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24
Parsing Expression Grammars: A RecognitionBased Syntactic Foundation
 Symposium on Principles of Programming Languages
, 2004
"... For decades we have been using Chomsky's generative system of grammars, particularly contextfree grammars (CFGs) and regular expressions (REs), to express the syntax of programming languages and protocols. The power of generative grammars to express ambiguity is crucial to their original purpose of ..."
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Cited by 77 (1 self)
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For decades we have been using Chomsky's generative system of grammars, particularly contextfree grammars (CFGs) and regular expressions (REs), to express the syntax of programming languages and protocols. The power of generative grammars to express ambiguity is crucial to their original purpose of modelling natural languages, but this very power makes it unnecessarily difficult both to express and to parse machineoriented languages using CFGs. Parsing Expression Grammars (PEGs) provide an alternative, recognitionbased formal foundation for describing machineoriented syntax, which solves the ambiguity problem by not introducing ambiguity in the first place. Where CFGs express nondeterministic choice between alternatives, PEGs instead use prioritized choice. PEGs address frequently felt expressiveness limitations of CFGs and REs, simplifying syntax definitions and making it unnecessary to separate their lexical and hierarchical components. A lineartime parser can be built for any PEG, avoiding both the complexity and fickleness of LR parsers and the inefficiency of generalized CFG parsing. While PEGs provide a rich set of operators for constructing grammars, they are reducible to two minimal recognition schemas developed around 1970, TS/TDPL and gTS/GTDPL, which are here proven equivalent in effective recognition power.
The language of RNA: A formal grammar that includes pseudoknots
 Bioinformatics
"... Motivation: In a previous paper, we presented a polynomial time dynamic programming algorithm for predicting optimal RNA secondary structure including pseudoknots. However a formal grammatical representation for RNA secondary structure with pseudoknots was still lacking. Results: Here we show a one ..."
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Cited by 60 (1 self)
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Motivation: In a previous paper, we presented a polynomial time dynamic programming algorithm for predicting optimal RNA secondary structure including pseudoknots. However a formal grammatical representation for RNA secondary structure with pseudoknots was still lacking. Results: Here we show a onetoone correspondence between that algorithm and a formal transformational grammar. This grammar class encompasses the contextfree grammars and goes beyond to generate pseudoknotted structures. The pseudoknot grammar avoids the use of general contextsensitive rules by introducing a small number of auxiliary symbols used to reorder the strings generated by an otherwise contextfree grammar. This formal representation of the residue correlations in RNA structure is important because it means we can build full probabilistic models of RNA secondary structure, including pseudoknots, and use them to optimally parse sequences in polynomial time. Contact: eddy@genetics.wustl.edu 1 ...
Parsing Some Constrained Grammar Formalisms
 Computational Linguistics
, 1994
"... this paper we present a scheme to extend a recognition algorithm for ContextFree Grammars (CFG) that can be used to derive polynomialtime recognition algorithms for a set of formalisms that generate a superset of languages generated by CFG. We describe the scheme by developing a CockeKasamiYoung ..."
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Cited by 56 (6 self)
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this paper we present a scheme to extend a recognition algorithm for ContextFree Grammars (CFG) that can be used to derive polynomialtime recognition algorithms for a set of formalisms that generate a superset of languages generated by CFG. We describe the scheme by developing a CockeKasamiYounger (CKY)like pure bottomup recognition algorithm for Linear Indexed Grammars and show how it can be adapted to give algorithms for Tree Adjoining Grammars and Combinatory Categorial Grammars. This is the only polynomialtime recognition algorithm for Combinatory Categorial Grammars that we are aware of
On the rational subset problem for groups
 Journal of Algebra
"... We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensi ..."
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Cited by 13 (9 self)
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We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensions with finite associated subgroups. We provide a simple proof of a result of Grunschlag showing that the decidability of this problem is a virtual property. We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for Gautomaton subsets of M. It follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership. © 2006 Elsevier Inc. All rights reserved.
Observations on Strict Derivational Minimalism
 ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
, 2001
"... Deviating from the denition originally presented in [12], Stabler [13] introduced inspired by some recent proposals in terms of a minimalist approach to transformational syntaxa (revised) type of a minimalist grammar (MG) as well as a certain type of a strict minimalist grammar (SMG). These two type ..."
