operation
periodic constants
univariate equation
2022-08-04T17:16
number
implications
growth
super-exponential growth
2008-01-01
symbols
solution
equations
time
complement
Union
form x
constants
chapters
Equations of the form X=φ(X) are considered, where the unknown X is a set of natural numbers. The expression φ(X) may contain the operations of set addition, defined as S+T=
{m+n ∣ m ∈ S, n ∈ T}, union and intersection, as well as ultimately periodic constants. An equation with a non-periodic solution of exponential growth is constructed. At the same time it is demonstrated that no sets with super-exponential growth can be represented. It is also shown that a restricted class of these equations cannot represent sets with super-linearly growing complements. The results have direct implications on the power of conjunctive grammars with one nonterminal symbol.
https://doi.org/10.1007/978-0-387-09680-3_15
set
chapter
On the expressive power of univariate equations over sets of natural numbers
nonterminal symbols
true
2008-01-01
non-periodic solutions
intersection
grammar
https://scigraph.springernature.com/explorer/license/
215-227
addition
expression
set addition
conjunctive grammars
natural numbers
power
exponential growth
direct implications
results
expressive power
same time
class
pub.1032518557
dimensions_id
Information Systems
Ausiello
Giorgio
Dept. of Informatics and Telecommunications, University of Athens, Greece
Dept. of Informatics and Telecommunications, University of Athens, Greece
Luke
Ong
Giancarlo
Mauri
Springer Nature
Okhotin
Alexander
Fifth Ifip International Conference On Theoretical Computer Science – Tcs 2008
978-0-387-09679-7
978-0-387-09680-3
Panos
Rondogiannis
Information and Computing Sciences
Karhumäki
Juhani
Springer Nature - SN SciGraph project
doi
10.1007/978-0-387-09680-3_15
Dept. of Mathematics, University of Turku, Finland
Academy of Finland, Finland
Dept. of Mathematics, University of Turku, Finland