Abstract
The existence of maximal dense intervals of grammar forms is shown, and an explicit example of such an interval is given. It is shown to be decidable whether or not two given context-free grammars make up a maximal dense interval. The results are based on a construction that builds a new language from subsets of a given language. Directed graphs are studied as an application.
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References
H. A. Maurer, A. Salomaa and D. Wood, Dense hierarchies of grammatical families Journal of the ACM 29 (1982), 118–126.
H. A. Maurer, A. Salomaa, E. Welzl and D. Wood, Denseness, maximality and decidability of grammatical families, Ann. Acad. Scient. Fennicae 11 (1986), 167–178.
V. Niemi, Density of grammar forms (Parts I and II), Intern. Journal of Computer Mathematics 20 (1986), 3–21 and 91–114.
E. Welzl, Color-families are dense, Theoretical Computer Science 17 (1982), 29–42.
D. Wood, Grammar and L Forms: An Introduction, Springer-Verlag Lecture Notes in Comp. Science No. 91, New York, 1980.
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© 1988 Springer-Verlag Berlin Heidelberg
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Niemi, V. (1988). Maximal dense intervals of grammar forms. In: Lepistö, T., Salomaa, A. (eds) Automata, Languages and Programming. ICALP 1988. Lecture Notes in Computer Science, vol 317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19488-6_132
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DOI: https://doi.org/10.1007/3-540-19488-6_132
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