Characterizations of the LL(k) property

Abstract

Characterizations of the LL(k) property for context-free grammars are given, which lead to efficient algorithms for testing an arbitrary context-free grammar for the LL(k) property. The characterizations are based on succinct nondeterministic representations of a finite-state automaton used for constructing a canonical LL(k) parser. The resulting testing algorithms are usually of the same order to time complexity as their LR(k) counterparts. For example, one characterization (the LR(k) counterpart of which has been used by Hunt, Szymanski and Ullman for obtaining the fastest known algorithm for LR(k) testing) implies an 0(n^k+2) algorithm for LL(k) testing, where n is the size of the grammar in question and k is considered to be a fixed integer. This time bound for LL(k) testing has previously only been obtained indirectly, by a linear time-bounded reduction of LL(k) testing to LR(k) testing. Moreover, it is shown that the LL(k) property allows an especially convenient characterization, one which allows an 0(n^k+1) algorithm for LL(k) testing. This new time bound suggests that the LL(k) property might be strictly easier to test than the LR(k) property.

On leave from the University of Helsinki as an ASLA Fulbright Research Scholar. The work of this author was additionally supported by the National Science Foundation under Grant No. MCS77-11360.