In this paper we investigate P systems whose compartments contain sets of symbolobjects rather than multisets of objects, as it is common in membrane computing. If the number of membranes cannot grow, then in this framework we can characterize exactly the regular languages. If membrane creation or membrane division is allowed, then the Parikh sets of recursively enumerable languages can be gene...

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...

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...

Marco Buratti has conjectured that, given an odd prime p and a multiset L containing p − 1 integers taken from {1, . . . , p−1 2 }, there exists a Hamiltonian path in the complete graph with p vertices whose multiset of edge-lengths is equal to L modulo p. We give a positive answer to this conjecture in the case of multisets of the type {1, 2, 3} by completely classifying such multisets that ar...

We present in this paper a formalization of multiset relations in the ACL2 theorem prover [6], and we show how multisets can be used to mechanically prove non-trivial termination properties. Every relation on a set A induces a relation on finite multisets over A; it can be shown that the multiset relation induced by a well-founded relation is also wellfounded [3]. We have carried out a mechanic...

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...

Merge functions informally combine information from a certain universe into a solution over that same universe. This typically results in a, preferably optimal, summarization. In previous research, merge functions over sets have been looked into extensively. A specific case concerns sets that allow elements to appear more than once, multisets. In this paper we compare two types of merge functio...