## An Optimal Tabular Parsing Algorithm (0)

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Venue: | In 32nd Annual Meeting of the Association for Computational Linguistics, Proceedings of the Conference |

Citations: | 17 - 10 self |

### BibTeX

@INPROCEEDINGS{Nederhof_anoptimal,

author = {Mark-jan Nederhof},

title = {An Optimal Tabular Parsing Algorithm},

booktitle = {In 32nd Annual Meeting of the Association for Computational Linguistics, Proceedings of the Conference},

year = {},

pages = {117--124},

publisher = {ACL}

}

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### Abstract

In this paper we relate a number of parsing algorithms which have been developed in very different areas of parsing theory, and which include deterministic algorithms, tabular algorithms, and a parallel algorithm. We show that these algorithms are based on the same underlying ideas.

### Citations

188 |
Ef�cient Parsing for Natural Language
- Tomita
- 1986
(Show Context)
Citation Context ...ch parsing algorithm working on a stack there is a realisation using a parse table, where the parse table allows sharing of computation between different search paths. For example, Tomita's algorithm =-=[18]-=- can be seen as a tabular realisation of nondeterministic LR parsing. At this point we use the term state to indicate the symbols occurring on the stack of the original algorithm, which also occur as ... |

119 | The Structure of Shared Forests in Ambiguous Parsing
- Billot, Lang
- 1989
(Show Context)
Citation Context ...n the table, and in the latter case, sophistication leads to more entries, provided this sophistication is realised by an increase in the number of states. This is corroborated by empirical data from =-=[1, 4]-=-, which deal with tabular LR parsing. As we will explain, CP and ELR parsing are more deterministic than most other parsing algorithms for many grammars, but their tabular realizations can never compu... |

95 | Parser Generation for Interactive Environments
- Rekers
- 1992
(Show Context)
Citation Context ...me subderivation, then computation of that subderivation may be done more than once, which leads to parse forests (compact representations of collections of parse trees) which are not optimally dense =-=[1, 12, 7]-=-. Schabes proposes to tune a parser to a grammar, or in other words, to use a combination of parsing techniques in order to find an optimal parser for a certain grammar. 7 This idea has until now not ... |

49 |
Deterministic left corner parsing
- Rosenkrantz, Lewis
- 1970
(Show Context)
Citation Context ...to E, i.e. by [T --~ T • **F], [E ~ T. T El, or [E ~ T •]. [] LC parsing with k symbols of lookahead can handle deterministically the so called LC(k) grammars. This class of grammars is formalized=-= in [13]-=-. 1 How LC parsing can be improved to handle common su~xes efficiently is discussed in [6]; in this paper we restrict our attention to common prefixes. PLR, ELR, and CP parsing In this section we inve... |

26 | Polynomial time and space shift-reduce parsing of arbitrary context-free grammars
- Schabes
- 1991
(Show Context)
Citation Context ...parsing is presented in [20]. Some useful data structures for practical implementation of tabular and non-tabular PLR, ELR and CP parsing are described in [S], Finding an optimal tabular algorithm In =-=[14]-=- Schabes derives the LC algorithm from LR parsing similar to the way that ELR parsing can be derived from LR parsing. The LC algorithm is obtained by not only splitting up the goto function into goto ... |

23 | Generalized left-corner parsing
- Nederhof
- 1993
(Show Context)
Citation Context ...sed as an alternative to top-down (TD) parsing, which cannot handle left recursion and is generally less efficient. Nondeterministic LC parsing is the foundation of a very efficient parsing algorithm =-=[7]-=-, related to Tomita's algorithm and Earley's algorithm. It has one disadvantage however, which becomes noticeable when the grammar contains many rules whose right-hand sides begin with the same few gr... |

22 | How to cover a grammar
- Leermakers
- 1989
(Show Context)
Citation Context ...le corresponding with one of the items in Q. A consequence of the action in the first case is that upon reduction we need to pop only one state off the stack. Further work in this area is reported in =-=[5]-=-, which treats nondeterministic ELR parsing and therefore does not regard it as an obstacle if a choice between cases a) and b) cannot be uniquely made. We are not concerned with extended context-free... |

18 |
Complete evaluation of Horn Clauses, an automata theoretic approach
- Lang
- 1988
(Show Context)
Citation Context ...ted if (Init, w) F-* (Fin, e), where Fin E Alph is a distinguished stack symbol. LC parsing For the definition of left-corner (LC) recognition [7] we need stack symbols (items) of the form [A --~ a ��=-=� [3], wher-=-e A --~ c~[3 is a rule, and a ¢ e. (Remember that we do not allow epsilon rules.) The informal meaning of an item is "The part before the dot has just been recognized, the first symbol after the... |

17 | A recursive ascent Earley parser - Leermakers - 1992 |

13 |
The computational complexity of GLR parsing
- Johnson
- 1991
(Show Context)
Citation Context ...of states (the items in I Lc) which is linear in the size of the grammar. By contrast, the LR algorithm requires a number of states (the sets of items) which is exponential in the size of the grammar =-=[2]-=-. The differences in the number of states complicates the choice of a tabular algorithm as the one giving optimal behaviour for all grammars. If a grammar is very simple, then a sophisticated algorith... |

