The string generating power of context-free hypergraph grammars
Journal of Computer and System Sciences
On multiple context-free grammars
Theoretical Computer Science
Relating attribute grammars and lexical-functional grammars
Information Sciences: an International Journal
Petri Net Theory and the Modeling of Systems
Petri Net Theory and the Modeling of Systems
Context-free grammars on trees
STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
A study of tree adjoining grammars
A study of tree adjoining grammars
Characterizing mildly context-sensitive grammar formalisms
Characterizing mildly context-sensitive grammar formalisms
Characterizing structural descriptions produced by various grammatical formalisms
ACL '87 Proceedings of the 25th annual meeting on Association for Computational Linguistics
Linear context-free rewriting systems and deterministic tree-walking transducers
ACL '92 Proceedings of the 30th annual meeting on Association for Computational Linguistics
Incremental parsing with parallel multiple context-free grammars
EACL '09 Proceedings of the 12th Conference of the European Chapter of the Association for Computational Linguistics
PGF: A Portable Run-time Format for Type-theoretical Grammars
Journal of Logic, Language and Information
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A number of grammatical formalisms were introduced to define the syntax of natural languages. Among them are parallel multiple context-free grammars (pmcfg's) and lexical-functional grammars (lfg's). Pmcfg's and their subclass called multiple context-free grammars (mcfg's) are natural extensions of cfg's, and pmcfg's are known to be recognizable in polynomial time. Some subclasses of lfg's have been proposed, but they were shown to generate an NP-complete language. Finite state translation systems (fts') were introduced as a computational model of transformational grammars. In this paper, three subclasses of lfg's called nc-lfg's, dc-lfg's and fc-lfg's are introduced and the generative capacities of the above mentioned grammatical formalisms are investigated. First, we show that the generative capacity of fts' is equal to that of nc-lfg's. As relations among subclasses of those formalisms, it is shown that the generative capacities of deterministic fts', dc-lfg's, and pmcfg's are equal to each other, and the generative capacity of fc-lfg's is equal to that of mcfg's. It is also shown that at least one NP-complete language is generated by fts'. Consequently, deterministic fts', dc-lfg's and fc-lfg's can be recognized in polynomial time. However, fts' (and nc-lfg's) cannot, if P ≠ NP.