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.

type ref t = id:N{witnessed (has_a_t id t)} let has (id:N) (H h _) = match h id with Used _ _ (Untyped _)→⊤ | _→⊥ abstract type uref = id:N{witnessed (has id)}type uref = id:N{witnessed (has id)} To enforce these invariants on state-manipulating operations, we define a preorder rel on heap, that constrains the heap evolution. It states that every Used identifier remains Used; every Typed refere...

Groote and Vaandrager introduced the tyft format, which is a congruence format for strong bisimulation equivalence. This article proposes additional syntactic requirements on the tyft format, extended with predicates, to obtain a precongruence format for language preorder.

This paper presents, by means of Alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces, a systematic investigation of the interrelationship between fuzzy preordered sets, topological spaces, and fuzzy topological spaces. © 2006 Elsevier B.V. All rights reserved.

This paper studies the (in)equational theory of simulation preorder and equivalence over the process algebra BCCSP. We prove that in the presence of a finite alphabet with at least two actions, the (in)equational theory of BCCSP modulo simulation preorder or equivalence does not have a finite basis. In contrast, in the presence of an alphabet that is infinite or a singleton, the equational theo...

One-counter nets (OCN) are Petri nets with exactly one unbounded place. They are equivalent to a subclass of one-counter automata with just a weak test for zero. Unlike many other semantic equivalences, strong and weak simulation preorder are decidable for OCN, but the computational complexity was an open problem. We show that both strong and weak simulation preorder on OCN are PSPACE-complete....