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10
Recognition Of Linear ContextFree Rewriting Systems
, 1992
"... has been introduced as a generalization of a class of grammar formalisms known as mildly contextsensitive. The recognition problem for linear contextfree rewriting languages is studied at length here, presenting evidence that, even in some restricted cases, it cannot be solved efficiently. This en ..."
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Cited by 20 (7 self)
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has been introduced as a generalization of a class of grammar formalisms known as mildly contextsensitive. The recognition problem for linear contextfree rewriting languages is studied at length here, presenting evidence that, even in some restricted cases, it cannot be solved efficiently. This entails the existence of a gap between, for example, tree adjoining languages and the subclass of linear contextfree rewriting languages that generalizes the former class; such a gap is attributed to "crossing configurations". A few other interesting consequences of the main result are discussed, that concern the recognition problem for linear contextfree rewriting languages.
Chinese NumberNames, Tree Adjoining Languages, and Mild ContextSensitivity
 COMPUTATIONAL LINGUISTICS
, 1991
"... ... this paper that the numbername system of Chinese is generated neither by this formalism nor by any other equivalent or weaker ones, suggesting that such a task might require the use of the more powerful Indexed Grammar formalism. Given that our formal results apply only to a proper subset of Ch ..."
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Cited by 14 (0 self)
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... this paper that the numbername system of Chinese is generated neither by this formalism nor by any other equivalent or weaker ones, suggesting that such a task might require the use of the more powerful Indexed Grammar formalism. Given that our formal results apply only to a proper subset of Chinese, we extensively discuss the issue of whether they have any implications for the whole of that natural language. We conclude that our results bear directly either on the syntax of Chinese or on the interface between Chinese and the cognitive component responsible for arithmetic reasoning. Consequently, either Tree Adjoining Grammars, as currently defined, fail to generate the class of natural languages in a way that discriminates between linguistically warranted sublanguages, or formalisms with generative power equivalent to Tree Adjoining Grammar cannot serve as a basis for the interface between the human linguistic and mathematical faculties.
Linear ContextFree Rewriting Systems and Deterministic TreeWalking Transducers
, 1992
"... We show that the class of string languages generated by linear contextfree rewriting systems is equal to the class of output languages of deterministic tree walking transducers. From equivalences that have previously been established we know that this class of languages is also equal to the string ..."
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Cited by 12 (0 self)
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We show that the class of string languages generated by linear contextfree rewriting systems is equal to the class of output languages of deterministic tree walking transducers. From equivalences that have previously been established we know that this class of languages is also equal to the string languages generated by contextfree hypergraph grammars, multicomponent treeadjoining grammars, and multiple contextfree grammars and to the class of yields of images of the regular tree languages under finitecopying top down tree transducers.
A TwoDimensional Hierarchy for Parallel Rewriting Systems
, 1994
"... The class of parallel rewriting systems is considered in this work, and the interaction between two complexity measures, that in the literature have been called synchronous parallelism and independent parallelism, is investigated. It is shown that, when the degree of synchronous parallelism is bound ..."
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Cited by 7 (1 self)
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The class of parallel rewriting systems is considered in this work, and the interaction between two complexity measures, that in the literature have been called synchronous parallelism and independent parallelism, is investigated. It is shown that, when the degree of synchronous parallelism is bounded by some constant greater than one, the degree of independent parallelism induces an infinite noncollapsing hierarchy within the family of generated languages. The result is obtained using an original characterization of parallel rewriting systems. Our result combines with other well known properties of synchronous parallelism to reveal the existence of a twodimensional hierarchy for the family of languages generated by so called finite copying parallel We are grateful to Joost Engelfriet and Ryuichi Nakanisi for helpful discussion on topics related to this paper. This research was conducted while the second author was a postdoctoral fellow at the Institute for Research in Cognitive ...
An Efficient Recognition Algorithm for Multiple ContextFree Languages
 In Proceedings of the Fifth Meeting on Mathematics of Language, MOL5
, 1997
"... : Valiant proposed an O(n 2 ) time algorithm which reduces the recognition problem for contextfree languages (CFLs) to the boolean matrices multiplication problem. By this algorithm, the recognition problem for CFLs can be solved in O(maxfn 2 ; M(n)g) time where n is the length of an input stri ..."
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Cited by 4 (0 self)
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: Valiant proposed an O(n 2 ) time algorithm which reduces the recognition problem for contextfree languages (CFLs) to the boolean matrices multiplication problem. By this algorithm, the recognition problem for CFLs can be solved in O(maxfn 2 ; M(n)g) time where n is the length of an input string and M(k) is the time needed for multiplying two k \Theta k boolean matrices. The best known value for M(k) is O(k 2:376 ). Multiple contextfree grammars (MCFGs) were introduced to denote the syntax of natural languages. By the known fastest algorithm, the recognition problem for multiple contextfree languages (MCFLs) can be solved in O(n e ) time where e is a constant which depends only on a given MCFG G, called the degree of G. In this paper, we propose an algorithm which reduces the recognition problem for MCFLs to the boolean matrices multiplication problem. By this algorithm, the recognition problem for MCFLs can be solved in O(n e 0 \Gamma3i 0 +1 \Delta M(n i 0 )) t...
