Abstract
The membership problem for fixed context-sensitive languages is polynomial if the right hand side of every production is strictly longer than the left hand side.
This research was done while the authors were visiting the Hebrew University of Jerusalem. The first author was supported by the Minerva Foundation and the second author by the United States-Israel Binational Foundation, grant no. 2439-82.
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References
Y. M. Bar-Hillel, M. Perles, and E. Shamir, "On Formal Properties of Simple Phase Structure Grammars," Z. Phonetik Sprachwiss. Kommunikationsforschung, Vol. 14, pp. 143–172 (1961).
R. V. Book, "Time Bounded Grammars and their Languages," Journal of Computer and Systems Sciences, Vol. 5, pp. 397–429 (1971).
R. V. Book, "On the Structure of Context-Sensitive Grammar," International Journal of Computer and Information Sciences, Vol. 2, No. 2, pp. 129–139 (1973).
R. V. Book, "On the Complexity of Formal Grammars," Acta Informatica, Vol. 9, pp. 171–182 (1978).
N. Chomsky, "A Note on Phase-Structure Grammars," Information and Control, Vol. 2, pp. 137–167 (1959).
S. A. Cook, "Path Systems and Language Recognition," Proc. Second Annual ACM Symposium on Theory of Computing, pp. 70–72 (1970).
A. Gladkii, "On the Complexity of Derivations in Phase-Structure Grammars," (in Russian), Algebri i Logika, Sem. 3, Nr. 5–6, pp.29–44 (1964).
J. Gonczarowski and E. Shamir, "Pattern Selector Grammars and Several Parsing Algorithms in the Context-Free Style," Journal of Computer and System Sciences, Vol. 30, No. 3, pp. 249–273 (1985).
J. Gonczarowski and M. K. Warmuth, "Applications of Scheduling Theory to Formal Language Theory," Fundamental Studies Issue of Theoretical Computer Science, Vol. 37, No. 2, pp. 217–243 (1985).
J. Gonczarowski and M. K. Warmuth, "Manipulating Derivation Forests by Scheduling Techniques," Technical Report 85-3, Department of Computer Science, Hebrew University of Jerusalem.
J. Gonczarowski and M. K. Warmuth, "On the Complexity of Scattered Grammars," in preparation.
S. Greibach and J. Hopcraft, "Scattered Context Grammars," Journal of Computer and Systems Sciences, Vol. 3, pp. 233–249 (1969).
M. A. Harrison, Introduction to Formal Language Theory, Addison-Wesley, Reading, Mass. (1978).
R. M. Karp, "Reducibility among Combinatorial Problems," in: R. E. Miller and J. W. Thatcher (eds.) Complexity of Computer Computations, Plenum Press, pp. 85–103, New York (1972).
S. Y. Kuroda, "Classes of Languages and Linear Bounded Automata," Information and Control, Vol. 7, pp. 207–223 (1964).
J. Loeckx, "The Parsing of General Phase-Structure Grammars," Information and Control, Vol. 16, pp. 443–464 (1970).
W. L. Ruzzo, "Tree-Size Bounded Alternation," Journal of Computer and System Sciences, Vol. 21, pp. 218–235 (1980).
A. Salomaa, Formal Languages, Academic Press, N.Y. (1973).
P. M. Lewis, R. E. Stearns and J. Hartmanis, "Memory Bounds for Recognition of Context-Free and Context-Sensitive Languages," Proc. Sixth Annual IEEE Symposium Switching Circuit Theory and Logical Design, pp. 191–212 (1965).
H. Sudborough, "On the Tape Complexity of Deterministic Context-Free Languages," Journal of the ACM, Vol. 25, pp. 405–414 (1978).
J. D. Ullman and A. V. Gelder, "Parallel Complexity of Logical Query Programs," Technical Report, Department of Computer Science, Stanford University (1985).
D. H. Younger, "Recognition and Parsing of Context-Free Languages in Time n3," Information and Control, Vol. 10, pp. 189–208 (1967).
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© 1986 Springer-Verlag
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Dahlhaus, E., Warmuth, M.K. (1986). Membership for growing context sensitive grammars is polynomial. In: Franchi-Zannettacci, P. (eds) CAAP '86. CAAP 1986. Lecture Notes in Computer Science, vol 214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022661
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DOI: https://doi.org/10.1007/BFb0022661
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