We introduce a new cryptographic tool: multiset hash functions. Unlike standard hash functions which take strings as input, multiset hash functions operate on multisets (or sets). They map multisets of arbitrary finite size to strings (hashes) of fixed length. They are incremental in that, when new members are added to the multiset, the hash can be updated in time proportional to the change. Th...

athemat s.2012.1 Abstract Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we define and investigate three types of lower and upper multiset approximations of any multiset. These types based on the multiset bas...

We propose extending constraint solvers with multiset variables. That is, variables whose values are multisets. Such an extension can help prevent introducing unnecessary symmetry into a model. We identify a number of different representations for multiset variables, and suggest primitive and global constraints on multiset variables. Surprisingly, unlike finite domain variables, decomposition o...

In this paper we begin with the basics of multisets and their operations introduced in [5, 22] and define a multiset relation, an equivalence multiset relation and explore some of their basic properties. We also define a partially ordered multiset as a multiset relation being reflexive, antisymmetric and transitive, chains and antichains of a partially ordered multiset, and extend Dilworth’s Th...

We study the problem of multiset prediction. The goal of multiset prediction is to train a predictor that maps an input to a multiset consisting of multiple items. Unlike existing problems in supervised learning, such as classification, ranking and sequence generation, there is no known order among items in a target multiset, and each item in the multiset may appear more than once, making this ...

The exterior square of a multiset is a natural combinatorial construction which is related to the exterior square of a vector space. We consider multisets of elements of an abelian group. Two properties are defined which a multiset may satisfy: recognisability and involution-recognisability. A polynomial-time algorithm is described which takes an input multiset and returns either (a) a multiset...

In a previous work [12], we proposed a method for generating permutations in lexicographic order. In this study, we extend it to generate multiset permutations. A multiset is a collection of items that are not necessarily distinct. The guideline of the extension is to skip, as soon as possible, those partially-formed permutations that are less than or equal to the latest generated eligible perm...

In the -calculus with replication, two processes are multiset congruent if they have the same semantics in the multiset transition system M . It is proved that (extended) structural congruence is the same as multiset congruence, and that it is decidable.