We enhance Gamma, a multiset rewriting language, with a notion of structured multiset. A structured multiset is a set of addresses satisfying speci c relations which can be used in the rewriting rules of the program. A type is de ned by a context-free graph grammar and a structured multiset belongs to a type T if its underlying set of addresses satis es the invariant expressed by the grammar de...

The paper determines the algebraic and logic structure of the multiset semantics of the core patterns of SPARQL. We prove that the fragment formed by AND, UNION, OPTIONAL, FILTER, MINUS and SELECT corresponds precisely to both, the intuitive multiset relational algebra (projection, selection, natural join, arithmetic union and except), and the multiset non-recursive Datalog with safe negation.

The previously introduced multiset language classes defined by multiset storage automata are being explored with respect to their closure properties and alternative characterizations.

Set variables in constraint satisfaction problems (CSPs) are typically propagated by enforcing set bounds consistency together with cardinality reasoning, which uses some inference rules involving the cardinality of a set variable to produce more prunings than set bounds propagation alone. Multiset variables are a generalization of set variables by allowing the elements to have repetitions. In ...

Graphs are discrete structures that model relationships between objects. Graphs play an important role in many areas of computer science. In this reading we introduce basic notions of graph theory that are important in computer science. In particular we look directed graphs, undirected graphs, trees and some applications of graphs. We begin by discussing directed graphs, also known as digraphs....

We solve the problem of designing an O(1) time algorithm for generating adjacent multiset combinations in a different approach from Walsh [17]. By the word “adjacent”, we mean that two adjacent multiset combinations are different at two places by one in their vector forms. Previous O(1) time algorithms for multiset combinations generated non-adjacent multiset combinations. Our algorithm in this...

For positive integers and , consider a multiset of nonempty subsets such that there is unique partition these into partitions . We study the maximum possible size multiset. focus on regime show When for any this lower bound simplifies to we matching upper optimal up factor also compute exactly when