K. Vijay-Shanker and David J. Weir. 1990. Parsing constrained grammar formalisms. Computational Linguistics, 19(4), 591--636.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the VPP. The Earley type parser developed for TAGs [Schabes and Joshi1988] is bottom up and uses top down prediction. It maintains the VPP at a cost to its worst case complexity O(n 9 ) time in the worst case. Other parsers for TAGs have been proposed [Lang1988, Lavelli and Satta1991, Vijay Shanker and Weir1990] Although they achieve O(n 6 ) worst case time complexity, none of these algorithms satisfies the VPP. To our knowledge, Schabes and Joshi s parser (1988) is the only known polynomial time parser for TAG which satisfies the valid prefix property. It is still an open problem whether a better ....

....result follows from Thatcher [Thatcher1971] who defines frontier to root finite state tree automata. 29 The parser is also reported in Vijay Shanker [Vijay Shanker1987] Joshi and Schabes The second observation is in the context of deterministic left to right parsing of TAGs [Schabes and Vijay Shanker1990] where it was for the first time explicitly noticed that VPP is problematic to obtain. The authors were not able to define a bottom up deterministic machine that satisfies the valid prefix property and which recognizes exactly tree adjoining languages when used non deterministically. Instead, they ....

K. Vijay-Shanker and David J. Weir. 1990. Parsing constrained grammar formalisms. Computational Linguistics, 19(4), 591--636.

.... weakly equivalent to Head Grammars (HG) Linear Index Grammars (LIG) and Tree Adjoining Grammars (TAG) known as mildly context sensitive grammars [Vijay Shanker and Weir, 1994] CCG Std is also shown to be polynomially parsable [Vijay Shanker and Weir, 1990, Vijay Shanker and Weir, 1991, Vijay Shanker and Weir, 1993]. 4 But, unrestricted use of variables can destroy these properties. For example, Hoffman [1993] showed that a grammar involving categories of the form (Tnx) Tny) can generate a language a n b n c n d n e n , which is no longer equivalent to LIGs. The use of variables in the ....

K. Vijay-Shanker and David J. Weir. 1993. Parsing Constrained Grammar Formalisms. Computational Linguistics, 19(4).

....with the lexical items in the input sentence, and in the second stage the sentence is parsed with respect to this set. Schabes and Joshi (1989) discuss in more detail the relevance of lexicalization to parsing. More recently, deterministic parsing of TAGs has been investigated by Schabes and Vijay Shanker (1990). 1.5 Organization of the Grammar The grammar consists of a morphological lexicon, which lists the possible morphological variations for a word, and a syntactic lexicon, which is the domain of structural choice, subcategorization and selectional information. Currently, we are including only ....

K. Vijay-Shanker and David J. Weir. 1990. Parsing constrained grammar formalisms. In preparation.

....We take lexical approach to avoid the procedural aspects associated with dynamic type raising. Polymorphic forms also have advantage of underspecification which avoids unnecessary proliferation of categories. be polynomially parsable [Vijay Shanker and Weir, 1990, Vijay Shanker and Weir, 1991, Vijay Shanker and Weir, 1993]. 5 A few extension of CCGs, Multiset CCGs, are also shown to be polynomially parsable [Hoffman, 1995] 6 But, use of variables can change the situation. For example, Hoffman [1993] showed that a grammar involving categories of the form (Tnx) Tny) can generate a language a n b n c n d ....

....on the syntax. Note that equivalence depends on 18 Each instance of GTRC must be assigned a new variable when the GTRC is instantiated at a particular string position in order to avoid unintended variable binding. 19 Our definition does not include the empty string in the domain of f as in [Vijay Shanker and Weir, 1993] but unlike [Vijay Shanker and Weir, 1994] 20 Due to the introduction of GTRC, the rule instances may involve variables even at the first argument of the functor category and at the input category. 21 Shieber [1986] contains a detailed discussion of subsumption. the semantic representation ....

K. Vijay-Shanker and David J. Weir. 1993. Parsing Constrained Grammar Formalisms. Computational Linguistics, 19(4).

.... Grammars (HG) Linear Index Grammars (LIG) and Tree Adjoining Grammars (TAG) collectively called mildly context sensitive grammars [Joshi et al. 1991, Vijay Shanker and Weir, 1994] CCG Std is also shown to be polynomially parsable [Vijay Shanker and Weir, 1990, Vijay Shanker and Weir, 1991, Vijay Shanker and Weir, 1993]. But, use of variables can destroy these properties. For example, Hoffman [1993] 1 The category S= SnNP) is associated with a higher order semantics lP:Pa where a is the semantics of NP. Composition of lP:Pa and lQ:Qb (left to right) is lQ:Qba. In a sense, this semantics anticipates that of a ....

....of the category. In addition, although the GTRC 17 Each instance of GTRC must be assigned a new variable when the GTRC is instantiated at a particular string position in order to avoid unintended variable binding. 18 Our definition does not include the empty string in the domain of f as in [Vijay Shanker and Weir, 1993] but unlike [Vijay Shanker and Weir, 1994] 19 Due to the introduction of GTRC, the rule instances may involve variables even at the first argument of the functor category and at the input category. 20 This finiteness corresponds to the instantiation of the input categories. The functor ....

K. Vijay-Shanker and David J. Weir. 1993. Parsing Constrained Grammar Formalisms. Computational Linguistics, 19(4).

....F may be seen as a grammar generating only the parsed sentence, with precisely the same parse trees as the original grammar G of the language, up to a renaming of the non terminals. This understanding, introduced in [Lan 74, BilL 89] was extended to other formalisms by Vijay Shanker and Weir [VijW 90]. As a corollary, all parses can be trivially enumerated from the shared forest in exactly the same way one generates all possible sentences of a langage in the formalism under consideration. It was also shown in [Lan 91] that, more generally, it is possible to build a grammar F that generates ....

Vijay-Shankar, K.; and Weir, D.J. 1990 Parsing Constrained Grammar Formalisms. Personal Communication.

....are stored in array entries. The extension over cfg involves the use of a four dimensional array to encode pairs of substrings of the input string. Given the close relationship between hg and tag established in this paper, it was possible to adapt this algorithm to give a tag parser [22] In [23, 24] a lig CKY style parsing algorithm is given. This algorithm extends the cfg case in that encodings of stacks are stored in the array entries. Given the close relationship between lig, ccg and tag described in this paper, it was possible to adapt this algorithm to give ccg and tag parsers [24] ....

....[23, 24] a lig CKY style parsing algorithm is given. This algorithm extends the cfg case in that encodings of stacks are stored in the array entries. Given the close relationship between lig, ccg and tag described in this paper, it was possible to adapt this algorithm to give ccg and tag parsers [24]. Obviously, as a result of the weak equivalence of ccg, hg, lig and tag any result shown for one formalism applies to the other three. Such results include the definition of a string automaton for this class [22] various closure and decidability properties including the result that it forms a ....

K. Vijay-Shanker and D. J. Weir. Parsing constrained grammar formalisms. Comput. Ling., in press.

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