311 research outputs found
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
A survey of normal form covers for context-free grammars
An overview is given of cover results for normal forms of context-free grammars. The emphasis in this paper is on the possibility of constructing É›-free grammars, non-left-recursive grammars and grammars in Greibach normal form. Among others it is proved that any É›-free context-free grammar can be right covered with a context-free grammar in Greibach normal form. All the cover results concerning the É›-free grammars, the non-left-recursive grammars and the grammars in Greibach normal form are listed, with respect to several types of covers, in a cover-table
Simple chain grammars and languages
A subclass of the LR(0)-grammars, the class of simple chain grammars is introduced. Although there exist simple chain grammars which are not LL(k) for any k>0, this new class of grammars is very closely related to the LL(1) and simple LL(1) grammars. In fact it can be shown that every simple chain grammar has an equivalent simple LL(1) grammar. Cover properties for simple chain grammars are investigated and a deterministic pushdown transducer which acts as a right parser for simple chain grammars is presented
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 ‘iff’ to mean ‘if and only if’.
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
Beyond operator-precedence grammars and languages
Operator Precedence Languages (OPL) are deterministic context-free and have desirable properties. OPL are parallely parsable, and, when structurally compatible, are closed under Boolean operations, concatenation and star; they include the Input Driven languages. OPL use three relations between two terminal symbols, to assign syntax structure to words. We extend such relations to k-tuples of consecutive symbols, in agreement with strictly locally testable regular languages. For each k, the new corresponding class of Higher-order Operator Precedence languages properly includes the OPL and enjoy many of their properties. OPL are a strict hierarchy based on k, which contains maximal languages
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