Let c () be the collapse of full transformation semigroup, Tn. Then the general formula to calculate the number of collapsible elements, | tα-1| 2 is derived for all n 0, which is an extension of [1] (A.O. Adeniji and S.O. Makanjuola (2008), ‘On some combinatorial results of collapse and properties of height in full transformation semigroups,’ African Journal of Computing & ICT (Journal of the...

We prove that any countable set of surjective functions on an infinite set of cardinality אn with n ∈ N can be generated by at most n2/2 + 9n/2 + 5 surjective functions of the same set; and there exist n2/2 + 9n/2 + 5 surjective functions that cannot be generated by any smaller number of surjections. If injective functions are considered instead of surjective functions, then n + 4 replaces n2/2...

The informal notion of constructive dynamical space, inspired by biochemical systems, gives the perspective from which a transformation semigroup can be considered as a programming language. This perspective complements a longer-term mathematical investigation into different understandings of the nature of computation that we see as fundamentally important for the realization of a formal framew...

We consider the complexity of Green’s relations when the semigroup is given by transformations on a finite set. Green’s relations can be defined by reachability in the (right/left/two-sided) Cayley graph. The equivalence classes then correspond to the strongly connected components. It is not difficult to show that, in the worst case, the number of equivalence classes is in the same order of mag...