Multiset orderings are a key ingredient in certain termination techniques like the recursive path ordering and a variant of size-change termination. In order to integrate these techniques in a certifier for termination proofs, we have added them to the Isabelle Formalization of Rewriting. To this end, it was required to extend the existing formalization on multiset orderings towards a generaliz...

A classical result of MacMahon states that inversion number and major index have the same distribution over permutations of a given multiset. In this work, we prove a strengthening of MacMahon’s theorem originally conjectured by Haglund. Our result can be seen as an equidistribution theorem over the ordered partitions of a multiset into sets, which we call ordered multiset partitions. Our proof...

This paper answers the following mathematical question: Can multiset permutations be ordered so that each permutation is a prefix shift of the previous permutation? Previously, the answer was known for the permutations of any set, and the permutations of any multiset whose corresponding set contains only two elements. This paper also answers the following algorithmic question: Can multiset perm...

We present an algorithm that generates multiset permutations in O(1) time for each permutation, that is, by a loop-less algorithm with O(n) extra memory requirement. There already exist several such algorithms that generate multiset permutations in various orders. For multiset permutations, we combine two loop-less algorithms that are designed in the same principle of tree traversal. Our order ...

Checking the structural boundedness and the structural termination of vector addition systems with states boils down to detecting pathological cycles. As opposed to their non-structural variants which require exponential space, these properties need polynomial time only. The algorithm searches for a counterexample in the form of a multiset of arcs computed by means of linear programming. Yet th...

Privacy preserving multiset union (PPMU) protocol allows a set of parties, each with a multiset, to collaboratively compute a multiset union secretly, meaning that any information other than union is not revealed. We propose efficient PPMU protocols, using multiplicative homomorphic cryptosystem. The novelty of our protocol is to directly encrypt a polynomial by representing it by an element of...

We present a modelling framework and computational paradigm called Colonies of Synchronizing Agents (CSAs), which abstracts intracellular and intercellular mechanisms of biological tissues. The model is based on a multiset of agents (cells) in a common environment. Each agent has a local contents, stored in the form of a multiset of atomic objects, updated by multiset rewriting rules which may ...

This paper describes Gammall og, a logic language based on multiset rewriting. The language combines the ability of describing parallel programs made of multiset transformation rules as in GAMMA with the execution model of logic programming in a strongly typed framework as in GG odel. We describe the design choices, the syntax and the semantics. Gammall og provides a standard model theoretic se...

This paper answers the following mathematical question: Can multiset permu-tations be ordered so that each permutation is a prefix shift of the previous permutation?Previously, the answer was known for the permutations of any set, and the permutationsof any multiset whose corresponding set contains only two elements. This paper also an-swers the following algorithmic question: C...