The purpose of present work is to study some algebraic aspect of fuzzy multiset regular languages. In between, we show the equivalence of multiset regular language and fuzzy multiset regular language. Finally, we introduce the concept of pumping lemma for fuzzy multiset regular languages, which we use to establish a necessary and sufficient condition for a fuzzy multiset language to be non-cons...

The geodesic length spectrum of a complete, finite volume, hyperbolic 3-orbifold M is fundamental invariant the topology via Mostow-Prasad Rigidity. Motivated by this, second author and Reid defined two-dimensional analogue given multiset isometry types totally geodesic, immersed, finite-area surfaces called geometric genus spectrum. They showed that if $M$ arithmetic contains surface, then det...

During the last decade, data on Protein-Protein Interactions (PPI) has increased in a huge manner. Searching for motifs in PPI Network has thus became a crucial problem to interpret this data. A large part of the literature is devoted to the query of motifs with a given topology. However, the biological data are, by now, so noisy (missing and erroneous information) that the topology of a motif ...

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...

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...