A TREE-HEIGHT HIERARCHY OF CONTEXT-FREE LANGUAGES

2007 ◽  
Vol 18 (06) ◽  
pp. 1383-1394 ◽  
Author(s):  
KLAUS REINHARDT
Keyword(s):  
Tree Height ◽  
Complexity Measure ◽  
New Method ◽  
Derivation Tree ◽  
Counter Example ◽  
Minimal Height ◽  
Successor Relation ◽  
Context Free ◽  
Arbitrary Tree

We consider the minimal height of a derivation tree as a complexity measure for context-free languages and show that this leads to a strict and dense hierarchy between logarithmic and linear (arbitrary) tree height. In doing so, we improve a result obtained by Gabarro in [7]. Furthermore, we provide a counter-example to disprove a conjecture of Čulik and Maurer in [6] who suggested that all languages with logarithmic tree height would be regular. As a new method, we use counter-representations where the successor relation can be handled as the complement of context-free languages. A similar hierarchy is obtained considering the ambiguity as a complexity measure.

A REGULARITY CONDITION FOR CONTEXT-FREE GRAMMARS

2008 ◽  
Vol 19 (04) ◽  
pp. 845-857
Author(s):  
BEATRICE PALANO
Keyword(s):  
Lower Bound ◽  
Regularity Condition ◽  
Complexity Measure ◽  
Context Free Grammar ◽  
Context Free ◽  
Context Free Grammars

We define a complexity measure on context-free grammars called end. Roughly speaking, for a context-free grammar G, endG(n) measures the distance of variables from the ends of sentential forms along the derivations of words in L(G) of length n. We prove in a constructive way the regularity of L(G)wheneverendG(n)is constant. Yet, we improve on this by showing that ifL(G)is nonregular thenendG(n) = Ω∞( log n). We establish the optimality of such bound. Finally, we show that, in case of unambiguous context-free grammars, the end lower bound for generating nonregular languages turns out to be linear.

scholarly journals A new method of syntactic analysis of context-free languages

2018 ◽  
Author(s):  
O. I. Egorushkin ◽  
I.V . Kolbasina ◽  
N. A. Popov ◽  
A .V. Tsokin
Keyword(s):  
New Method ◽  
Syntactic Analysis ◽  
Context Free

A new method for measuring tree height in tropical rain forest

1994 ◽  
Vol 5 (1) ◽  
pp. 139-140 ◽  
Author(s):  
Jørgen Korning ◽  
Karsten Thomsen
Keyword(s):  
Rain Forest ◽  
Tropical Rain Forest ◽  
Tree Height ◽  
New Method

scholarly journals Semantic Parsing of Ambiguous Input through Paraphrasing and Verification

2015 ◽  
Vol 3 ◽  
pp. 571-584
Author(s):  
Philip Arthur ◽  
Graham Neubig ◽  
Sakriani Sakti ◽  
Tomoki Toda ◽  
Satoshi Nakamura
Keyword(s):  
Natural Language ◽  
Language Model ◽  
Input String ◽  
New Method ◽  
Semantic Parsing ◽  
Search Queries ◽  
Input Sentence ◽  
Meaning Representation ◽  
Context Free ◽  
Do So

We propose a new method for semantic parsing of ambiguous and ungrammatical input, such as search queries. We do so by building on an existing semantic parsing framework that uses synchronous context free grammars (SCFG) to jointly model the input sentence and output meaning representation. We generalize this SCFG framework to allow not one, but multiple outputs. Using this formalism, we construct a grammar that takes an ambiguous input string and jointly maps it into both a meaning representation and a natural language paraphrase that is less ambiguous than the original input. This paraphrase can be used to disambiguate the meaning representation via verification using a language model that calculates the probability of each paraphrase.

GENERATIVE CAPACITY OF SUBREGULARLY TREE CONTROLLED GRAMMARS

2010 ◽  
Vol 21 (05) ◽  
pp. 723-740 ◽  
Author(s):  
JÜRGEN DASSOW ◽  
RALF STIEBE ◽  
BIANCA TRUTHE
Keyword(s):  
Regular Language ◽  
Regular Languages ◽  
Derivation Tree ◽  
Generative Capacity ◽  
The Family ◽  
Context Free ◽  
Context Free Grammars

Tree controlled grammars are context-free grammars where the associated language only contains those terminal words which have a derivation where the word of any level of the corresponding derivation tree belongs to a given regular language. We present some results on the power of such grammars where we restrict the regular languages to some known subclasses of the family of regular languages.

Méthode de classification des pins gris et détermination de leur susceptibilité aux insectes secondaires

1971 ◽  
Vol 47 (4) ◽  
pp. 201-204
Author(s):  
Paul Benoit
Keyword(s):  
Critical Point ◽  
Tree Height ◽  
Jack Pine ◽  
Usual Method ◽  
New Method ◽  
Total Height ◽  
Principal Objective

The usual method of estimating the defoliation of jack pine does not permit evaluation with any precision of the critical point at which the tree becomes susceptible to the invasion by secondary insects. The method here described does meet that principal objective. Moreover, it eliminates the differences in observations made by different persons and at different times. The new method uses two variables: 1/ the ratio, in percent, between the total height of the tree and the height of the crown, and 2/ the residual foliage to which a uniform mathematical value is given according to the ratio crown/tree height. The classification of the trees is obtained with the following equation:[Formula: see text]That equation, seemingly complex, is remarquably easy to apply in such forest investigation. Calculations have shown that the critical point of susceptibility of jack pine to secondary insects is when the tree reaches down to about Class 35. The application of that method in forestry is proposed.

Context-free spheres: A new method for rapid CPK image generation

1988 ◽  
Vol 6 (3) ◽  
pp. 149-154 ◽  
Author(s):  
Thomas C. Palmer ◽  
Frederick H. Hausheer
Keyword(s):  
New Method ◽  
Image Generation ◽  
Context Free

scholarly journals Intelligent Belief State Sampling for Conformant Planning

2017 ◽  
Author(s):  
Alban Grastien ◽  
Enrico Scala
Keyword(s):  
Necessary Conditions ◽  
Small Sample ◽  
Belief State ◽  
New Method ◽  
Planning Problem ◽  
Conformant Planning ◽  
Counter Example ◽  
Initial Belief ◽  
Candidate Solution ◽  
Deterministic Setting

We propose a new method for conformant planning based on two ideas. First given a small sample of the initial belief state we reduce conformant planning for this sample to a classical planning problem, giving us a candidate solution. Second we exploit regression as a way to compactly represent necessary conditions for such a solution to be valid for the non-deterministic setting. If necessary, we use the resulting formula to extract a counter-example to populate our next sampling. Our experiments show that this approach is competitive on a class of problems that are hard for traditional planners, and also returns generally shorter plans. We are also able to demonstrate unsatisfiability of some problems.

On Grammatical Inference and Derivational Complexity of Context-Free Grammars

1992 ◽  
Vol 17 (4) ◽  
pp. 363-368
Author(s):  
Erkki Mäkinen
Keyword(s):  
Complexity Measure ◽  
Grammatical Inference ◽  
Context Free ◽  
Context Free Grammars

Derivational complexity related to leftmost derivations of context-free grammars is studied by defining a new complexity measure based on characteristic samples of left Szilard languages.

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