is relevant to various areas of science, notably molecular biology, speech recognition, and computer science. In particular, the problem of finding the minimum “distance” between two strings (in general, two blocks of data) is of a practical importance. In this article we investigate the (string) pattern matching problem in a probabilistic framework, namely, it is assumed that both strings form an independent sequences of i.i.d. symbols. Given a text string a of length n and a pattern string b of length m, let Mm,n be the maximum number of matches between b and all m-substrings of a. Our main probabilistic result shows that for a wide range of input parameters in probability (pr.) provided m, n ∞ such that log n = o(m), where P is the probability of a match between any two symbols of these strings, and T is the probability of a match between two positions in the text string and a given position of the pattern string. We also prove that Mm,n/mP almost surely (a.s.) for log n = o(m). © 1993 John Wiley & Sons. Inc.

The eight-vertex model: Spectrum of the transfer matrix and classification of the excited states

We study the eigenvalue problem for the transfer matrix of the eight-vertex model by analyzing the Bethe Ansatz equations. Using functional equations and complex variable theory the excited states of the model are completely classified in terms of strings of “complex moments”. The different possible strings are determined. The main result of this paper is the derivation of a basic set of equations from which string positions can be calculated in terms of excitation parameters. The case of 2- and 4-particle excitations is analyzed in detail.

Gauge invariance over a group as the first principle of interacting string dynamics

It is stressed that the basic principle of the standard gauge theories is the invariance under internal symmetry transformations that do not commute with translations. This concept is generalized to the case where the translation group is replaced by an arbitrarily given non-abelian group G. The generalized Yang-Mills theory, called gauge theory over G, is an attractive extension of the standard formalism. The gauge theory over the conformal group is proposed as the fundamental theory of bosonic strings. As is usual in gauge theories, the interaction is uniquely specified by the invariance properties. For strings, overlap conditions between string positions come out in a natural way. The powerful machinery of Yang-Mills theories is fully applicable to the gauge theories over groups. In particular, an example of the Higgs-Kibble mechanism is given.

Improving the worst-case performance of the Hunt-Szymanski strategy for the longest common subsequence of two strings

Among the algorithms set up to date for finding the longest common subsequence of two strings, the one by Hunt and Szymanski exhibits the best known performance in favorable cases, but can be worse than any straightforward algorithm for a large variety of inputs. The new algorithm presented here pursues a schedule of primitive operations quite close to the one inherent to the Hunt-Szymanski strategy, but with substantially enhanced efficiency. In fact, the new algorithm improves on the former in two important respects. First, its worst case is never worse than linear in the product nm of the lengths of the two input strings. Second, its time bound does not always grow with the cardinality r of the set R of all pairs of matching positions of the input strings. Rather, it depends on the cardinality d of a specific subset of R, whose elements are called here dominant matches, and are elsewhere referred to as minimal candidates. This second improvement also appears of significance, since it seems that whenever r gets too close to mn, this forces d to be linear in m. The new algorithm requires standard preprocessing, and makes use of finger-trees. In a forthcoming paper, it will be shown among other things that the same performance can be achieved with simpler and handier auxiliary data structures.

Lower critical dimensions and curved backgrounds in string theories

We examine a string action consisting a of two-dimensional generally covariant field theory containing, besides the string position co-ordinates, conformal scalar fields. Its geometric interpretation as the world surface area traced out by the string can be maintained if the vacuum is associated with a nonflat higher-dimensional space. The quantized system is covariant in 26−r dimensions, wherer is the number of scalar fields. Further a nonzero background value for the scalar field, besides leading to a curved background, can also solve the tachyon ground-state problem.

The Theory and Practice of Constructing an Optimal Polyphase Sort

The construction of both an optimal read-forward polyphase sort and a near optimal read-backward version is described. The former minimizes the merge volume, for a given distribution of strings, without the use of auxiliary data structures, and incorporates a new technique for computing the positions of dummy strings. In the case of the readbackward version, an approach is developed which achieves a merge volume nearest to the minimum, inasmuch as the theoretical optimal read-backward polyphase sort cannot be realized. A dispersion algorithm is also described which optimizes the distribution of strings so that minimum merge volume is assured.

