Abstract
Let C be a finite set of n words having total length L where all words are taken over a k-element alphabet. The set C is numerically decipherable if any two factorizations of the same word over the given alphabet into words in C have the same length. An O(nL 2) time and O((n + k)L) space algorithm is presented for computing the finest homophonic partition of C provided that this set is numerically decipherable. Whether or not the set C is numerically decipherable can be decided by another algorithm requiring O(nL) time and O((n + k)L) space. These algorithms are based on a recently developed technique related to dominoes. The presentation includes similar procedures which decide in O(nL) time and O((n+k)L) space whether or not C is uniquely decipherable and in O(n 2L) time and O((n + k)L) space whether or not C is multiset decipherable.
This author recognizes partial support from NSF grant CCR-9201345.
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Weber, A., Head, T. (1994). The finest homophonic partition and related code concepts. In: Prívara, I., Rovan, B., Ruzička, P. (eds) Mathematical Foundations of Computer Science 1994. MFCS 1994. Lecture Notes in Computer Science, vol 841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58338-6_108
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DOI: https://doi.org/10.1007/3-540-58338-6_108
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