Abstract We obtain several characterizations of the existence greatest elements a total preorder. The pertain to unconstrained preorder and constrained on every nonempty compact subset its ground set. necessary sufficient conditions are purely topological and, in case elements, formulated by making use relation set all topologies that can be defined objective relation. Observing function into t...

The unification type of an equational theory is defined using a preorder on substitutions, called the instantiation preorder, whose scope is either restricted to the variables occurring in the unification problem, or unrestricted such that all variables are considered. It is known that the unification type of an equational theory may vary, depending on which instantiation preorder is used. More...

Should testing preorder was proposed as a liveness-preserving precongruence for a process algebra except for nondeterministic choice operator [22]. However, this precongruce result cannot be generalized to other languages before carefully proved. In this paper, we show that τDes format is a precongruence format for should testing preorder. A precongruence format guarantees the precongruence of ...

We study the monoid generalizationMk,1 of the Thompson-Higman groups, and we characterize the Rand the L-preorder ofMk,1. Although Mk,1 has only one non-zero J -class and k−1 non-zero D-classes, the Rand the L-preorder are complicated; in particular, <R is dense (even within an L-class), and <L is dense (even within an R-class). We study the computational complexity of the Rand the L-preorder. ...

Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is one of the most significant aspects of it. In this study, we prove that the order of a leaf (leaves) of a binary tree is the same in the main tree traversals; preorder, inorder, and postorder. Then, we prove that given the preorder and postorder traversals of a binary tree, the leaf (leaves) of a bi...

The exact unification type of an equational theory is based on a new preorder on substitutions, called the exactness preorder, which is tailored towards transferring decidability results for unification to disunification. We show that two important results regarding the unification type of commutative theories hold not only for the usual instantiation preorder, but also for the exactness preord...

This paper is devoted to the study of the (in)equational theory of the largest (pre)congruences over the language BCCSP induced by variations on the classic simulation preorder and equivalence that abstract from internal steps in process behaviours. In particular, the article focuses on the (pre)congruences associated with the weak simulation, the weak complete simulation and the weak ready sim...