Abstract
We associate a generating function of two formal variables with a given binary sequence and a generating function of three formal variables with a given pair of binary sequences. The first function gives information about all subsequences of the sequence and the second function gives information about all common subsequences of the pair of sequences. It is shown that, in many cases, these functions can be easily found, which is of interest for various applications such as reconstruction of sequences, pattern recognition, data transmission over channels with deletions, etc. [1],[2],[3]. This conclusion is demonstrated for random sequences chosen from a completely randomized probabilistic ensemble of binary sequences and from the ensemble of random sequences consisting of runs of lengths 1 and 2. The results show that the latter ensemble can be considered as a very good candidate for the ensemble of random codes capable of correcting deletion errors.
This work was supported by the Philips Research Laboratories (The Netherlands) and DFG (Germany).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Levenshtein, V.I.: Efficient reconstruction of sequences from their subsequences or supersequences. J. Combinatorial Theory, Ser. A 93, 310–332 (2001)
Hirschberg, D.S.: Bounds on the number of string subsequences. In: Crochemore, M., Paterson, M. (eds.) CPM 1999. LNCS, vol. 1645, p. 115. Springer, Heidelberg (1999)
Wagner, R.A., Fischer, M.J.: The string–to–string correction problem. Journal of the ACM 21(1), 168–173 (1974)
Calabi, L., Harnett, W.E.: Some general results of coding theory with applications to the study of codes for the correction of synchronization errors. Inform. Control 15(3), 235–249 (1969); Reprinted in : Harnett, W.E. (ed.), Foundation of Coding Theory, 107–121 (1974)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Balakirsky, V.B. (2005). Generating Functions Associated with Random Binary Sequences Consisting of Runs of Lengths 1 and 2. In: Helleseth, T., Sarwate, D., Song, HY., Yang, K. (eds) Sequences and Their Applications - SETA 2004. SETA 2004. Lecture Notes in Computer Science, vol 3486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11423461_24
Download citation
DOI: https://doi.org/10.1007/11423461_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26084-4
Online ISBN: 978-3-540-32048-7
eBook Packages: Computer ScienceComputer Science (R0)