Journal ArticleDOI
Conjunctive Grammars and Systems of Language Equations
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Every system of this kind of language equations that are resolved with respect to variables and contain the operations of concatenation, union and intersection is proved to have a least fixed point, and the equivalence of these systems to conjunctive grammars is established.Abstract:
This paper studies systems of language equations that are resolved with respect to variables and contain the operations of concatenation, union and intersection Every system of this kind is proved to have a least fixed point, and the equivalence of these systems to conjunctive grammars is established This allows us to obtain an algebraic characterization of the language family generated by conjunctive grammarsread more
Citations
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Journal ArticleDOI
Boolean grammars
TL;DR: In this paper, a new generalization of context-free grammars is introduced: Boolean Grammars, which allow the use of all set-theoretic operations as an integral part of the formalism of rules.
Journal ArticleDOI
On the equivalence of linear conjunctive grammars and trellis automata
TL;DR: Their equivalence implies the equivalence of several other formal systems, including a certain restricted class of Turing machines and a certain type of language equations, thus giving further evidence for the importance of the language family they all generate.
Journal ArticleDOI
Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth
Artur Jeż,Alexander Okhotin +1 more
TL;DR: The results imply undecidability of a number of decision problems of unary conjunctive grammars, as well as non-existence of a recursive function bounding the growth rate of the generated languages.
Journal ArticleDOI
Conjunctive and Boolean grammars: The true general case of the context-free grammars
TL;DR: This paper surveys the results on conjunctive and Boolean Grammars obtained over the last decade, comparing them to the corresponding results for ordinary context-free grammars and their main subfamilies.
Book ChapterDOI
Conjunctive Grammars Can Generate Non-regular Unary Languages
TL;DR: A negative answer is given, contrary to the conjectured positive one, by constructing a conjunctive grammar for the language \(\{ a^{4^{n}} : n \in \mathbb{N} \}\).
References
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Book ChapterDOI
Context-free languages and pushdown automata
TL;DR: This chapter is devoted to context-free languages, which were designed initially to formalize grammatical properties of natural languages and grammars and appeared to be well adapted to the formal description of the syntax of programming languages.
Conjunctive grammars
TL;DR: It is proved that conjunctive grammars can still be parsed in cubic time and that the notion of the derivation tree is retained, which gives reasonable hope for their practical applicability.
Book ChapterDOI
Semirings and formal power series: their relevance to formal languages and automata
TL;DR: The purpose of Chapter 9 is to develop some classical results on formal languages and automata by an algebraic treatment using semirings, formal power series and matrices.
Journal ArticleDOI
A Note on Tape-Bounded Complexity Classes and Linear Context-Free languages
TL;DR: The equivalence of the following statements, for 0 g ~ < 1, m shown by describing a log(n)-complete hnear language, is shown.
Journal ArticleDOI
A recognition and parsing algorithm for arbitrary conjunctive grammars
TL;DR: A cubic-time recognition and parsing algorithm for this family of grammars, which is applicable to an arbitrary conjunctive grammar without any initial transformations, and which can be modified to work in quadratic time and use linear space.