Abstract
A criterion to measure derivational complexity of formal grammars and languages is proposed and discussed. That is, the associate language and the L-associate language are defined for a grammar such that the former represents all the valid derivations and the latter represents all the valid leftmost derivations. It is shown that for any phrase\3-structure grammar, the associate language is a contex\3-sensitive language and the L\3-associate language is a context\3-free language. Necessary and sufficient conditions for an associate language to be a regular set and to be a context\3-free language are found. The idea in the above necessary and sufficient conditions is extended to the notion of "rank≓ for a measure of derivational complexity of context\3-free grammars and languages. It is shown that for each nonnegative integer k, there exists a context\3-free language whose rank is k. The paper also includes a few solvable decision problems concerning derivational complexity of grammars.
| Original language | English |
|---|---|
| Pages (from-to) | 139-162 |
| Number of pages | 24 |
| Journal | Information and control |
| Volume | 22 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1973 |
| Externally published | Yes |
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Associate languages and derivational complexity of formal grammars and languages. / Moriya, Etsuro.
In: Information and control, Vol. 22, No. 2, 1973, p. 139-162.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Associate languages and derivational complexity of formal grammars and languages
AU - Moriya, Etsuro
PY - 1973
Y1 - 1973
N2 - A criterion to measure derivational complexity of formal grammars and languages is proposed and discussed. That is, the associate language and the L-associate language are defined for a grammar such that the former represents all the valid derivations and the latter represents all the valid leftmost derivations. It is shown that for any phrase\3-structure grammar, the associate language is a contex\3-sensitive language and the L\3-associate language is a context\3-free language. Necessary and sufficient conditions for an associate language to be a regular set and to be a context\3-free language are found. The idea in the above necessary and sufficient conditions is extended to the notion of "rank≓ for a measure of derivational complexity of context\3-free grammars and languages. It is shown that for each nonnegative integer k, there exists a context\3-free language whose rank is k. The paper also includes a few solvable decision problems concerning derivational complexity of grammars.
AB - A criterion to measure derivational complexity of formal grammars and languages is proposed and discussed. That is, the associate language and the L-associate language are defined for a grammar such that the former represents all the valid derivations and the latter represents all the valid leftmost derivations. It is shown that for any phrase\3-structure grammar, the associate language is a contex\3-sensitive language and the L\3-associate language is a context\3-free language. Necessary and sufficient conditions for an associate language to be a regular set and to be a context\3-free language are found. The idea in the above necessary and sufficient conditions is extended to the notion of "rank≓ for a measure of derivational complexity of context\3-free grammars and languages. It is shown that for each nonnegative integer k, there exists a context\3-free language whose rank is k. The paper also includes a few solvable decision problems concerning derivational complexity of grammars.
UR - http://www.scopus.com/inward/record.url?scp=0015601117&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0015601117&partnerID=8YFLogxK
U2 - 10.1016/S0019-9958(73)90237-4
DO - 10.1016/S0019-9958(73)90237-4
M3 - Article
AN - SCOPUS:0015601117
VL - 22
SP - 139
EP - 162
JO - Information and Computation
JF - Information and Computation
SN - 0890-5401
IS - 2
ER -