237 research outputs found
Simulation of Two-Way Pushdown Automata Revisited
The linear-time simulation of 2-way deterministic pushdown automata (2DPDA)
by the Cook and Jones constructions is revisited. Following the semantics-based
approach by Jones, an interpreter is given which, when extended with
random-access memory, performs a linear-time simulation of 2DPDA. The recursive
interpreter works without the dump list of the original constructions, which
makes Cook's insight into linear-time simulation of exponential-time automata
more intuitive and the complexity argument clearer. The simulation is then
extended to 2-way nondeterministic pushdown automata (2NPDA) to provide for a
cubic-time recognition of context-free languages. The time required to run the
final construction depends on the degree of nondeterminism. The key mechanism
that enables the polynomial-time simulations is the sharing of computations by
memoization.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455
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
Probabilistic Parsing Strategies
We present new results on the relation between purely symbolic context-free
parsing strategies and their probabilistic counter-parts. Such parsing
strategies are seen as constructions of push-down devices from grammars. We
show that preservation of probability distribution is possible under two
conditions, viz. the correct-prefix property and the property of strong
predictiveness. These results generalize existing results in the literature
that were obtained by considering parsing strategies in isolation. From our
general results we also derive negative results on so-called generalized LR
parsing.Comment: 36 pages, 1 figur
Efficient Tabular LR Parsing
We give a new treatment of tabular LR parsing, which is an alternative to
Tomita's generalized LR algorithm. The advantage is twofold. Firstly, our
treatment is conceptually more attractive because it uses simpler concepts,
such as grammar transformations and standard tabulation techniques also know as
chart parsing. Secondly, the static and dynamic complexity of parsing, both in
space and time, is significantly reduced.Comment: 8 pages, uses aclap.st
Tabular Parsing
This is a tutorial on tabular parsing, on the basis of tabulation of
nondeterministic push-down automata. Discussed are Earley's algorithm, the
Cocke-Kasami-Younger algorithm, tabular LR parsing, the construction of parse
trees, and further issues.Comment: 21 pages, 14 figure
Automata theory and formal languages
These lecture notes present some basic notions and results on Automata Theory,
Formal Languages Theory, Computability Theory, and Parsing Theory. I prepared
these notes for a course on Automata, Languages, and Translators which I am
teaching at the University of Roma Tor Vergata. More material on these topics and
on parsing techniques for context-free languages can be found in standard textbooks
such as [1, 8, 9]. The reader is encouraged to look at those books.
A theorem denoted by the triple k.m.n is in Chapter k and Section m, and within
that section it is identified by the number n. Analogous numbering system is used
for algorithms, corollaries, definitions, examples, exercises, figures, and remarks. We
use âiffâ to mean âif and only ifâ.
Many thanks to my colleagues of the Department of Informatics, Systems, and
Production of the University of Roma Tor Vergata. I am also grateful to my stu-
dents and co-workers and, in particular, to Lorenzo Clemente, Corrado Di Pietro,
Fulvio Forni, Fabio Lecca, Maurizio Proietti, and Valerio Senni for their help and
encouragement.
Finally, I am grateful to Francesca Di Benedetto, Alessandro Colombo, Donato
Corvaglia, Gioacchino Onorati, and Leonardo Rinaldi of the Aracne Publishing Com-
pany for their kind cooperation
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