The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intuitively, tolerating errors (while counting them) in the alternating simulation game. We show that the interfa...

In a regular category $$\mathbb {E}$$ , the direct image along epimorphism f of preorder is not in general. Set, its best approximation then cocartesian above f. category, existence such S actually equivalent to supremum $$R[f]\vee S$$ among preorders. We investigate here some conditions ensuring these images or equivalently suprema. They apply two very dissimilar contexts: any topos with supre...

In this paper, we present a new simple axiomatization of useful topologies, i.e., topologies on an arbitrary set, with respect to which every continuous total preorder admits utility representation. particular, show that, for completely regular spaces, topology is useful, if and only it separable, isolated chain open closed sets countable. As specific application optimization theory, characteri...

We study the succinctness of different classes of succinctly presented finite transition systems with respect to bisimulation equivalence. Our results show that synchronized product of finite automata, hierarchical graphs, and timed automata are pairwise incomparable in this sense. We moreover study the computational complexity of deciding simulation preorder and bisimulation equivalence on the...

In this article, we relate the spectrum of discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties graph: existence perfect matching and Hamiltonian cycle underlying graph. particular, give family spectral obstructions parametrised by potential for to be matchable (i.e., having matching) or cycle. We base our analysis special case preorder introduced in [8], us...

We consider skew metrics (equivalently, transitive relations that are tournaments, linear orderings) valued in Sugihara semigroups on autodual chains. prove that, for odd chains and without a unit, classify certain tree-like structures we call perfect augmented plane towers. When the chain is finite has cardinality \(2K+1\), set X give rise to rooted trees of height K whose frontier preorder X.

Abstract We consider two preorder-enriched categories of ordered partial combinatory algebras: OPCA, where the arrows are functional (i.e., projective) morphisms, and OPCA † , applicative morphisms. show that has small products finite biproducts, coproducts, all in a suitable 2-categorical sense. On other hand, lacks nontrivial binary products. deduce from this pushout, over Set, realizability ...

Abstract We introduce an upper semicontinuity condition concerning a not necessarily total preorder on topological space, namely strong , and in this way we extend to the nontotal case famous Rader’s theorem, which guarantees existence of semicontinuous order-preserving function for second countable space. show that theorem is generalizable if adopt weaker conditions already introduced literatu...

A quasiconvex function f being given, does there exist an increasing and continuous k which makes $$k\circ f$$ convex? How to build such a k? Some words on least convex (concave) functions. The ratio of two positive numbers is neither locally convexifiable nor concavifiable. Finally, some considerations the approximation preorder from finite number observations revealed preference problem are d...