Abstract
It is shown that the recently discovered computational universality in systems of language equations over a unary alphabet occurs already in systems of the simplest form, with one unknown X and two equations XXK = XXL and XM = N, where K, L, M, N ⊆ a * are four regular constants. Every recursive (r.e., co-r.e.) set can be encoded in a unique (least, greatest) solution of a system of such a form. The proofs are carried out in terms of equations over sets of numbers.
Supported by the Academy of Finland under grants 134860 and 218315.
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Lehtinen, T., Okhotin, A. (2010). On Language Equations XXK = XXL and XM = N over a Unary Alphabet. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds) Developments in Language Theory. DLT 2010. Lecture Notes in Computer Science, vol 6224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14455-4_27
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DOI: https://doi.org/10.1007/978-3-642-14455-4_27
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