Regular Closure of Deterministic Languages

Bertsch, Eberhard; Nederhof, Mark-Jan

doi:10.1137/s009753979528682x

Cited by 17 publications

(11 citation statements)

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“…And though representing a regular language by a finite-state automaton (FSA) is useful for other purposes, we argued that the FSA in this case can be large, and that recognition and parsing are much more efficient with a modified version of a context-free chart parsing algorithm. Bertsch and Nederhof (1999) gave a linear-time recognition algorithm for the recognition of the regular closure of deterministic context-free languages. Our result is slightly related, since a vine grammar is the Kleene closure of a different kind of restricted CFL (not deterministic, but restricted in its dependency length, hence regular).…”

Section: Related Workmentioning

confidence: 99%

Favor Short Dependencies: Parsing with Soft and Hard Constraints on Dependency Length

Eisner

Smith

2010

Text, Speech and Language Technology

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In lexicalized phrase-structure or dependency parses, a word's modifiers tend to fall near it in the string. This fact can be exploited by parsers. We first show that a crude way to use dependency length as a parsing feature can substantially improve parsing speed and accuracy in English and Chinese, with more mixed results on German. We then show similar improvements by imposing hard bounds on dependency length and (additionally) modeling the resulting sequence of parse fragments. The approach with hard bounds, "vine grammar," accepts only a regular language, even though it happily retains a context-free parameterization and defines meaningful parse trees. We show how to parse this language in O(n) time, using a novel chart parsing algorithm with a low grammar constant (rather than an impractically large finite-state recognizer with an exponential grammar constant).

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Section: Related Workmentioning

confidence: 99%

Favor Short Dependencies: Parsing with Soft and Hard Constraints on Dependency Length

Eisner

Smith

2010

Text, Speech and Language Technology

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“…Proof. It is shown in [1] that Γ REG (DCFL e ) = Γ REG (DCFL). The above theorem shows that Γ REG (DCFL e ) = L ((∞, Z 0 )-nPDA e ).…”

Section: Theoremmentioning

confidence: 99%

“…It is claimed in [1] that the language {ww R | w ∈ {a, b} + } does not belong to Γ REG (DCFL). Due to the automata characterization of Γ REG (DCFL), which is used in the last theorem, we can now give a formal proof.…”

Section: Theoremmentioning

confidence: 99%

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Context-dependent nondeterminism for pushdown automata

Kutrib

Malcher

2007

Theoretical Computer Science

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Pushdown automata using a limited and unlimited amount of nondeterminism are investigated. Moreover, nondeterministic steps are allowed only within certain contexts, i.e., in configurations that meet particular conditions. The relationships of the accepted language families with closures of the deterministic context-free languages (DCFL) under regular operations are studied. For example, automata with unbounded nondeterminism that have to empty their pushdown store up to the initial symbol in order to make a guess are characterized by the regular closure of DCFL. Automata that additionally have to reenter the initial state are (almost) characterized by the Kleene star closure of the union closure of the prefix-free deterministic context-free languages. Pushdown automata with bounded nondeterminism are characterized by the union closure of DCFL in any of the considered contexts. Proper inclusions between all language classes discussed are shown. Finally, closure properties of these families under AFL operations are investigated.

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“…That set can, however, be described by the possible paths through a finite directed graph with nodes labeled by stack symbols and the states reached right after they are pushed and edges connecting such pairs of stack symbols and states. It would also be possible to express this fact in terms of finite automata over the stack alphabet as shown in [14]. The graph will here be represented by the relation On, over the set of pairs of stack symbols and states: On((s, a), (t, b)) is to mean that stack symbol a can be placed on stack symbol b such that the state reached after a gets pushed is s, and t was the state reached after b got pushed.…”

Section: The Set Of Possible Stacksmentioning

confidence: 99%