### Abstract

GF(2)-grammars, recently introduced by Bakinova et al. (“ Formal languages over GF(2) ”, LATA 2018), are a variant of ordinary context-free grammars, in which the disjunction is replaced by exclusive OR, whereas the classical concatenation is replaced by a new operation called GF(2)-concatenation: KʘL is the set of all strings with an odd number of partitions into a concatenation of a string in K and a string in L. This paper establishes several results on the family of languages defined by these grammars. Over the unary alphabet, GF(2)-grammars define exactly the 2-automatic sets. No language of the form (formula Presented), with uniformly superlinear f, can be described by any GF(2)-grammar. The family is not closed under union, intersection, classical concatenation and Kleene star, non-erasing homomorphisms. On the other hand, this family is closed under injective nondeterministic finite transductions, and contains a hardest language under reductions by homomorphisms.

Original language | English |
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Title of host publication | SOFSEM 2019 |

Subtitle of host publication | Theory and Practice of Computer Science - 45th International Conference on Current Trends in Theory and Practice of Computer Science, Proceedings |

Editors | Rastislav Královič, Giovanni Pighizzini, Jerzy Nawrocki, Barbara Catania |

Publisher | Springer Nature |

Pages | 310-323 |

Number of pages | 14 |

ISBN (Print) | 9783030108007 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

Event | 45th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2018 - Nový Smokovec Duration: 27 Jan 2019 → 30 Jan 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11376 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 45th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2018 |
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Country | Slovakia |

City | Nový Smokovec |

Period | 27/01/19 → 30/01/19 |

### Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*SOFSEM 2019: Theory and Practice of Computer Science - 45th International Conference on Current Trends in Theory and Practice of Computer Science, Proceedings*(pp. 310-323). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11376 LNCS). Springer Nature. https://doi.org/10.1007/978-3-030-10801-4_25