10 | An extended theory of head-driven parsing
- Nederhof, Satta
- 1994
(Show Context)
Citation Context ...e closely. Further, we briefly describe how rules with empty right-hand sides complicate the parsing process. The ideas described in this paper can be generalized to head-driven parsing, as argued in =-=[9]-=-. We will take some liberty in describing algorithms from the existing literature, since using the original descriptions would blur the similarities of the algorithms to one another. In particular, we... |

10 |
Parsing extended LR(k) grammars
- Brown
- 1981
(Show Context)
Citation Context ...reduction cannot be realised in this way since the regular expression of which the rhs is composed may describe strings of various lengths, so that it is unknown how many states need to be popped. In =-=[11]-=- this problem is solved by forcing the parser to decide at each call goto(Q, X) whether a) X is one more symbol of an item in Q of which some symbols have already been recognized, or whether b) X is t... |

7 |
A method for transforming grammars into LL(k) form
- Soisalon-Soininen, Ukkonen
- 1979
(Show Context)
Citation Context ...this section we investigate a number of algorithms which exhibit a better treatment of common prefixes. Predictive LR parsing Predictive LR (PLR) parsing with k symbols of lookahead was introduced in =-=[17]-=- as an algorithm which yields efficient parsers for a subset of the LR(k) grammars [16] and a superset of the LC(k) grammars. How deterministic PLR parsing succeeds in handling a larger class of gramm... |

6 |
CIGALE: a tool for interactive grammar construction and expression parsing
- Voisin
- 1986
(Show Context)
Citation Context ...rammar from Example 1. It is clear that a÷a T ais not acorrect string according to this grammar. The CP algorithm may go through the following sequence of configurations: 2An attempt has been made in=-= [19]-=- but this paper does not describe the algorithm in its full generality. 3The original algorithm in [21] applies an optimization concerning unit rules, irrelevant to our discussion. 121 1 2 F] 3 [--*][... |

6 |
A botttom-up adaptation of Earley's parsing algorithm
- Voisin
- 1988
(Show Context)
Citation Context ... C]}. Pseudo ELR parsing can be more easily realised than full ELR parsing, but the correct-prefix property can no longer be guaranteed. Pseudo ELR parsing is the foundation of a tabular algorithm in =-=[20]-=-. Common-prefix parsing One of the more complicated aspects of the ELR algorithm is the treatment of the sets of nonterminals in the left-hand sides of items. A drastically simplified algorithm is the... |

5 |
An empirical comparison of generalized LR tables
- Lankhorst
- 1991
(Show Context)
Citation Context ...n the table, and in the latter case, sophistication leads to more entries, provided this sophistication is realised by an increase in the number of states. This is corroborated by empirical data from =-=[1, 4]-=-, which deal with tabular LR parsing. As we will explain, CP and ELR parsing are more deterministic than most other parsing algorithms for many grammars, but their tabular realizations can never compu... |

4 |
A new, Bottom-up, General Parsing Algorithm
- Voisin, Raoult
- 2000
(Show Context)
Citation Context ...e more complicated aspects of the ELR algorithm is the treatment of the sets of nonterminals in the left-hand sides of items. A drastically simplified algorithm is the basis of a tabular algorithm in =-=[21]-=-. Since in [21] the algorithm itself is not described but only its tabular realisation, 2 we take the liberty of giving this algorithm our own name: common-prefix (CP) parsing, since it treats all rul... |

3 |
A Parallel Bottom-Up Tomita Parser. 1. Konferenz Verarbeitung naturlicher Sprache
- Sikkel, Lankhorst
- 1992
(Show Context)
Citation Context ... a = ai where there is A --* ac~ • pt 3. Add [--* A] to Tj,i for [--+ o~] • Tj,i where there are A ---* a, D --* A6 • pt In the resulting algorithm, no set Tc,j depends on any set Tg,h with g < =-=i. In [15]-=- this fact is used to construct a parallel parser with n processors Po,..., Pn-1, with each Pi processing the sets Ti,j for all j > i. The flow of data is strictly from right to left, i.e. items compu... |

1 |
A multidisciplinary approach to a parsing algorithm
- Nederhof
- 1993
(Show Context)
Citation Context ...processing of all common prefixes. It is hard to imagine a practical parsing technique more deterministic than ELR parsing which also satisfies the previous two properties. In particular, we argue in =-=[8] that refi-=-nement of the LR technique in such a way that the first property above holds whould require an impractically large number of LR states. 7This is reminiscent of the idea of "optimal cover" [5... |

1 |
Generalized LR parsing and attribute evaluation
- Luttighuis, Sikkel
- 1993
(Show Context)
Citation Context ...goto 1 and goto 2 but also splitting up goto~ even further, so that it nondeterministically yields the closure of one single kernel item. (This idea was described earlier in [5], and more recently in =-=[10]-=-.) Schabes then argues that the LC algorithm can be determinized (i.e. made more deterministic) by manipulating the goto functions. One application of this idea is to take a fixed grammar and choose d... |

1 |
Parsing Theory, Vol. H: LR(k) and LL(k
- Sippu, Soisalon-Soininen
- 1990
(Show Context)
Citation Context ...common prefixes. Predictive LR parsing Predictive LR (PLR) parsing with k symbols of lookahead was introduced in [17] as an algorithm which yields efficient parsers for a subset of the LR(k) grammars =-=[16]-=- and a superset of the LC(k) grammars. How deterministic PLR parsing succeeds in handling a larger class of grammars (the PLR(k) grammars) than the LC(k) grammars can be explained by identifying PLR p... |