Size Of Grammar Research Articles

CORRELATION AMONG GRAMMAR MASTERY AND VOCABULARY SIZE TOWARD TRANSLATION ABILITY ON REPORT TEXT

The crucial problem of translating Indonesia to English language are the students’ lack of knowledge and mother tongue (source language) that two of them are grammar and vocabulary. The researcher focused to measure the correlation among grammar mastery and vocabulary size toward translation ability on report text at seventh semester students in State Islamic Institute of Palangka Raya that use quantitative method with a correlational design. The researcher’s instruments were three test which were grammar mastery, vocabulary size, and translation test that were tested to the 32 students’ translation class in academic year 2017/2018. The numerical data were analyzed by Pearson Product Moment that showed that: (1) the most students got “fail” (43.75%) grammar mastery, (2) the most students got “excellent” (46.875%) vocabulary size, (3) the most students got “enough” (87.5%) translation ability. The significant correlation among three variables were proved by correlation coefficient 0.604 (strong category), Fchange > Ftable = 8.349 > 3.33, and the contribution of grammar mastery and vocabulary size delivered 36.5%. Thus, it sums that students’ grammar mastery and vocabulary size correlate with the quality of students’ translation ability on report text at seventh semester students in academic year 2017/2018. Keywords: Grammar Mastery, Vocabulary, Translation

Balancing Straight-line Programs

We show that a context-free grammar of size that produces a single string of length (such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for of size , whose unique derivation tree has depth . This solves an open problem in the area of grammar-based compression, improves many results in this area, and greatly simplifies many existing constructions. Similar results are shown for two formalisms for grammar-based tree compression: top dags and forest straight-line programs. These balancing results can be all deduced from a single meta-theorem stating that the depth of an algebraic circuit over an algebra with a certain finite base property can be reduced to with the cost of a constant multiplicative size increase. Here, refers to the size of the unfolding (or unravelling) of the circuit. In particular, this results applies to standard arithmetic circuits over (noncommutative) semirings.

Approximation Ratios of RePair, LongestMatch and Greedy on Unary Strings

A grammar-based compressor is an algorithm that receives a word and outputs a context-free grammar that only produces this word. The approximation ratio for a single input word is the size of the grammar produced for this word divided by the size of a smallest grammar for this word. The worst-case approximation ratio of a grammar-based compressor for a given word length is the largest approximation ratio over all input words of that length. In this work, we study the worst-case approximation ratio of the algorithms Greedy, RePair and LongestMatch on unary strings, i.e., strings that only make use of a single symbol. Our main contribution is to show the improved upper bound of O((logn)8·(loglogn)3) for the worst-case approximation ratio of Greedy. In addition, we also show the lower bound of 1.34847194⋯ for the worst-case approximation ratio of Greedy, and that RePair and LongestMatch have a worst-case approximation ratio of log2(3).

Improved descriptional complexity results on generalized forbidding grammars

In formal language theory, if a grammar consists of rules of the type ( r , F r ) , where r is a context-free rule and F r is an associated finite set of strings called the forbidding set, such that r can be applied to a string only if none of the strings in F r is present in the string, then the grammar is said to be a generalized forbidding (GF) grammar. There are four main parameters that describe the size of a GF grammar, namely, (1) d , the maximum length of strings in the forbidding sets, (2) i , the maximum cardinality of the forbidding sets, (3) n , the number of nonterminals used in the grammar, and (4) c , the number of rules with nonempty forbidding set. The family of languages described by a GF grammar of size (at most) ( d , i , n , c ) is denoted by GF ( d , i , n , c ) . We study for what sizes of GF grammars one can obtain the computational power of Turing machines. We specifically show this result for sizes (2, 6, 8, 6), (2, 5, 9, 7), (2, 4, 7, 8) and (2, 3, 20, 18).

