Diagrams are always used when communicating complex situations. As a special case, dynamic processes like the token game in Petri-nets are made clear using dynamic diagrams. Animation techniques have to be used in order to achieve a comprehensible visualization. The paper discusses dynamic diagram languages with animations, i.e., animated diagram languages, and how to specify them. Specificatio...

In this paper we introduce the concept of directed hypergraph. It is a generalisation of the concept of digraph and is closely related with hypergraphs. The basic idea is to take a hypergraph, partition its edges non-trivially (when possible), and give a total order to such partitions. The elements of these partitions are called levels. In order to preserve the structure of the underlying hyper...

A transversal of a hypergraph is a set of vertices meeting all the hyperedges. A k-fold transversal of a hypergraph is a set of vertices such that every hyperedge has at least k elements of. In this paper, we prove that a k-fold transversal of a balanced hypergraph can be expressed as a union of k pairwise disjoint transversals and such partition can be obtained in polynomial time. We give an N...

Patterned self-assembly is a process whereby coloured tiles self-assemble to build a rectangular coloured pattern. We propose selfassembly (SA) hypergraph automata as an automata-theoretic model for patterned self-assembly. We investigate the computational power of SAhypergraph automata and show that for every recognizable picture language, there exists an SA-hypergraph automaton that accepts t...

We consider the problem of learning a hypergraph using edge-detecting queries. In this model, the learner may query whether a set of vertices induces an edge of the hidden hypergraph or not. We show that an r-uniform hypergraph with m edges and n vertices is learnable with O(24rm · poly(r, logn)) queries with high probability. The queries can be made in O(min(2r(logm + r)2, (logm + r)3)) rounds...

We present a theoretical study of new families of stochastic complex information modules encoded in the hypergraph states which are defined by the fractional entropic descriptor. The essential connection between the Lyapunov exponents and d-regular hypergraph fractal set is elucidated. To further resolve the divergence in the complexity of classical and quantum representation of a hypergraph, w...

We consider the following definition of connectedness in k-uniform hypergraphs: two j-sets (sets of j vertices) are j-connected if there is a walk of edges between them such that two consecutive edges intersect in at least j vertices. The hypergraph is jconnected if all j-sets are pairwise j-connected. We determine the threshold at which the random k-uniform hypergraph with edge probability p b...

My intention is to better understand message passing methods and algorithms so that I can develop and implement an algorithm to solve for a Nash equilibrium on a hypergraph (a graph in which the edges can contain more than two vertices). Although hypergraphs can be mapped to the space of bipartite graphs (by setting one part of the bipartite graph to be vertices and the other part to be edges i...

We present a dynamic data structure that keeps track of an acyclic hypergraph (equivalently, a triangulated graph) and enables verifying that adding a candidate hyperedge (clique) will not break the acyclicity of the augmented hypergraph. This is a generalization of the use of Tarjan’s Union-Find data structure for maintaining acyclicity when augmenting forests, and the amortized time per opera...

The hypergraph partitioning problem has many applications in scientific computing and provides a more accurate inter-processor communication model for distributed systems than the equivalent graph problem. In this paper, we propose a sequential multi-level hypergraph partitioning algorithm. The algorithm makes novel use of the technique of rough set clustering in categorising the vertices of th...