C-grammars and tree-codifications (original) (raw)
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Oxford Handbooks Online, 2005
This article introduces the preliminaries of classical formal language theory. It outlines the main classes of grammars as language-generating devices and automata as language-recognizing devices. It offers a number of definitions and examples and presents the basic results. It classifies grammar according to several criteria. The most widespread one is the form of their productions. This article presents a systematic study of the common properties of language families has led to the theory of abstract families of languages. It shows that a context-free grammar generates not only a set of strings, but a set of trees too: each one of the trees is associated with a string and illustrates the way this string is derived in the grammar.
On the complexity of the syntax of tree languages
Lecture Notes in Computer Science, 2009
The syntactic complexity of a tree language is defined according to the number of the distinct syntactic classes of all trees with a fixed yield length. This leads to a syntactic classification of tree languages and it turns out that the class of recognizable tree languages is properly contained in that of languages with bounded complexity. A refined syntactic complexity notion is also presented, appropriate exclusively for the class of recognizable tree languages. A tree language is recognizable if and only if it has finitely many refined syntactic classes. The constructive complexity of a tree automaton is also investigated and we prove that for any reachable tree automaton it is equal with the refined syntactic complexity of its behavior. © 2009 Springer.
Algebraic properties of structured context-free languages: old approaches and novel developments
Eprint Arxiv 0907 2130, 2009
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.
1988
Recent results have established that there is a family of languages that is exactly the class of languages generated by three independently developed grammar formalisms: Tree Adjoining Grammm~, Head Grammars, and Linear Indexed Grammars. In this paper we show that Combinatory Categorial Grammars also generates the same class of languages. We discuss the slruclm'al descriptions produced by Combinawry Categorial Grammars and compare them to those of grammar formalisms in the class of Linear Context-Free Rewriting Systems. We also discuss certain extensions of CombinaWry Categorial Grammars and their effect on the weak generative capacity.
Some Grammatical Structures of Programming Languages as Simple Bracketed Languages
Informatica, 2000
We consider in this paper so called simple bracketed languages having special limita- tions. They are sometimes used for the definitions of some grammatical structures of programming languages. Generally speaking, these languages are context-free, but not deterministic context- free, i.e., they cannot be defined by deterministic push-down automata. For the simple bracketed languages having special limitations, the equivalence problem is decidable. We obtain the sufficient conditions for the representation some language by special sequences of simple bracketed languages. We also consider the examples of grammatical structures as the simple bracketed languages. Therefore, we can decide equivalence problem for some grammatical structures of programming languages, and such structures define neither regular, nor deterministic context-free languages.
2016
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 students and co-workers and, in particular, to
Language classes generated by tree controlled grammars with bounded nonterminal complexity
Theoretical Computer Science, 2012
A tree controlled grammar is specified as a pair (G, G ′ ) where G is a context-free grammar and G ′ is a regular grammar. Its language consists of all terminal words with a derivation in G such that all levels of the corresponding derivation tree -except the last level -belong to L(G ′ ). We define the nonterminal complexity Var(H) of H = (G, G ′ ) as the sum of the numbers of nonterminals of G and G ′ . In Turaev et al. (2011) [23] it is shown that tree controlled grammars H with Var(H) ≤ 9 are sufficient to generate all recursively enumerable languages. In this paper, we improve the bound to seven. Moreover, we show that all linear and regular simple matrix languages can be generated by tree controlled grammars with a nonterminal complexity bounded by three, and we prove that this bound is optimal for the mentioned language families. Furthermore, we show that any contextfree language can be generated by a tree controlled grammar