A Boolean matrix method for the computation of linear precedence functions

Authors:
David F. Martin
Affiliations:
Univ. of California, Los Angeles, Los Angeles
Venue:
Communications of the ACM
Year:
1972

Citing 7
Cited 3

A Theorem on Boolean Matrices

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Syntactic Analysis and Operator Precedence

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A new method for determining linear precedence functions for precedence grammars

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Some properties of precedence languages

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The storage requirement in precedence parsing

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A improvement to Martin's algorithm for computation of linear precedence functions

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Abstract

A modified version of Bell's Boolean matrix method for the computation of linear precedence functions associated with a conflict-free matrix of precedence relations is given. This algorithm not only detects when the precedence functions do not exist, but also provides an indication of why they do not exist, so that corrective action can be taken if possible. Necessary and sufficient conditions for the existence of precedence functions are given. The use of Boolean matrices to prove the existence of precedence functions associated with classes of conflict-free grammars is illustrated through an example.