Given integers k ≥ 2 $k\ge 2$ and a 1 , … ${a}_{1},\ldots ,{a}_{k}\ge 1$ let ≔ ( ) ${\boldsymbol{a}}:= ({a}_{1},\ldots ,{a}_{k})$ n + ⋯ $n:= {a}_{1}+\cdots \,\,+{a}_{k}$ . An a-multiset permutation is string of length $n$ that contains exactly i ${a}_{i}$ symbols $i$ for each = $i=1,\ldots ,k$ In this work we consider the problem exhaustively generating all ${\boldsymbol{a}}$ -multiset permutat...

We introduce the multiset sampler (MSS), a new Metropolis-Hastings algorithm for drawing samples from a posterior distribution. The MSS is designed to be effective when the posterior has the feature that the parameters can be divided into two sets: X, the parameters of interest and Y , the nuisance parameters. We contemplate a Metropolis-within-Gibbs sampler that iterates between X moves and Y ...

Rule-based languages are being used for ever more ambitious applications. As program size grows however, so does the overhead of team-based development, reusing components, and just keeping a large flat collection of rules from interfering. In this paper, we propose a module system for a small logicallymotivated rule-based language. The resulting modules are nothing more than rewrite rules of a...

We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different applications including breaking symmetry and fuzzy constraint satisfaction. We propose and implement an efficient linear time algorithm for enforcing generalised ar...

Traditional multiset rewriting arises from a fragment of polarized linear logic, deriving its semantics from focused proof search. In recent years, languages based on multiset rewriting have been used for ever more ambitious applications. As program size grows however, so does the overhead of team-based development and the need for reusing components. Furthermore, there is a point where keeping...

We revise multiset rewriting with name binding, by combining the two main existing approaches to the study of concurrency by means of multiset rewriting, multiset rewriting with existential quantification and constrained multiset rewriting. We obtain ν-MSRs, where we rewrite multisets of atomic formulae, in which some names may be restricted. We prove that ν-MSRs are equivalent to a class of Pe...