705 research outputs found
Capturing CFLs with Tree Adjoining Grammars
We define a decidable class of TAGs that is strongly equivalent to CFGs and
is cubic-time parsable. This class serves to lexicalize CFGs in the same manner
as the LCFGs of Schabes and Waters but with considerably less restriction on
the form of the grammars. The class provides a normal form for TAGs that
generate local sets in much the same way that regular grammars provide a normal
form for CFGs that generate regular sets.Comment: 8 pages, 3 figures. To appear in proceedings of ACL'9
Tree transducers, L systems, and two-way machines
A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the “copying power” of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying. Among the parallel rewriting systems considered are the top-down tree transducer; the generalized syntax-directed translation scheme and the ETOL system, and among the two-way machines are the tree-walking automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton. The. relationship of these devices to macro grammars is also considered. An effort is made .to provide a systematic survey of a number of existing results
On Descriptive Complexity, Language Complexity, and GB
We introduce , a monadic second-order language for reasoning about
trees which characterizes the strongly Context-Free Languages in the sense that
a set of finite trees is definable in iff it is (modulo a
projection) a Local Set---the set of derivation trees generated by a CFG. This
provides a flexible approach to establishing language-theoretic complexity
results for formalisms that are based on systems of well-formedness constraints
on trees. We demonstrate this technique by sketching two such results for
Government and Binding Theory. First, we show that {\em free-indexation\/}, the
mechanism assumed to mediate a variety of agreement and binding relationships
in GB, is not definable in and therefore not enforcible by CFGs.
Second, we show how, in spite of this limitation, a reasonably complete GB
account of English can be defined in . Consequently, the language
licensed by that account is strongly context-free. We illustrate some of the
issues involved in establishing this result by looking at the definition, in
, of chains. The limitations of this definition provide some insight
into the types of natural linguistic principles that correspond to higher
levels of language complexity. We close with some speculation on the possible
significance of these results for generative linguistics.Comment: To appear in Specifying Syntactic Structures, papers from the Logic,
Structures, and Syntax workshop, Amsterdam, Sept. 1994. LaTeX source with
nine included postscript figure
Algebraic properties of structured context-free languages: old approaches and novel developments
The historical research line on the algebraic properties of structured CF
languages initiated by McNaughton's Parenthesis Languages has recently
attracted much renewed interest with the Balanced Languages, the Visibly
Pushdown Automata languages (VPDA), the Synchronized Languages, and the
Height-deterministic ones. Such families preserve to a varying degree the basic
algebraic properties of Regular languages: boolean closure, closure under
reversal, under concatenation, and Kleene star. We prove that the VPDA family
is strictly contained within the Floyd Grammars (FG) family historically known
as operator precedence. Languages over the same precedence matrix are known to
be closed under boolean operations, and are recognized by a machine whose pop
or push operations on the stack are purely determined by terminal letters. We
characterize VPDA's as the subclass of FG having a peculiarly structured set of
precedence relations, and balanced grammars as a further restricted case. The
non-counting invariance property of FG has a direct implication for VPDA too.Comment: Extended version of paper presented at WORDS2009, Salerno,Italy,
September 200
Multiple Context-Free Tree Grammars: Lexicalization and Characterization
Multiple (simple) context-free tree grammars are investigated, where "simple"
means "linear and nondeleting". Every multiple context-free tree grammar that
is finitely ambiguous can be lexicalized; i.e., it can be transformed into an
equivalent one (generating the same tree language) in which each rule of the
grammar contains a lexical symbol. Due to this transformation, the rank of the
nonterminals increases at most by 1, and the multiplicity (or fan-out) of the
grammar increases at most by the maximal rank of the lexical symbols; in
particular, the multiplicity does not increase when all lexical symbols have
rank 0. Multiple context-free tree grammars have the same tree generating power
as multi-component tree adjoining grammars (provided the latter can use a
root-marker). Moreover, every multi-component tree adjoining grammar that is
finitely ambiguous can be lexicalized. Multiple context-free tree grammars have
the same string generating power as multiple context-free (string) grammars and
polynomial time parsing algorithms. A tree language can be generated by a
multiple context-free tree grammar if and only if it is the image of a regular
tree language under a deterministic finite-copying macro tree transducer.
Multiple context-free tree grammars can be used as a synchronous translation
device.Comment: 78 pages, 13 figure
Tree-Adjoining Grammars and Lexicalized Grammars
In this paper, we will describe a tree generating system called tree-adjoining grammar(TAG)and state some of the recent results about TAGs. The work on TAGS is motivated by linguistic considerations. However, a number of formal results have been established for TAGs, which we believe, would be of interest to researchers in tree grammars and tree automata. After giving a short introduction to TAG, we briefly state these results concerning both the properties of the string sets and tree sets (Section 2). We will also describe the notion of lexicalization of grammars (Section 3) and investigate the relationship of lexicalization to context-free grammars (CFGs) and TAGS (Section 4)
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