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Descriptional complexity measures of context-free languages. (English) Zbl 0535.68039
The paper defines some variants of the measure Prod, of syntactic complexity of context-free languages [J. Gruska, Inf. Control 14, 152-179 (1969; Zbl 0174.289)], namely one counts only the production rules containing at least one terminal symbol, containing only terminals (or no terminals or a terminal in the left end of the right hand member) etc. It is proved that all these measures induce infinite hierarchies without gaps on the family of context-free languages and that the decision problems usual in this frame [J. Gruska, Descriptional complexity of context-free languages, Proc. Math. Found. Comput. Sci. ’73, High Tatras, 71-83 (1973)] are undecidable for them.
Reviewer: C.Calude
MSC:
68Q45 Formal languages and automata
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References:
[1] S. Ginsburg: The Mathematical Theory of Context-Free Languages. McGraw-Hill, New York 1966. · Zbl 0184.28401
[2] J. Gruska: Some classifications of context-free languages. Information and Control 14 (1969), 2, 152-179. · Zbl 0174.28901 · doi:10.1016/S0019-9958(69)90055-2
[3] J. Gruska: Complexity and unambiguity of context-free grammars and languages. Information and Control 18 (1971), 5, 502-519. · Zbl 0238.68022 · doi:10.1016/S0019-9958(71)90519-5
[4] J. Gruska: Descriptional complexity of context-free languages. Proceedings MFCS’ 73, High Tatras, 71-83.
[5] A. Salomaa: Formal Languages. Academic Press, New York and London 1973. · Zbl 0262.68025
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