A Polynomial Time Extension of Parallel Multiple ContextFree Grammar
 In LACL 2005
, 2005
"... Abstract. It is already known that parallel multiple contextfree grammar (PMCFG) [1] is an instance of the equivalent formalisms simple literal movement grammar (sLMG) [2,3] and range concatenation grammar (RCG) [4,5]. In this paper we show that by adding the single operation of intersection, borro ..."
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Abstract. It is already known that parallel multiple contextfree grammar (PMCFG) [1] is an instance of the equivalent formalisms simple literal movement grammar (sLMG) [2,3] and range concatenation grammar (RCG) [4,5]. In this paper we show that by adding the single operation of intersection, borrowed from conjunctive grammar [6], PMCFG becomes equivalent to sLMG and RCG. As a corollary we get that PMCFG with intersection describe exactly the class of languages recognizable in polynomial time. The layout of this paper is as follows. The first section contains definitions of the basic grammar formalisms we are interested in. The second section introduces the intersection operation for PMCFG. The third section contains the main result of the paper – that PMCFG extended with the intersection operation is equivalent to simple LMG and RCG. The fourth and last section is a small discussion of the results.
Parallel Multiple ContextFree Grammars, FiniteState Translation Systems, And PolynomialTime Recognizable Subclasses Of LexicalFunctional Grammars
 In 31st Meeting of the Association for Computational Linguistics (ACL'93
, 1993
"... A number of grammatical formalisms were introduced to define the syntax of natural languages. Among them are parallel multiple contextfree grammars (pmcfg's) and lexicalfunctional grammars (lfg's). Pmcfg's and their subclass called multiple contextfree grammars (mcfg's) are natural extensions of ..."
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Cited by 2 (0 self)
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A number of grammatical formalisms were introduced to define the syntax of natural languages. Among them are parallel multiple contextfree grammars (pmcfg's) and lexicalfunctional grammars (lfg's). Pmcfg's and their subclass called multiple contextfree grammars (mcfg's) are natural extensions of cfg's, and pmcfg's are known to be recognizable in polynomial time. Some subclasses of lfg's have been proposed, but they were shown to generate an A/'7complete language. Finite state translation systems (fts') were intro duced as a computational model of transformational grammars. In this paper, three subclasses of lfg's called nclfg's, dclfg's and fclfg's are introduced and the generafive capacities of the above mentioned grammatical formalisms are investigated. First, we show that the generafive capacity of fts' is equal to that of nclfg's. As relations among subclasses of those formalisms, it is shown that the generatire capacities of deterministic fts', dclfg's, and pmcfg's are equal to each other, and the generatire capacity of fclfg's is equal to that of mcfg's. It is also shown that at least one Af7complete language is generated by fts'. Consequently, deterministic fts', dclfg's and fclfg's can be recognized in polynomial time. However, fts' (and nclfg's) cannot, if 7 Af7 .
Genome Informatics 14: 470471 (2003) A Comparative Study on
"... Introduction Much attention has been paid to RNA secondary structure predicition based on contextfree grammar (cfg) since cfg can represent stemloop structure by its derivation tree. Especially, techniques based on CKY (CockeKasamiYounger) algorithm have been widely investigated [1]. Pseudoknot ..."
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Introduction Much attention has been paid to RNA secondary structure predicition based on contextfree grammar (cfg) since cfg can represent stemloop structure by its derivation tree. Especially, techniques based on CKY (CockeKasamiYounger) algorithm have been widely investigated [1]. Pseudoknots play an important role in RNA functions such as ribosomal frameshifting and splicing. A database (PseudoBase) for RNA pseudoknots has been constructed [9]. Unfortunately, it is known that cfg cannot represent pseudoknot structure and a few grammars have been proposed to represent pseudoknots [5, 8]. However, the relation among the expressive (generative) power of these grammars and/or other grammars in formal language theory beyond cfg has not been clarified. The authors have proposed a class of grammars called multiple contextfree grammars [3, 7]. In this research, we identify grammars for RNA secondary structure [5, 8] as subclasses of mcfg and also clarify the inclusion relation among
IRCS Report 9402ATwoDimensional Hierarchy for Parallel Rewriting Systems
, 1994
"... The class of parallel rewriting systems is considered in this work, and the interaction between two complexity measures, that in the literature have been called synchronous parallelism and independent parallelism, is investigated. It is shown that, when the degree of synchronous parallelism is bound ..."
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The class of parallel rewriting systems is considered in this work, and the interaction between two complexity measures, that in the literature have been called synchronous parallelism and independent parallelism, is investigated. It is shown that, when the degree of synchronous parallelism is bounded by some constant greater than one, the degree of independent parallelism induces an in nite noncollapsing hierarchy within the family of generated languages. The result is obtained using an original characterization of parallel rewriting systems. Our result combines with other well known properties of synchronous parallelism to reveal the existence of a twodimensional hierarchy for the family of languages generated by so called nite copying parallel We are grateful to Joost Engelfriet and Ryuichi Nakanisi for helpful discussion on