Abstract
Relational expressions have finite binary relations as arguments and the operations are composition (·), closure (*), inverse (−1), and union (U). The efficient computation of the relation denoted by a rélational expression is considered, and a tight bound is established on the complexity of the algorithm suggested by Hunt, Szymanski and Ullman. The result implies a unified method for deriving efficient algorithms for many problems in parsing. For example, optimal algorithms are derived for strong LL(1) and strong LL(2) parser construction and an efficient polynomialtime algorithm is derived for determining the inessential error entries in an LR(1) parsing table.
The work of S. Sippu was supported by the Finnish Cultural Foundation. The work of E. Soisalon-Soininen was supported by the Academy of Finland.
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References
Aho AV, Ullman JD (1972, 1973) The theory of parsing, translation, and compiling, Vols 1 and 2. Prentice-Hall, Englewood Cliffs, N.J.
DeRemer FL, Pennello TJ (1982) Efficient computation of LALR(1) lookahead sets. ACM Trans. Prog. Lang. Syst. 4: 615–649
Harrison MA (1978) Introduction to formal language theory. Addison-Wesley, Reading, Mass.
Hunt HB III, Szymanski TG, Ullman JD (1974) Operations on sparse relations and efficient algorithms for grammar problems. In: 15th Annual IEEE Symp. on Switching and Automata Theory, Oct 1974. IEEE, New York, pp 127–132
Hunt HB III, Szymanski TG, Ullman JD (1975) On the complexity of LR(k) testing. Comm. ACM 18: 707–716
Hunt HB III, Szymanski TG, Ullman JD (1977) Operations on sparse relations. Comm. ACM 20: 171–176
Johnson DB, Sethi R (1975) Efficient construction of LL(1) parsers. Technical Report No. 164, Computer Science Department, The Pennsylvania State University, University Park, Penn.
Soisalon-Soininen E (1982) Inessential error entries and their use in LR parser optimization. ACM Trans. Prog. Lang. Syst. 4: 179–195
Tarjan RE (1972) Depth-first search and linear graph algorithms. SIAM J. Comput. 1: 146–160
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© 1985 Springer-Verlag Berlin Heidelberg
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Sippu, S., Soisalon-Soininen, E. (1985). On the use of relational expressions in the design of efficient algorithms. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015771
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DOI: https://doi.org/10.1007/BFb0015771
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