Phonological and orthographic factors in the word-superiority effect

Phonological and orthographic aspects of a letter string were found to affect the identification of a component letter in three experiments. All involved a fixed set of target vowels presented in a fixed position in letter strings. Manipulations of the phonological nature of the target or the orthographic character of the string were made by adding a letter with the postexposure mask to the original CVC trigram. In Experiment 1, the addition of an E with the mask as a final letter to the string changed the pronunciation of the target vowel, whereas the addition of an S did not. Identification accuracy was higher with the S mask. In Experiment 2, either E or D could be added to CVCs that were equally orthographic but differentially pronounceable. The same added letter had quite different effects on accuracy, depending on its effect on target pronunciation and the orthographic regularity of the string. In Experiment 3, performance on targets in orthographic CVCs was lowered to the level of nonorthographic CVCs by adding a letter that rendered the entire string nonorthographic. The results are explained by assuming that phonological and graphemic codes are developed simultaneously but maintained in a nonindependent manner.

Observation of violin string motion with optical sensors and acoustic excitation

Optical sensors [C. E. Gough, Acustica 44, 113–123 (1980)] are practical nonperturbative detectors of string position at individual points. Acoustic excitation provides a driving force which also is nonperturbative [G. Weinreich and E. Arnold, J. Acoust. Soc. Am. Suppl. 1, 67, S84 (1980)]. This method provides sufficient information about the terminating impedances of the string that realistic models may be used. Data obtained suggest that the assumption of a rigid nut should not be accepted without careful consideration, and effects of flexible support at both ends of the string on normal modes and bowing response are considered. [Work supported by NSF.]

A FORTRAN IV program for generating anagrams and for computing several indices in anagram research

This paper describes a computer program which generates all possible anagrams from any five-letter solution word and which also computes a number of frequently employed predictors of problem difficulty for each anagram. The following discussion outlines these indices and their derivations. For the most part, anagram researchers utilize fiveletter problems considered to be composed of four successive bigrams that correspond to the pairs of letters found in positions 1-2, 2-3, 34, and 4-5 of the letter string. The anagram HICAR, for example, is composed of the bigrams HI, IC, CA, and AR; the respective bigrams of its solution word, CHAIR, are CH, HA, AI, and IR. The relative frequency with which any bigram occurs in English is known as its transitional probability (TP), and the TPs of all possible bigrams have been estimated in tables prepared by Mayzner and Tresselt (1965) and Underwood and Schulz (1960). The former table yields a more sensitive measure of bigram frequency since each TP value is estimated as a function both of the word length (WL) and of the letter position of the bigram (LP). As a result, the same bigram takes on different values when it appears in different-length letter strings or in different positions of a string of given length. For example, the Mayzner-Tresselt TP is 40 for CH as the first bigram in a five-letter string (e.g., CHAIR), but the TP is 126 for the same bigram when it is in the last two letter positions in a five-letter string and the TP is 7 for the same bigram in the last position of a six-letter string (e.g., CHURCH). The Underwood-Schulz values, on the other hand, make no adjustment for WL or LP, and thus the same TP value is assigned to CH in each of the three situations above. Both TP computations, however, are used in anagram research and are frequently cited in the literature. The TP index most often used to assess or control problem difficulty is obtained by adding the bigram frequencies of the four successive letter pairs (summed TP) in the anagram or in the solution word. For example, the four bigram frequencies of HICAR (5, 5, 10, 13) yield a summed TP of 33, while the summed TP of its solution word, CHAIR (40, 33, 40, 73), is 186. Two related indices that have proved useful in predicting problem difficulty (Gavurin, Note 1) are the transitional probability difference (TPD) and the transitional probability ratio (TPR). The former is obtained by subtracting the summed TP for the anagram f~om the summed TP for the solution word. The latter 1S calculated by dividing the solution word summed TP by the anagram summed TP. Using the bigram TPs presented above for HICAR, the TPD is 153 (186 33 = 153) and the TPR is 3.636 (186/33 = 3.636). Recently, Mendelsohn and O'Brien (1974) developed a TP predictor of anagram difficulty in the form o~ a bigram rank measure. This index is obtained by counting the number of bigrams, in the pool of all bigrams formed by the solution word letters, that exceed in TP value the solution word bigrams. The Mayzner-Tresselt values are used in this index. For example, a total of 20 different bigrams can be formed from the letters of the word CHAIR. Table 1 presents these bigrams and their TP values in each of the four letter positions. Using Table 1, the number of bigram TP values that exceed CH in LP 1-2 is 10. Similarly, for HA in LP 2-3, AI in LP 34, and IR in LP 4-5, the number of higher values are 11, 10, and 4, respectively. The four ranks when added together yield a value of 35, which represents the Mendelsohn-O'Brien summed rank index for the solution word CHAIR. A factor unrelated to TP that also affects anagram difficulty is letter order. Easy letter orders more closely approximate the solution word in that a minimal number of letter moves are necessary to achieve solution. Thus, if the solution word (e.g., CHAIR) letter order is considered to be 12345, an easy letter order would be 12435 (CHIAR) and a hard letter order would be 52413 (RHICA).

