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Multi-dimensional sets recognizable in all abstract numeration systems

Émilie Charlier, Anne Lacroix, Narad Rampersad (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We prove that the subsets of that are S-recognizable for all abstract numeration systems S are exactly the 1-recognizable sets. This generalizes a result of Lecomte and Rigo in the one-dimensional setting.

Multi-dimensional sets recognizable in all abstract numeration systems

Émilie Charlier, Anne Lacroix, Narad Rampersad (2012)

RAIRO - Theoretical Informatics and Applications

We prove that the subsets of that are S-recognizable for all abstract numeration systems S are exactly the 1-recognizable sets. This generalizes a result of Lecomte and Rigo in the one-dimensional setting.

Multigenerative grammar systems and matrix grammars

Roman Lukáš, Alexander Meduna (2010)

Kybernetika

Multigenerative grammar systems are based on cooperating context-free grammatical components that simultaneously generate their strings in a rule-controlled or nonterminal-controlled rewriting way, and after this simultaneous generation is completed, all the generated terminal strings are combined together by some common string operations, such as concatenation, and placed into the generated languages of these systems. The present paper proves that these systems are equivalent with the matrix grammars....

Multi-island finite automata and their even computation

Dušan Kolář, Alexander Meduna, Martin Tomko (2021)

Kybernetika

This paper discusses n -island finite automata whose transition graphs can be expressed as n -member sequences of islands i 1 , i 2 , , i n , where there is a bridge leaving i j and entering i j + 1 for each 1 j n - 1 . It concentrates its attention on even computation defined as any sequence of moves during which these automata make the same number of moves in each of the islands. Under the assumption that these automata work only in an evenly computational way, the paper proves its main result stating that n -island finite automata...

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