Abstract
We consider the following problem: Given a set Γ = {c 1,...,c n} of nonempty strings over a fixed, finite alphabet Σ, is every string in Γ+ uniquely decipherable, or does the equation cx = dy, where c, d ∈ Γ, c ≠ d, and x,y ∈ Γ*, have a solution? We give an O(n L) algorithm for this problem, where L = |c 1| + ... + |c n|, and use this algorithm to investigate the impact of structural properties of Γ on the complexity of testing unique decipherability. We then give an O(L log(n)) unique decipherability test for sets Γ which may be linearly ordered by the prefix relation.
This work was supported in part by the National Science Foundation under Grant MCS 80-21066
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© 1984 Springer-Verlag Berlin Heidelberg
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Hoffmann, C.M. (1984). A note on unique decipherability. In: Chytil, M.P., Koubek, V. (eds) Mathematical Foundations of Computer Science 1984. MFCS 1984. Lecture Notes in Computer Science, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030289
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DOI: https://doi.org/10.1007/BFb0030289
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