Recently, Aceto, Fokkink & Ingólfsdóttir proposed an algorithm to turn any sound and ground-complete axiomatisation of any preorder listed in the linear time – branching time spectrum at least as coarse as the ready simulation preorder, into a sound and ground-complete axiomatisation of the corresponding equivalence—its kernel. Moreover, if the former axiomatisation is ω-complete, so is the lat...

This paper considers a weak simulation preorder for Markov chains that allows for stuttering. Despite the second-order quantification in its definition, we present a polynomial-time algorithm to compute the weak simulation preorder of a finite Markov chain.  2003 Elsevier B.V. All rights reserved.

We consider the problem of simulation preorder/equivalence between innnite-state processes and nite-state ones. We prove that simulation preorder (in both directions) and simulation equivalence are intractable between all major classes of innnite-state systems and nite-state ones. This result is obtained by showing that the problem whether a BPA (or BPP) process simulates a nite-state one is PS...

We characterize the existence of a nonnegative, sublinear and continuous order-preserving function for a not necessarily complete preorder on a real convex cone in an arbitrary topological real vector space. As a corollary of the main result, we present necessary and sufficient conditions for the existence of such an order-preserving function for a complete preorder.

A preorder consists of linearly ordered equivalence classes called blocks, and an alignment is a sequence of cycles on n labelled elements. We investigate the block structure of a random preorder chosen uniformly at random among all preorders on n elements, and also the distribution of cycles in a random alignment chosen uniformly at random among all alignments on n elements, as n →∞.

Let 1R be the preorder of embeddability between countable linear orders colored with elements of Rado’s partial order (a standard example of a wqo which is not a bqo). We show that 1R has fairly high complexity with respect to Borel reducibility (e.g. if P is a Borel preorder then P ≤B 1R), although its exact classification remains open.