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Cited by 11 (5 self)
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Deviating from the denition originally presented in [12], Stabler [13] introduced inspired by some recent proposals in terms of a minimalist approach to transformational syntaxa (revised) type of a minimalist grammar (MG) as well as a certain type of a strict minimalist grammar (SMG). These two types can be shown to determine the same class of derivable string languages.
Model Theoretic Syntax
 The Glot International State of the Article Book 1, Studies in Generative Grammar 48, Mouton de Gruyter
, 1998
"... this article appeared in Glot, the main issue agitating researchers in model theoretic syntax was the problem of the contextfree barrier. We have seen that the hierarchy of logics collapses, when applied to trees, at the border of the tree languages strongly generated by context free (string) gramm ..."
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Cited by 9 (1 self)
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this article appeared in Glot, the main issue agitating researchers in model theoretic syntax was the problem of the contextfree barrier. We have seen that the hierarchy of logics collapses, when applied to trees, at the border of the tree languages strongly generated by context free (string) grammars, in the sense that distinctions between the different tree logics reduce to apparently superficial distinctions in how much memory allocation is hidden in the logic. The problem which researchers set themselves was not just breaking the context free barrier but remaining decidable in the process. This is a very difficult problem, and it must be admitted right off that it is somewhat artificial in that there is no a priori reason to suppose that natural languages can be described in a decidable logic. The arguments on either side are something like the following. First, the rather slight increases in computational complexity required to get the "mildly context sensitive" languages do suggest that this might be possible. The hunch here would be that the qualities that characterize the mildly context sensitive languages (polynomial parsability, constant growth property) as being like the contextfree languages are going to turn out to be reflections of decidability. The problems must not be underestimated, however! It is well known that the monadic second order logic of trees is one of the most powerful decidable logics known. It seems unlikely that any primitive relations can be added to the repertoire of tree description primitives that we have already seen, without making the logic undecidable. Many attempts have been made within logic and all have failed. So it is equally tempting to conjecture that the contextfree boundary coincides in some deep sense with the bounda...
Recursive Adaptable Grammars
 Master’s Thesis, Worchester Polytechnic Institute
, 1998
"... ContextFree Grammars (CFGs) are a simple and intuitively appealing formalism for the description of programming languages, but lack the computational power to describe many common language features. Over the past three decades, numerous extensions of the CFG model have been developed. Most of these ..."
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Cited by 9 (2 self)
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ContextFree Grammars (CFGs) are a simple and intuitively appealing formalism for the description of programming languages, but lack the computational power to describe many common language features. Over the past three decades, numerous extensions of the CFG model have been developed. Most of these extensions retain a CFG kernel, and augment it with a distinct facility with greater computational power. However, in all the most powerful CFG extensions, the clarity of the CFG kernel is undermined by the opacity of the more powerful extending facility. An intuitively appealing strategy for CFG extension is grammar adaptability, the principle that declarations in a program effectively modify the contextfree grammar of the programming language. An adaptable grammar is equipped with some formal means for modifying its own CFG kernel. Most previous adaptable grammar formalisms have, unfortunately, failed to realize the potential clarity of this concept. In this thesis, a representative samp...
A Formal Model for ContextFree Languages Augmented with Reduplication
 Computational Linguistics
, 1989
"... Family of Languages), which in some circles invests the class with a certain respectability. This is because such closure properties determine much of the character of wellknown language classes, such as contextfree languages and finitestate languages. (A Full AFL is any class of languages that c ..."
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Cited by 5 (0 self)
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Family of Languages), which in some circles invests the class with a certain respectability. This is because such closure properties determine much of the character of wellknown language classes, such as contextfree languages and finitestate languages. (A Full AFL is any class of languages that contains at least one nonempty language and that is closed under union, Afree concatenation of two lan guages, homomorphism, inverse homomorphism, and intersection with any finitestate language. See Salomaa 1973, for more details.) The notion of a finitestate transduction is important when analyzing pushdown machines. If a finitestate control reads a string of input while pushing some string onto the stack (without any popping), then the string in the stack is a finitestate transduction of the input string. Unfortunately, the concept of a finitestate transduction is fading out of the popular textbooks. We will therefore give a brief informal definition of the concept.