Parsing Mildly Context-Sensitive Languages

Miha Drole (2011) Parsing Mildly Context-Sensitive Languages. EngD thesis.

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Abstract

In this thesis we discuss four formalisms, that lie between context-free grammars (KNG) and context-sensitive grammars (KOG) in the Chomsky hierarchy, namely tree-adjoining grammars (TAG), head grammars (HG), linear indexed grammars (LIG) and combinatory categorial grammars (KKG). For each formalism discussed we include its description with basic definitions and descriptions of proofs of their placement in the hierarchy. For TAG we give the proof that they can generate all the languages that can be generated by KNG and some that cannot. In chapters dedicated to HG, LIG and KKG we describe proofs for their mutual equivalence and equivalence with TAG using the transitivity of equivalence. Each proof of equivalence consists of two steps. For the chosen formalism we first give the proof that the set of languages generated by it can also be generated by another formalism in the group. In the second part of the proof we provide a description of the proof that the chosen formalism can generate all the languages that another formalism in the group can generate. For TAG, LIG and KKG we also present recognition algorithms. All algorithms presented have O(n^6) time complexity. In case of KKG we also present an algorithm that builds a description of all parse trees for an input.

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