3,193 research outputs found
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
Formal Properties of XML Grammars and Languages
XML documents are described by a document type definition (DTD). An
XML-grammar is a formal grammar that captures the syntactic features of a DTD.
We investigate properties of this family of grammars. We show that every
XML-language basically has a unique XML-grammar. We give two characterizations
of languages generated by XML-grammars, one is set-theoretic, the other is by a
kind of saturation property. We investigate decidability problems and prove
that some properties that are undecidable for general context-free languages
become decidable for XML-languages. We also characterize those XML-grammars
that generate regular XML-languages.Comment: 24 page
Higher-Order Operator Precedence Languages
Floyd's Operator Precedence (OP) languages are a deterministic context-free
family having many desirable properties. They are locally and parallely
parsable, and languages having a compatible structure are closed under Boolean
operations, concatenation and star; they properly include the family of Visibly
Pushdown (or Input Driven) languages. OP languages are based on three relations
between any two consecutive terminal symbols, which assign syntax structure to
words. We extend such relations to k-tuples of consecutive terminal symbols, by
using the model of strictly locally testable regular languages of order k at
least 3. The new corresponding class of Higher-order Operator Precedence
languages (HOP) properly includes the OP languages, and it is still included in
the deterministic (also in reverse) context free family. We prove Boolean
closure for each subfamily of structurally compatible HOP languages. In each
subfamily, the top language is called max-language. We show that such languages
are defined by a simple cancellation rule and we prove several properties, in
particular that max-languages make an infinite hierarchy ordered by parameter
k. HOP languages are a candidate for replacing OP languages in the various
applications where they have have been successful though sometimes too
restrictive.Comment: In Proceedings AFL 2017, arXiv:1708.0622
Generalizing input-driven languages: theoretical and practical benefits
Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks
to their simplicity they enjoy various nice algebraic and logic properties that
have been successfully exploited in many application fields. Practically all of
their related problems are decidable, so that they support automatic
verification algorithms. Also, they can be recognized in real-time.
Context-free languages (CFL) are another major family well-suited to
formalize programming, natural, and many other classes of languages; their
increased generative power w.r.t. RL, however, causes the loss of several
closure properties and of the decidability of important problems; furthermore
they need complex parsing algorithms. Thus, various subclasses thereof have
been defined with different goals, spanning from efficient, deterministic
parsing to closure properties, logic characterization and automatic
verification techniques.
Among CFL subclasses, so-called structured ones, i.e., those where the
typical tree-structure is visible in the sentences, exhibit many of the
algebraic and logic properties of RL, whereas deterministic CFL have been
thoroughly exploited in compiler construction and other application fields.
After surveying and comparing the main properties of those various language
families, we go back to operator precedence languages (OPL), an old family
through which R. Floyd pioneered deterministic parsing, and we show that they
offer unexpected properties in two fields so far investigated in totally
independent ways: they enable parsing parallelization in a more effective way
than traditional sequential parsers, and exhibit the same algebraic and logic
properties so far obtained only for less expressive language families
Graph Interpolation Grammars: a Rule-based Approach to the Incremental Parsing of Natural Languages
Graph Interpolation Grammars are a declarative formalism with an operational
semantics. Their goal is to emulate salient features of the human parser, and
notably incrementality. The parsing process defined by GIGs incrementally
builds a syntactic representation of a sentence as each successive lexeme is
read. A GIG rule specifies a set of parse configurations that trigger its
application and an operation to perform on a matching configuration. Rules are
partly context-sensitive; furthermore, they are reversible, meaning that their
operations can be undone, which allows the parsing process to be
nondeterministic. These two factors confer enough expressive power to the
formalism for parsing natural languages.Comment: 41 pages, Postscript onl
Recovering Grammar Relationships for the Java Language Specification
Grammar convergence is a method that helps discovering relationships between
different grammars of the same language or different language versions. The key
element of the method is the operational, transformation-based representation
of those relationships. Given input grammars for convergence, they are
transformed until they are structurally equal. The transformations are composed
from primitive operators; properties of these operators and the composed chains
provide quantitative and qualitative insight into the relationships between the
grammars at hand. We describe a refined method for grammar convergence, and we
use it in a major study, where we recover the relationships between all the
grammars that occur in the different versions of the Java Language
Specification (JLS). The relationships are represented as grammar
transformation chains that capture all accidental or intended differences
between the JLS grammars. This method is mechanized and driven by nominal and
structural differences between pairs of grammars that are subject to
asymmetric, binary convergence steps. We present the underlying operator suite
for grammar transformation in detail, and we illustrate the suite with many
examples of transformations on the JLS grammars. We also describe the
extraction effort, which was needed to make the JLS grammars amenable to
automated processing. We include substantial metadata about the convergence
process for the JLS so that the effort becomes reproducible and transparent
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