Given a graph G, a dominating set D is a set of vertices such that any vertex in G has at least one neighbor (or possibly itself) in D. A {k}-dominating multiset Dk is a multiset of vertices such that any vertex in G has at least k vertices from its closed neighborhood in Dk when counted with multiplicity. In this paper, we utilize the approach developed by Clark and Suen (2000) and properties ...

Whether P systems with only one catalyst can already be computationally complete, is still an open problem. Here we establish computational completeness by using specific variants of additional control mechanisms. At each step using only multiset rewriting rules from one set of a finite number of sets of multiset rewriting rules allows for obtaining computational completeness with one catalyst ...

Formal analysis of security protocols is largely based on a set of assumptions commonly referred to as the Dolev-Yao model. Two formalisms that state the basic assumptions of this model are related here: strand spaces [6] and multiset rewriting with existential quantification [2, 5]. Although it is fairly intuitive that these two languages should be equivalent in some way, a number of modificat...

Scheduling The problem of all optimizations is to decide if their modifications to the reservation vector are valid or not. I.e. if the constrains for scheduling instructions remain exactly the same before and after the (possibly illegal) optimization. The problem can be solved by converting the reservation vector back into the unambiguous set of relevant issue-multisets. If – after modifying t...