Non-erasing Chomsky-Schützenberger theorem with grammar-independent alphabet

The famous theorem by Chomsky and Schützenberger (CST) says that every context-free language L over an alphabet Σ is representable as h(D∩R), where D is a Dyck language over a set Ω of brackets, R is a local language and h is an alphabetic homomorphism that erases unboundedly many symbols. Berstel found that the number of erasures can be linearly limited if the grammar is in Greibach normal form; Berstel and Boasson (and later, independently, Okhotin) proved a non-erasing variant of CST for grammars in Double Greibach Normal Form. In all these CST statements, however, the size of the Dyck alphabet Ω depends on the grammar size for L. In the Stanley variant of the CST, |Ω| only depends on |Σ| and not on the grammar, but the homomorphism erases many more symbols than in the other versions of CST; also, the regular language R is strictly locally testable but not local. We prove a new version of CST which combines both features of being non-erasing and of using a grammar-independent alphabet. In our construction, |Ω| is polynomial in |Σ|, namely O(|Σ|46), and the regular language R is strictly locally testable. Using a recent generalization of Medvedev's homomorphic characterization of regular languages, we prove that the degree in the polynomial dependence of |Ω| on |Σ| may be reduced to just 2 in the case of linear grammars in Double Greibach Normal Form.

Features of calculating the information entropy of the text in case of attacking the linguistic stegosystem by semantic compression

The article deals with the improvement of well-known methods for calculating the entropy of the text, and the description of the information entropy of the text calculating peculiarities in case of the semantic compression attack on the linguistic stegosystem, implemented in the cognominal program complex. The problem of determining the natural language text entropy in the context of further discursive analysis and semantic redundancy removal is formalized. Additional parameters that contribute to determining the semantic entropy of meaningful and artificially generated text for a semantic compression attack on the linguistic stegosystem, the container of which is textual information of natural (English) language are entered. The entropy variety for different language styles is substantiated and its changing according to the style is explained due to the need of adding specialized terminology dictionaries to the general terminology dictionary. In addition to the calculation features of conditional and unconditional entropy in case of using the software complex for attack the linguistic stegosystem, the dictionary size used in it and the prescribed grammar rules size are given, which are the additional parameters determining the entropy calculation in a particular case. The maximum entropy calculation for meaningless texts and the amount of information of a single word or a grammatical form calculation in case of maximum and real entropy are shown. In addition, the calculation of the semantic compression limit is given and the task of determining the semantic information redundancy is formalized. Thus, it becomes possible to determine the quality of the compression attack, carried out on the basis of the software complex use. The obtained results can be used in further research to improve the means of conducting an attack, which will increase its efficiency by maximally approximating the semantic compression limit.

Hierarchical Back-off Modeling of Hiero Grammar based on Non-parametric Bayesian Model

In hierarchical phrase-based machine translation, a rule table is automatically learned by heuristically extracting synchronous rules from a parallel corpus. As a result, spuriously many rules are extracted which may be composed of various incorrect rules. The larger rule table incurs more run time for decoding and may result in lower translation quality. To resolve the problems, we propose a hierarchical back-off model for Hiero grammar, an instance of a synchronous context free grammar (SCFG), on the basis of the hierarchical Pitman-Yor process. The model can extract a compact rule and phrase table without resorting to any heuristics by hierarchically backing off to smaller phrases under SCFG. Inference is efficiently carried out using two-step synchronous parsing of Xiao et al., (2012) combined with slice sampling. In our experiments, the proposed model achieved higher or at least comparable translation quality against a previous Bayesian model on various language pairs; German/French/Spanish/JapaneseEnglish. When compared against heuristic models, our model achieved comparable translation quality on a full size GermanEnglish language pair in Europarl v7 corpus with significantly smaller grammar size; less than 10% of that for heuristic model.

On translating Lambek grammars with one division into context-free grammars

We describe a method of translating a Lambek grammar with one division into an equivalent context-free grammar whose size is bounded by a polynomial in the size of the original grammar. Earlier constructions by Buszkowski and Pentus lead to exponential growth of the grammar size.

Parallel Algorithms for Unsupervised Tagging

We propose a new method for unsupervised tagging that finds minimal models which are then further improved by Expectation Maximization training. In contrast to previous approaches that rely on manually specified and multi-step heuristics for model minimization, our approach is a simple greedy approximation algorithm DMLC (Distributed-Minimum-Label-Cover) that solves this objective in a single step. We extend the method and show how to efficiently parallelize the algorithm on modern parallel computing platforms while preserving approximation guarantees. The new method easily scales to large data and grammar sizes, overcoming the memory bottleneck in previous approaches. We demonstrate the power of the new algorithm by evaluating on various sequence labeling tasks: Part-of-Speech tagging for multiple languages (including low-resource languages), with complete and incomplete dictionaries, and supertagging, a complex sequence labeling task, where the grammar size alone can grow to millions of entries. Our results show that for all of these settings, our method achieves state-of-the-art scalable performance that yields high quality tagging outputs.

