Abstract
We consider alphabetic coding of superwords. We establish an unambiguity coding criterion for the cases of finite and infinite codes. We prove that in the case of an infinite code the ambiguity detection problem is m-complete in the ∃1∀0 class of Kleene’s analytical hierarchy.
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References
Markov, Al.A., On Alphabet Coding, Dokl. Akad. Nauk SSSR, 1960, vol. 132, no. 3, pp. 521–523 [Soviet Math. Dokl. (Engl. Transl.), 1960, vol. 1, pp. 596-598].
Markov, Al.A., Non-recurrent Coding, Probl. Kibern., 1962, vol. 8, pp. 169–186.
Markov, A.A., Vvedenie v teoriyu kodirovaniya (Introduction to Coding Theory), Moscow: Nauka, 1982.
Rogers, H., Theory of Recursive Functions and Effective Computability, New York: McGraw-Hill, 1967. Translated under the title Teoriya rekursivnykh funktsii i effektivnaya vychislimost', Moscow: Mir, 1972.
Marchenkov, S.S., Definability in the Language of Functional Equations of a Countable-Valued Logic, Diskret. Mat., 2013, vol. 25, no. 4, pp. 13–23 [Discrete Math. Appl. (Engl. Transl.), 2013, vol. 23, no. 5–6, pp. 451–462].
Marchenkov, S.S., On Complexity of Solving Systems of Functional Equations in Countable-Valued Logic, Diskretn. Anal. Issled. Oper., 2015, vol. 22, no. 2, pp. 49–62.
Marchenkov, S.S. and Kalinina, I.S., The FE-Closure Operator in Countable-Valued Logic, Vestn ik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 2013, no. 3, pp. 42–47 [Moscow Univ. Comput. Math. Cybernet. (Engl. Transl.), 2013, vol. 37, no. 3, pp. 131-136].
Acknowledgement
The author is grateful to a reviewer for pointing out a gap in the proof.
Funding
The research was supported in part by the Russian Foundation for Basic Research, project no. 19-01-00200.
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Russian Text © The Author(s), 2019, published in Problemy Peredachi Informatsii, 2019, Vol. 55, No. 3, pp. 83–92.
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Marchenkov, S.S. On Alphabetic Coding for Superwords. Probl Inf Transm 55, 275–282 (2019). https://doi.org/10.1134/S0032946019030062
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DOI: https://doi.org/10.1134/S0032946019030062