A groupoid is a small category in which all morphisms are isomorphisms. An inductive specialized whose object set regular biordered and the admit partial order. normal strict preorder factorization property. pair of ‘related’ categories constitutes cross-connection. Both groupoids cross-connections were identified by Nambooripad as categorical models semigroups. We explore inter-relationship be...

Variants of the must testing approach have been successfully applied in service oriented computing for analysing compliance between (contracts exposed by) clients and servers or, more generally, two peers. It has however argued that multiparty scenarios call permissive notions because partners usually do not full coordination capabilities. We propose new preorders, which are obtained by restric...

Zak Mesyan1,∗, James D. Mitchell2,∗∗, Michał Morayne3,∗∗∗, and Yann H. Péresse2,† 1 Department of Mathematics, University of Colorado, 1420 Austin Bluffs Parkway, Colorado Springs, CO 80918, United States of America 2 Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland 3 Institute of Mathematics and Computer Science, Wrocław University of Technolo...

Most approaches to iterated belief revision are accompanied by some motivation for the use of the proposed revision operator (or family of operators), and typically encode enough information in the epistemic state of an agent for uniquely determining one-step revision. But in those approaches describing a family of operators there is usually little indication of how to proceed uniquely after th...

We investigate the complexity of preorder checking when the specification is a flat finite-state system whereas the implementation is either a non-flat finite-state system or a standard timed automaton. In both cases, we show that simulation checking is EXPTIME-hard, and for the case of a non-flat implementation, the result holds even if there is no synchronization between the parallel componen...

Properties of preordered monoids are investigated and important subclasses such structures studied. The corresponding full subcategories related between them by appropriate functors as well with the categories sets monoids. Schreier split extensions described in subcategory whose preorder is determined positive cone.

In this paper, we will show the correlation between the notion of implementation relations known from formal methods and ideas of conformance testing. We will show that the implementation relations realized through the practical testing of systems come from a family of parameterized implementation relations. We will also show that for glass box testing, implementation relations parameterized by...

We show how bisimulation equivalence and simulation preorder on probabilistic LTSs (PLTSs), namely the main behavioural relations on probabilistic nondeterministic processes, can be characterized by abstract interpretation. Both bisimulation and simulation can be obtained as completions of partitions and preorders, viewed as abstract domains, w.r.t. a pair of concrete functions that encode a PL...

The content of the dissertation falls in the area of formal verification of probabilistic systems. It comprises four parts listed below: 1. the decision problem of (probabilistic) simulation preorder between probabilistic pushdown automata (pPDAs) and finite probabilistic automata (fPAs); 2. the decision problem of a bisimilarity metric on finite probabilistic automata (fPAs); 3. the approximat...

Economic literature on inequality measurement is mainly concerned with the comparison of univariate indices of well-being, which record the differences in distribution of income (and/or wealth) within and between populations. However, such an approach is considered an inadequate basis for comparing individual disparities because people differ in many aspects besides income. The analysis of diff...