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Synchronous context-free grammars and optimal linear parsing strategies. (English) Zbl 1320.68106

Summary: Synchronous Context-Free Grammars (SCFGs), also known as syntax-directed translation schemata, are unlike context-free grammars in that they do not have a binary normal form. In general, parsing with SCFGs takes space and time polynomial in the length of the input strings, but with the degree of the polynomial depending on the permutations of the SCFG rules. We consider linear parsing strategies, which add one nonterminal at a time. We show that for a given input permutation, the problems of finding the linear parsing strategy with the minimum space and time complexity are both NP-hard.

MSC:

68Q42 Grammars and rewriting systems
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
68Q45 Formal languages and automata

References:

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