An Online Algorithm for Lightweight Grammar-Based Compression

Grammar-based compression is a well-studied technique to construct a context-free grammar (CFG) deriving a given text uniquely. In this work, we propose an online algorithm for grammar-based compression. Our algorithm guarantees O(log2 n)- approximation ratio for the minimum grammar size, where n is an input size, and it runs in input linear time and output linear space. In addition, we propose a practical encoding, which transforms a restricted CFG into a more compact representation. Experimental results by comparison with standard compressors demonstrate that our algorithm is especially effective for highly repetitive text.

Parameter reduction and automata evaluation for grammar-compressed trees

Trees can be conveniently compressed with linear straight-line context-free tree grammars. Such grammars generalize straight-line context-free string grammars which are widely used in the development of algorithms that execute directly on compressed structures (without prior decompression). It is shown that every linear straight-line context-free tree grammar can be transformed in polynomial time into a monadic (and linear) one. A tree grammar is monadic if each nonterminal uses at most one context parameter. Based on this result, polynomial time algorithms are presented for testing whether a given (i) nondeterministic tree automaton or (ii) nondeterministic tree automaton with sibling-constraints or (iii) nondeterministic tree walking automaton, accepts a tree represented by a linear straight-line context-free tree grammar. It is also shown that if tree grammars are nondeterministic or non-linear, then reducing their numbers of parameters cannot be done without an exponential blow-up in grammar size.

A note on the descriptional complexity of semi-conditional grammars

In formal language theory, if a grammar consists of rules of the type (r,Fr), where r is a context-free rule and Fr is an associated finite set of strings called the forbidding set, such that r can be applied to a string only if none of the strings in Fr is present in the string, then the grammar is said to be a generalized forbidding (GF) grammar. There are four main parameters that describe the size of a GF grammar, namely, (1) d, the maximum length of strings in the forbidding sets, (2) i, the maximum cardinality of the forbidding sets, (3) n, the number of nonterminals used in the grammar, and (4) c, the number of rules with nonempty forbidding set. The family of languages described by a GF grammar of size (at most) (d,i,n,c) is denoted by GF(d,i,n,c). We study for what sizes of GF grammars one can obtain the computational power of Turing machines. We specifically show this result for sizes (2, 6, 8, 6), (2, 5, 9, 7), (2, 4, 7, 8) and (2, 3, 20, 18).

The word problem for visibly pushdown languages described by grammars

Visibly pushdown languages are an interesting subclass of deterministic context-free languages that can model nonregular properties of interest in program analysis. Such class properly contains typical classes of parenthesized languages such as "parenthesis", "bracketed", "balanced" and "input-driven" languages. It is closed under boolean operations and has decidable decision problems such as emptiness, inclusion and universality. We study the membership problem for visibly pushdown languages, and show that it can be solved in time linear in both the size of the input grammar and the length of the input word. The algorithm relies on a reduction to the reachability problem for game graphs. We also discuss the time complexity of the membership problem for the class of balanced languages which is the largest among those cited above. Besides the intrinsic theoretical interest, we further motivate our main result showing an application to the validation of XML documents against Schema and Document Type Definitions (DTDs).

The Smallest Grammar Problem

This paper addresses the smallest grammar problem: What is the smallest context-free grammar that generates exactly one given string /spl sigma/? This is a natural question about a fundamental object connected to many fields such as data compression, Kolmogorov complexity, pattern identification, and addition chains. Due to the problem's inherent complexity, our objective is to find an approximation algorithm which finds a small grammar for the input string. We focus attention on the approximation ratio of the algorithm (and implicitly, the worst case behavior) to establish provable performance guarantees and to address shortcomings in the classical measure of redundancy in the literature. Our first results are concern the hardness of approximating the smallest grammar problem. Most notably, we show that every efficient algorithm for the smallest grammar problem has approximation ratio at least 8569/8568 unless P=NP. We then bound approximation ratios for several of the best known grammar-based compression algorithms, including LZ78, B ISECTION, SEQUENTIAL, LONGEST MATCH, GREEDY, and RE-PAIR. Among these, the best upper bound we show is O(n/sup 1/2/). We finish by presenting two novel algorithms with exponentially better ratios of O(log/sup 3/n) and O(log(n/m/sup */)), where m/sup */ is the size of the smallest grammar for that input. The latter algorithm highlights a connection between grammar-based compression and LZ77.

