The notion of Σ-monoids is proposed by Fiore, Plotkin and Turi, to give abstract algebraic model of languages with variable binding and substitutions. In this paper, we give a free construction of Σ-monoids. The free Σ-monoid over a given presheaf serves a well-structured term language involving binding and substitutions. Moreover, the free Σ-monoid naturally contains interesting syntactic obje...

The order of hypersubstitutions, all idempotent elements on the monoid of all hypersubstitutions of type τ 2 were studied by K. Denecke and Sh. L. Wismath and all idempotent elements on the monoid of all hypersubstitutions of type τ 2, 2 were studied by Th. Changpas and K. Denecke. We want to study similar problems for the monoid of all generalized hypersubstitutions of type τ 2 . In this paper...

Let $n \in \mathbb{Z}^{+}$ and $X_{n}=\{1,2,\ldots,n\}$ be a finite set. $\mathcal ODCT_{n}$ the order-preserving order-decreasing full contraction mappings on $X_{n}$. It is well known that monoid. In this paper, we have found monoid rank presentation of ODCT_{n}$. particular, proved $n-1$ for $$ \geq 3$.

Motivated by the Babai conjecture and the Černý conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set. For automata with n states in this class, we prove that the reset thresholds are upperbounded by 2n − 6n + 5 and can attain the value n(n−1) 2 . In addition, we study diameters of the pair digraphs of permu...