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49
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.
A Recognition and Parsing Algorithm for Arbitrary Conjunctive Grammars
"... Conjunctive grammars are basically contextfree grammars with an explicit set intersection operation added to the formalism of rules. This paper presents a cubictime recognition and parsing algorithm for this family of grammars, which is applicable to an arbitrary conjunctive grammar without any ini ..."
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Cited by 18 (17 self)
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Conjunctive grammars are basically contextfree grammars with an explicit set intersection operation added to the formalism of rules. This paper presents a cubictime recognition and parsing algorithm for this family of grammars, which is applicable to an arbitrary conjunctive grammar without any initial transformations.
Expressiveness and complexity of graph logic
, 2007
"... We investigate the complexity and expressive power of a spatial logic for reasoning about graphs. This logic was previously introduced by Cardelli, Gardner, and Ghelli, and provides the simplest setting in which to explore such results for spatial logics. We study several forms of the logic: the log ..."
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Cited by 15 (1 self)
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We investigate the complexity and expressive power of a spatial logic for reasoning about graphs. This logic was previously introduced by Cardelli, Gardner, and Ghelli, and provides the simplest setting in which to explore such results for spatial logics. We study several forms of the logic: the logic with and without recursion, and with either an exponential or a linear version of the basic composition operator. We study the combined complexity and the expressive power of the four combinations. We prove that, without recursion, the linear and exponential versions of the logic correspond to significant fragments of firstorder (FO) and monadic secondorder (MSO) logics; the two versions are actually equivalent to FO and MSO on graphs representing strings. However, when the two versions are enriched withstyle recursion, their expressive power is sharply increased. Both are able to express PSPACEcomplete problems, although their combined complexity and data complexity still belong to PSPACE.
On the Closure Properties of Linear Conjunctive Languages
"... Linear conjunctive grammars are conjunctive grammars in which the body of each conjunct contains no more than a single nonterminal symbol. They can at the same time be thought of as a special case of conjunctive grammars and as a generalization of linear contextfree grammars. ..."
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Cited by 13 (12 self)
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Linear conjunctive grammars are conjunctive grammars in which the body of each conjunct contains no more than a single nonterminal symbol. They can at the same time be thought of as a special case of conjunctive grammars and as a generalization of linear contextfree grammars.
Automaton Representation of Linear Conjunctive Languages
 Developments in Language Theory (Proc. of DLT 2002), LNCS
, 2002
"... This paper introduces a new family of automata that turns out to be computationally equivalent to linear conjunctive grammars  which are linear contextfree grammars extended with an explicit intersection operation. ..."
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Cited by 11 (9 self)
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This paper introduces a new family of automata that turns out to be computationally equivalent to linear conjunctive grammars  which are linear contextfree grammars extended with an explicit intersection operation.
COMPLEXITY OF SOLUTIONS OF EQUATIONS OVER SETS OF NATURAL NUMBERS
, 2008
"... Systems of equations over sets of natural numbers (or, equivalently, language equations over a oneletter alphabet) of the form Xi = ϕi(X1,..., Xn) (1 � i � n) are considered. Expressions ϕi may contain the operations of union, intersection and pairwise sum A+B = {x+y  x ∈ A, y ∈ B}. A system with ..."
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Cited by 6 (2 self)
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Systems of equations over sets of natural numbers (or, equivalently, language equations over a oneletter alphabet) of the form Xi = ϕi(X1,..., Xn) (1 � i � n) are considered. Expressions ϕi may contain the operations of union, intersection and pairwise sum A+B = {x+y  x ∈ A, y ∈ B}. A system with an EXPTIMEcomplete least solution is constructed, and it is established that least solutions of all such systems are in EXPTIME. The general membership problem for these equations is proved to be EXPTIMEcomplete.
Whale Calf, a parser generator for conjunctive grammars
, 2002
"... Whale Calf is a parser generator that uses conjunctive grammars, a generalization of contextfree grammars with an explicit intersection operation, as the formalism of specifying the language. All existing parsing algorithms for conjunctive grammars are implemented { namely, the tabular algorith ..."
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Cited by 6 (5 self)
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Whale Calf is a parser generator that uses conjunctive grammars, a generalization of contextfree grammars with an explicit intersection operation, as the formalism of specifying the language. All existing parsing algorithms for conjunctive grammars are implemented { namely, the tabular algorithms for grammars in the binary normal form, the tabular algorithm for grammars in the linear normal form, the tabular algorithm for arbitrary grammars, the conjunctive LL, the conjunctive LR, and the algorithm based on simulation of the automata equivalent to linear conjunctive grammars. The generated C++ programs can recognize strings and, if necessary, create parse trees.
The Hardest Linear Conjunctive Language
 Information Processing Letters
"... This paper demonstrates that the Pcomplete language of yesinstances of Circuit Value Problem under a suitable encoding can be generated by a linear conjunctive grammar, or, equivalently, accepted by a triangular trellis automaton. This result has several implications on the properties of the langu ..."
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Cited by 5 (4 self)
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This paper demonstrates that the Pcomplete language of yesinstances of Circuit Value Problem under a suitable encoding can be generated by a linear conjunctive grammar, or, equivalently, accepted by a triangular trellis automaton. This result has several implications on the properties of the languages generated by conjunctive grammars of the general form and on the relationship between the abstract models of parallel computation.
Strict language inequalities and their decision problems
 Mathematical Foundations of Computer Science (MFCS 2005
, 2005
"... Abstract. Systems of language equations of the form {ϕ(X1,..., Xn) = ∅, ψ(X1,..., Xn) � = ∅} are studied, where ϕ, ψ may contain settheoretic operations and concatenation; they can be equivalently represented as strict inequalities ξ(X1,..., Xn) ⊂ L0. It is proved that the problem whether such an ..."
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Cited by 5 (3 self)
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Abstract. Systems of language equations of the form {ϕ(X1,..., Xn) = ∅, ψ(X1,..., Xn) � = ∅} are studied, where ϕ, ψ may contain settheoretic operations and concatenation; they can be equivalently represented as strict inequalities ξ(X1,..., Xn) ⊂ L0. It is proved that the problem whether such an inequality has a solution is Σ2complete, the problem whether it has a unique solution is in (Σ3 ∩Π3)\(Σ2 ∪Π2), the existence of a regular solution is a Σ1complete problem, while testing whether there are finitely many solutions is Σ3complete. The class of languages representable by their unique solutions is exactly the class of recursive sets, though a decision procedure cannot be algorithmically constructed out of an inequality, even if a proof of solution uniqueness is attached. 1
H.: To CNF or not to CNF ? An efficient yet presentable version of the CYK algorithm
 Informatica Didactica
"... The most familiar algorithm to decide the membership problem for contextfree grammars is the one by Cocke, Younger and Kasami (CYK) using grammars in Chomsky normal form (CNF). We propose to teach a simple modification of the CYK algorithm that uses grammars in a much less restrictive binary normal ..."
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Cited by 5 (0 self)
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The most familiar algorithm to decide the membership problem for contextfree grammars is the one by Cocke, Younger and Kasami (CYK) using grammars in Chomsky normal form (CNF). We propose to teach a simple modification of the CYK algorithm that uses grammars in a much less restrictive binary normal form (2NF) and two precomputations: the set of nullable nonterminals and the inverse of the unit relation between symbols. The modified algorithm is equally simple as the original one, but highlights that the at most binary branching rules alone are responsible for the O(n 3) time complexity. Moreover, the simple transformation to 2NF comes with a linear increase in grammar size, whereas some transformations to CNF found in most prominent textbooks on formal languages may lead to an exponential increase. 1