Partitioned Binary Relations

Partitioned Binary Relations

We define the category of partitioned binary relations and show that it contains many classical diagram categories, including categories of binary relations, maps, injective maps, partitions, (oriented) Brauer diagrams and (oriented) Temperley-Lieb diagrams. We construct a one-parameter deformation of the category of partitioned binary relations and show that it gives rise to classical one-para...

Binary Relations

The notion of a relation between two sets of objects is quite common and intuitively clear. Let X be the set of all living human females and Y the set of all living human males. The wife-husband relation R can be defined from X to Y . Thus, if x ∈ X and y ∈ Y , then x is related to y by the relation R if x is a wife of y, and we write xRy. To describe the relation R, we may take the collection ...

Symbolic Model Checking with Partitioned Transistion Relations

Symbolic Model Checking with Partitioned Transition Relations

We signiicantly reduce the complexity of BDD-based symbolic veriication by using partitioned transition relations to represent state transition graphs. This method can be applied to both synchronous and asynchronous circuits. The times necessary to verify a synchronous pipeline and an asynchronous stack are both bounded by a low polynomial in the size of the circuit. We were able to handle stac...

Learning Binary Preference Relations

It is a truth universally acknowledged that e-commerce platform users in search of an item that best suits their preferences may be o‚ered a lot of choices. An item may be characterised by many aŠributes, which can complicate the process. Here the classic approach in decision support systems to put weights on the importance of each aŠribute is not always helpful as users may €nd it hard to form...