Bell, PC, Reidenbach, D and Shallit, JO (2020) Unique decipherability in formal languages. Theoretical Computer Science, 804. 149 - 160. ISSN 0304-3975

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We consider several language-theoretic aspects of various notions of unique decipherability (or unique factorization) in formal languages. Given a language L at some position within the Chomsky hierarchy, we investigate the language of words UD(L) in L∗ that have unique factorization over L. We also consider similar notions for weaker forms of unique decipherability, such as numerically decipherable words ND(L), multiset decipherable words MSD(L) and set decipherable words SD(L). Although these notions of unique factorization have been considered before, it appears that the languages of words having these properties have not been positioned in the Chomsky hierarchy up until now. We show that UD(L), ND(L), MSD(L) and SD(L) need not be context-free if L is context-free. In fact ND(L) and MSD(L) need not be context-free even if L is finite, although UD(L) and SD(L) are regular in this case. We show that if L is context-sensitive, then so are UD(L), ND(L), MSD(L) and SD(L). We also prove that the membership problem (resp., emptiness problem) for these classes is PSPACE-complete (resp., undecidable). We finally determine upper and lower bounds on the length of the shortest word of L∗ not having the various forms of unique decipherability into elements of L

Item Type: Article
Additional Information: The final version of this article and all relevant information related to it, including copyrights, can be found on the publisher website.
Subjects: Q Science > QA Mathematics
T Technology > T Technology (General)
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 25 Jul 2022 14:37
Last Modified: 25 Jul 2022 14:37

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