On the complexity of LR(k) testing

Authors:
Harry B. Hunt, III;Thomas G. Szymanski;Jeffrey D. Ullman
Affiliations:
University of Wisconsin, Madison;Princeton University;Princeton University
Venue:
POPL '75 Proceedings of the 2nd ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Year:
1975

Citing 1
Cited 2

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A complexity theory of grammar problems

POPL '76 Proceedings of the 3rd ACM SIGACT-SIGPLAN symposium on Principles on programming languages

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Abstract

In this paper we derive upper bounds on the complexity of LR(k) testing both when k is considered to be a fixed integer and also when k is considered to be a parameter of the problem. In the latter case, we show that the lower bounds on the running time of such algorithms depend very strongly on the representation chosen for k. Thus LR(k) testing is NP-complete when k is expressed in unary and complete for nondeterministic exponential time when k is expressed in binary.These results carry over to many other parameterized classes of grammars, such as the LL(k), strong LL(k), SLR(k), LC(k), strong LC(k), BRC(l,k), BC(l,k) and extended precedence (l,k) grammars.