Multisets are the fundamental data structure of P systems [12]. In this paper we relate P systems with the language and theory for multisets presented in [5]. This allows us, on the one hand, to define and implement P systems using multiset constraints in a constraint logic programming framework, and, on the other hand, to define and implement constraint solving procedures used to test multiset...

The element reduction of a multiset S is to reduce the number of repetitions of an element in S by a predetermined number. Privacypreserving element reduction of a multiset is an important tool in private computation over multisets. It can be used by itself or by combination with other private set operations. Recently, an efficient privacy-preserving element reduction method was proposed by Kis...

We prove that the pair of statistics (des,maj) on multiset permutations is equidistributed with the pair (stc, inv) on certain quotients of the symmetric groups. We define an analogue of the statistic stc on multiset permutations whose joint distribution with the inversions equals that of (des,maj). We extend the definition of the statistic stc to hyperoctahedral and even hyperoctahedral groups...

Let F1 and F2 be two families of subsets of an n-element set. We say that F1 and F2 are multiset-union-free if for any A,B ∈ F1 and C,D ∈ F2 the multisets A ⊎ C and B ⊎D are different, unless both A = B and C = D. We derive a new upper bound on the maximal sizes of multiset-union-free pairs, improving a result of Urbanke and Li.

The paper considers techniques for grouping objects that are described with many quantitative and qualitative attributes and may exist in several copies. Such multi-attribute objects may be represented as multisets or sets with repeating elements. Multiset characteristics and operations under an arbitrary number of multisets are determined. The various options for the objects’ aggregation (addi...

Starting from Shannon theory of information, we present the case of producing information in the form of multisets, and encoding information using multisets. We compute the entropy of a multiset information source by constructing an equientropic string source (with interdependent symbols), and we compare this with a string information source with independent symbols. We then study the encoder a...

Formal analysis of security protocols is largely based on a set of assumptions commonly referred to asthe Dolev-Yao model. Two formalisms that state the basic assumptions of this model are related here:strand spaces and multiset rewriting with existential quantification. Strand spaces provide a simple andeconomical approach to analysis of completed protocol runs by emphasizing causa...

Graphs are useful for analysing the structure models in computer science, operations research, and sociology. The word metric dimension is basis of distance function, which has a symmetric property. Moreover, finding resolving set graph NP-complete, possibilities reduced due to behaviour graph. In this paper, we introduce idea edge-multiset graphs. A representation an edge defined as multiset d...

Current methods which compress multisets at an optimal rate have computational complexity that scales linearly with alphabet size, making them too slow to be practical in many real-world settings. We show how convert a compression algorithm for sequences into one multisets, exchange additional term is quasi-linear sequence length. This allows us of exchangeable symbols rate, decoupled from the ...

This paper describes a general framework for designing purely functional datatypes that automatically satisfy given size or structural constraints. Using the framework we develop implementations of different matrix types (eg square matrices) and implementations of several tree types (eg Braun trees, 2-3 trees). Consider, for instance, representing square /102/ matrices. The usual representation...