The outer multiset dimension $$\textrm{dim}_\textrm{ms}(G)$$ of a graph G is the cardinality smallest set vertices that uniquely recognize all outside this by using multisets distances to set. It proved $$\textrm{dim}_\textrm{ms}(G) = n(G) - 1$$ if and only regular with diameter at most 2. Graphs $$\textrm{dim}_\textrm{ms}(G)=2$$ are described recognized in polynomial time. A lower bound on lex...

For a finite subset A of Z>0, Lazar and Wachs (2019) conjectured that the number cycles on with only even-odd drops is equal to D-cycles A. In this note, we introduce multiset prove bijectively version their conjecture. As consequence, [2n] equals Genocchi gn. With Laguerre histories as an intermediate structure, also construct bijection between class permutations length 2n?1 known be counted b...

Concurrent traces are sequences of computational steps where independent steps can be permuted and executed in any order. We study the problem of matching on concurrent traces. We give a sound and complete algorithm for matching traces with one variable standing for an unknown subtrace. 1 State-Transition Concurrency Computation in a concurrent system results from the interactions of computing ...

This research note outlines an alternative proof of the well-foundedness of the nested multiset ordering. It is first shown that the set M∗(S) of nested multisets over a given base set S forms a cumulative type structure. Then, by exploiting the notion of sets bounded in rank, it is proved that (M∗(S), >>∗) is well-founded if and only if (S, >) is well-founded, where >>∗denotes a nested multise...

We show that for Multiplicative Exponential Linear Logic (without weakenings) the syntactical equivalence relation on proofs induced by cut-elimination coincides with the semantic equivalence relation on proofs induced by the multiset based relational model: one says that the interpretation in the model (or the semantics) is injective. We actually prove a stronger result: two cut-free proofs of...