The Solution of Patterned String Problems By Birds

1. Three budgerigars quickly learned to pull to their cage a 15 cm long black string to which a small food container was attached. Then two strings of the same length but of different colour were offered, one of which was cosmected with a food container. One budgerigar learned successively with significant percentages of correct choices to pull the string with the container when both strings were arranged in one of 7 different patterns (Fig. 2 A-G). The bird mastered 2 of these arrangements spontaneously. Finally the budgerigar chose correctly in significant percentages of choices when 4 of these tasks were offered in predetermined irregular sequence in series of 30 trials. In these cases also the colours of the strings, the position of the correct string to the right or to the left, and the normal or the reflected arrangement changed in predetermined, irregular succession. These continuously changing situations always required different associative processes and new decisions. A second budgerigar mastered such tasks only when not more than string patterns were offered in irregular sequence. A third budgerigar learned to choose the correct string only when one of the simple string patterns A, B or C was offered in a series of trials. An Indian starling (Acridotheres tristis) and a jackdaw (Coloeus monedula) quickly learned to pull a string with a food container, but proved to be inappropriate for experiments with two strings because the handling of the strings in itself appeared rewarding to them. 2. The results of these experiments confirm that the brain achievements of birds are not inferior to those of mammals, although their forebrain lacks a cortex with several layers of neurons. They support the hypothesis that the specific configuration of forebrain regions is less important for more difficult brain achievements than the number and differentiation of neurons and the number of synapses.

Retinal location and string position as important variables in visual information processing

Three experiments were conducted to isolate the effects of retinal locus and string position in tachistoscopic letter recognition. Retinal locus proved to be an important variable even when its range was restricted to less than a degree from the center of the fovea. Performance was maximal at the center of the fovea, dropping off rapidly to about 1.5 deg from the center. From that distance on, the decline in performance was quite gradual. String position was also an important factor. Retinal locus and string position interacted in such a way that the end positions were less affected by retinal locus than the middle positions. It was also found that processing order, as distinct from report order, was a significant component of the string position effect.

Decay Characteristics of Piano Tones

Measurements have been made on a high-quality spinet piano to determine the initial amplitude and decay characteristics of the principal harmonic components of notes covering the entire scale. Decay rates of individual components varied from 1 to 100 db/sec as a function principally of frequency and string position in the scale rather than of harmonic number. An exception was noted in the third to fifth octaves, where the fundamental of a given string decayed at a considerably higher rate than the harmonics. This pattern appears to have a strong influence in determining typical piano tone in this region. Frequency spectra of the initial amplitudes of individual notes over the entire scale show, on the average, a sharp cutoff below 100 cps, a fairly flat region between 100 and 1000 cps, and a roll-off of at least 12 db per octave above 1000 cps, with negligible energy above 8000 cps.