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The pseudovariety of semigroups of triangular matrices over a finite field

Jorge Almeida, Stuart W. Margolis, Mikhail V. Volkov (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We show that semigroups representable by triangular matrices over a fixed finite field form a decidable pseudovariety and provide a finite pseudoidentity basis for it.

The range of non-linear natural polynomials cannot be context-free

Dömötör Pálvölgyi (2020)

Kybernetika

Suppose that some polynomial f with rational coefficients takes only natural values at natural numbers, i. e., L = { f ( n ) n } . We show that the base- q representation of L is a context-free language if and only if f is linear, answering a question of Shallit. The proof is based on a new criterion for context-freeness, which is a combination of the Interchange lemma and a generalization of the Pumping lemma.

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