Computing a Context-Free Grammar-Generating Series

The parallel complexity of computing context-free grammar generating series is investigated. It is known that this problem is in DIV, but in terms of nσ rather than n, where n is the index of the desired coefficient and σ is the grammar size. A new method is presented which is in DIV in terms of 22O(σ)·n. Evidence is provided that any direct application of elimination theory to this problem leads to a space and time resource factor that is nearly exponential in grammar size.

Restricted representation of phrase structure grammar for building a tree annotated corpus of Korean

In this paper, we introduce a method to represent phrase structure grammars for building a large annotated corpus of Korean syntactic trees. Korean is different from English in word order and word compositions. As a result of our study, it turned out that the differences are significant enough to induce meaningful changes in the tree annotation scheme for Korean with respect to the schemes for English. A tree annotation scheme defines the grammar formalism to be assumed, categories to be used, and rules to determine correct parses for unsettled issues in parse construction. Korean is partially free in word order and the essential components such as subjects and objects of a sentence can be omitted with greater freedom than in English. We propose a restricted representation of phrase structure grammar to handle the characteristics of Korean more efficiently. The proposed representation is shown by means of an extensive experiment to gain improvements in parsing time as well as grammar size. We also describe the system named Teb that is a software environment set up with a goal to build a tree annotated corpus of Korean containing more than one million units.

Characteristic Sets for Polynomial Grammatical Inference

When concerned about efficient grammatical inference two issues are relevant: first one is to determine quality of result, and second is to try to use polynomial time and space. A typical idea to deal with first point is to say that an algorithm performs well if it infers {\it the limit} correct language. The second point has led to debate about how to define polynomial time: main definitions of polynomial inference have been proposed by Pitt and Angluin. We return in this paper to a definition proposed by Gold that requires a characteristic set of strings to exist for each grammar, and this set to be polynomial in size of grammar or automaton that is to be learned, where size of sample is sum of lengths of all strings it includes. The learning algorithm must also infer correctly as soon as characteristic set is included in data. We first show that this definition corresponds to a notion of teachability as defined by Goldman and Mathias. By adapting their teacher/learner model to grammatical inference we prove that languages given by context-free grammars, simple deterministic grammars, linear grammars and nondeterministic finite automata are not identifiable in limit from polynomial time and data.

Best parse parsing with Earley's and Inside algorithms on probabilistic RTN

AbstractInside parsing is a best parse parsing method based on the Inside algorithm that is often used in estimating probabilistic parameters of stochastic context free grammars. It gives a best parse in O(N3G3) time where N is the input size and G is the grammar size. Earley algorithm can be made to return best parses with the same complexity in N.By way of experiments, we show that Inside parsing can be more efficient than Earley parsing with sufficiently large grammar and sufficiently short input sentences. For instance, Inside parsing is better with sentences of 16 or less words for a grammar containing 429 states. In practice, parsing can be made efficient by employing the two methods selectively.The redundancy of Inside algorithm can be reduced by the topdown filtering using the chart produced by Earley algorithm, which is useful in training the probabilistic parameters of a grammar. Extensive experiments on Penn Tree corpus show that the efficiency of Inside computation can be improved by up to 55%.

Efficient parallel recognition of context-free languages

This paper presents an efficient parallel approach for recognition of context-free languages. The algorithm takes O(log n) time of computations on a fixed configuration of processors array with reconfigurable bus system. The number of processors required is O( n 3). Processor architecture consists of multibus and multiple internal switches in the processors. A specific arrangement of processors is required. Achievements in terms of time and processors requirement have been further supplemented with the elimination of dependence of processor complexity on the size of grammar.

A context-free language decision problem

Let k, lϵ N and L ⊆ { a, b}∗ be a context-free language and L k, l be the set of words w such that k| w| a - l| w| b = 0 where |w| a and |w| b are the numbers of occurrences of a and b in w, respectively. We give an EXPTIME (in grammar size) algorithm to decide whether or not (1) L∩ L k, l = ø, (2) L ⊆ L k, l, and if L is unambiguous, (3) L = L k, l .