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.

BACKGROUND The standard three-tube, three-color flow cytometric method utilizing the TriTEST reagents in conjunction with the MultiSET software commonly used in most laboratories in Thailand for CD4 enumeration is expensive and thus unavailable to most HIV-infected patients. A more affordable method, i.e., the PanLeucogating protocol using only two monoclonal antibody reagents, has been describ...

Among private set operations, the privacy preserving element reduction of a multiset can be an important tool for privacy enhancing technology as itself or in the combination with other private set operations. Recently, a protocol, over-threshold-set-union-protocol, for a privacy preserving element reduction method of a multiset was proposed by Kissner and Song in Crypto 2005. In this paper, we...

We show that the family Sem = mREG = mCF of regular multiset languages is closed under applications of finite and iterated multiset-union, finite and iterated multiset-intersection, and multiset-subtraction. For the class Sem(šk) of semilinear subsets of šk, or that of Žk, Sem := ⋃k≥0 Sem(Žk), this amounts to verify, that the component-wise maximum, minimum or non-negative subtraction of pairs ...