Lu
Hanlin
2010
system
recursive sets
unary alphabet
On Language Equations XXK = XXL and XM = N over a Unary Alphabet
2010-01-01
simple form
chapters
XXL
equations
false
terms of equations
https://doi.org/10.1007/978-3-642-14455-4_27
chapter
number
set
computational universality
proof
set of numbers
universality
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.
form
language equations
alphabet
constants
terms
solution
unique solution
regular constants
XM
https://scigraph.springernature.com/explorer/license/
2022-08-04T17:20
291-302
Okhotin
Alexander
Developments in Language Theory
978-3-642-14454-7
978-3-642-14455-4
Springer Nature
10.1007/978-3-642-14455-4_27
doi
pub.1036694593
dimensions_id
Lehtinen
Tommi
Academy of Finland
Department of Mathematics, University of Turku, Finland
Academy of Finland
Seki
Shinnosuke
Sheng
Yu
Linguistics
Yuan
Gao
Language, Communication and Culture
Turku Centre for Computer Science
Turku Centre for Computer Science
Department of Mathematics, University of Turku, Finland
Springer Nature - SN SciGraph project