# Conjunctive Grammars Can Generate Non-regular Unary Languages

@inproceedings{Je2008ConjunctiveGC, title={Conjunctive Grammars Can Generate Non-regular Unary Languages}, author={Artur Jeż}, booktitle={International Conference on Developments in Language Theory}, year={2008} }

Conjunctive grammars were introduced by A. Okhotin in [1] as a natural extension of context-free grammars with an additional operation of intersection in the body of any production of the grammar. Several theorems and algorithms for context-free grammars generalize to the conjunctive case. Still some questions remained open. A. Okhotin posed nine problems concerning those grammars. One of them was a question, whether a conjunctive grammar over unary alphabet can generate only regular languages…

## 53 Citations

### Unambiguous Conjunctive Grammars over a One-Letter Alphabet

- Computer ScienceDevelopments in Language Theory
- 2013

It is demonstrated that unambiguous conjunctive grammars over a unary alphabet Σ = {a} have non-trivial expressive power, and that their basic properties are undecidable. The key result is that for…

### One-Nonterminal Conjunctive Grammars over a Unary Alphabet

- Computer ScienceTheory of Computing Systems
- 2011

The compressed membership problem for one-nonterminal conjunctive grammars over {a} is proved to be EXPTIME-complete; the same problem for the context-free grammar is decidable in NLOGSPACE, but becomes NP-complete if the grammar is compressed as well.

### Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth

- Computer ScienceTheory of Computing Systems
- 2008

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.

### Conjunctive and Boolean grammars: The true general case of the context-free grammars

- Computer ScienceComput. Sci. Rev.
- 2013

### Conjunctive and Boolean Grammars

- Computer Science, Linguistics
- 2010

This thesis examines four interesting classes of formal languages and presents a more general criterion that can be used to show that certain languages can not be produced by oneNon terminal context-free and one non terminal conjunctive grammars.

### Defining Contexts in Context-Free Grammars

- Computer ScienceLATA
- 2012

This paper gives two equivalent definitions of the model and establishes its basic properties, including a transformation to a normal form, a cubic-time parsing algorithm, and another recognition algorithm working in linear space.

### Input-driven languages are linear conjunctive

- Computer Science, LinguisticsTheor. Comput. Sci.
- 2016

### On the Number of Nonterminal Symbols in Unambiguous Conjunctive Grammars

- Computer Science, LinguisticsDCFS
- 2012

It is demonstrated that the family of languages generated by unambiguous conjunctive grammars with 1 nonterminal symbol is strictly included in the languages generated by 2-nonterminal grammars,…

### Nine Open Problems on Conjunctive and Boolean Grammars

- Computer ScienceBull. EATCS
- 2007

This note is aimed to report on the two solved problems, as well as to correct a couple of small errors, in the survey of conjunctive and Boolean grammars.

## References

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Conjunctive Grammars were introduced in 2000 as a generalization of context-free grammars that allows the use of an explicit intersection oper-ation in rules and several theoretical results on their properties have been obtained and numerous open problems are proposed.

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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.

### Nine Open Problems on Conjunctive and Boolean Grammars

- Computer ScienceBull. EATCS
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This note is aimed to report on the two solved problems, as well as to correct a couple of small errors, in the survey of conjunctive and Boolean grammars.

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A new class of formal grammars, which allow the use of all set-theoretic operations as an integral part of the formalism of rules, are introduced, which allows to conjecture the practical applicability of the new concept.

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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.