TY - GEN

T1 - Unambiguous conjunctive grammars over a one-letter alphabet

AU - Jez, Artur

AU - Okhotin, Alexander

PY - 2013/9/19

Y1 - 2013/9/19

N2 - It is demonstrated that unambiguous conjunctive grammars over a unary alphabet ∑ = {a} have non-trivial expressive power, and that their basic properties are undecidable. The key result is that for every base k ≥ 11 and for every one-way real-time cellular automaton operating over the alphabet of base-k digits {⌊k+9/4⌋,..., ⌊k+1/2⌋}, the language of all strings an with the base-k notation of the form 1 w 1, where w is accepted by the automaton, is generated by an unambiguous conjunctive grammar. Another encoding is used to simulate a cellular automaton in a unary language containing almost all strings. These constructions are used to show that for every fixed unambiguous conjunctive language L0, testing whether a given unambiguous conjunctive grammar generates L0 is undecidable.

AB - It is demonstrated that unambiguous conjunctive grammars over a unary alphabet ∑ = {a} have non-trivial expressive power, and that their basic properties are undecidable. The key result is that for every base k ≥ 11 and for every one-way real-time cellular automaton operating over the alphabet of base-k digits {⌊k+9/4⌋,..., ⌊k+1/2⌋}, the language of all strings an with the base-k notation of the form 1 w 1, where w is accepted by the automaton, is generated by an unambiguous conjunctive grammar. Another encoding is used to simulate a cellular automaton in a unary language containing almost all strings. These constructions are used to show that for every fixed unambiguous conjunctive language L0, testing whether a given unambiguous conjunctive grammar generates L0 is undecidable.

UR - http://www.scopus.com/inward/record.url?scp=84880697852&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-38771-5_25

DO - 10.1007/978-3-642-38771-5_25

M3 - Conference contribution

AN - SCOPUS:84880697852

SN - 9783642387708

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 277

EP - 288

BT - Developments in Language Theory - 17th International Conference, DLT 2013, Proceedings

T2 - 17th International Conference on Developments in Language Theory, DLT 2013

Y2 - 18 June 2013 through 21 June 2013

ER -