language
article
recursive functions
class
simulations
false
number
unary languages
27
equations
notation
results
essential step
articles
automata
large class
alphabet
unbounded growth
step
undecidability
non-regular languages
language equations
Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth
https://scigraph.springernature.com/explorer/license/
2008-08-21
paper
cellular automata
one-letter alphabet
problem
It has recently been proved (Jeż, DLT 2007) that conjunctive grammars (that is, context-free grammars augmented by conjunction) generate some non-regular languages over a one-letter alphabet. The present paper improves this result by constructing conjunctive grammars for a larger class of unary languages. The results imply undecidability of a number of decision problems of unary conjunctive grammars, as well as non-existence of a recursive function bounding the growth rate of the generated languages. An essential step of the argument is a simulation of a cellular automaton recognizing positional notation of numbers using language equations.
decision problem
2008-08-21
https://doi.org/10.1007/s00224-008-9139-5
growth
unary alphabet
conjunctive grammars
present paper
function
argument
rate
grammar
2022-08-04T16:57
positional notation
growth rate
Springer Nature
1432-4350
1433-0490
Theory of Computing Systems
Mathematical Sciences
doi
10.1007/s00224-008-9139-5
Information and Computing Sciences
Okhotin
Alexander
Computation Theory and Mathematics
Applied Mathematics
Springer Nature - SN SciGraph project
Artur
Jeż
pub.1032338044
dimensions_id
46
Distributed Computing
1
Academy of Finland, Helsinki, Finland
Academy of Finland, Helsinki, Finland
Department of Mathematics, University of Turku, Turku, Finland
Institute of Computer Science, University of Wrocław, Wrocław, Poland
Institute of Computer Science, University of Wrocław, Wrocław, Poland