Duration of search for a fixed pattern in random data: Distribution function and variance

A New Approach to Cross-Bifix-Free Sets

“…Rather than to the bifix, much attention has been devoted to a bifix-indicator, an indicator function implying the existence of the bifix [10]. Such indicators were shown to be without equal in performing various statistical analysis, mainly concerning the search process [3,10] However, an analytical study of simultaneous search for a set of sequences urged the invention of cross-bifix indicators [1,2] and, accordingly, turned attention to the sets of sequences which avoid cross-bifixes, called cross-bifix-free sets.…”

On Criteria for Short Acquisition Sequences Choice

“…Another two sequences are all-zero and repetitive sequences of length 10, both ones "punctured" at the "x" positions of minimal length distributed sequence (sequences 5 (12); all-zero sequence (7) and repetitive sequence (8) punctured at the "x" positions of maximal length sequence. Another experiments is to distribute random symbols uniformly between the 8 fixed bits (still with N=17) of maximal length sequence (11), all-zeros (2) and repetitive one (4).…”

“…The next two sequences with almost the same survival probability are 0101 ... ones-(4) with interleaved random data bits forming a structure xOxlxOxl ... and (3) contiguous. The worst sequences are all-zeros onesthe first one interleaved (x0x0..., (2) and the very worst one contiguous one (1).…”

“…Within an infinite stream of random data a bifix, a crossbifix and tail structures [1][2][3], in spite of their mathematical beauty, must remain what they actually are: mathematical abstractions. To give them a possibility of application, we must turn to the digital transmission systems where data (including the overhead symbols of various transmission purposes) are scrambled and may be regarded as random and equiprobable.…”

Search process and probabilistic bifix approach

“…Further research, by this author, added the probability distribution function and variance to already known expected value [3]. The results were later extended to the case of set of M sequences [4].…”