With the successful development of efficient algorithms for Frequent Subgraph Mining (FSM), this paper extends the scope of subgraph mining by proposing Vertex Unique labelled Subgraph Mining (VULSM). VULSM has a focus on the local properties of a graph and does not require external parameters such as the support threshold used in frequent pattern mining. There are many applications where the m...

We discuss a new notion of pattern avoidance motivatedby operad theory: pattern avoidance in planar labelled trees. It is a generalisation of various types of consecutive pattern avoidance studied before: consecutive patterns in words, permutations, colouredpermutations, etc. ThenotionofWilf equivalence for patterns in permutations admits a straightforward generalisation for (sets of) tree patt...

An Abstract The paper presents a labelled tableau system for S4.3, based on D'Agostino, Mondadori system KE [1] for Classical Propositional Logic and labelled rules for S4 of Fitting [4]. Weak connectedness is provided by the unique, nonbranching ν-rule. The system is analytic and provides decision procedure

In this paper we introduce a new class of labelled transition systems Labelled Markov Processes and define bisimulation for them. Labelled Markov processes are probabilistic labelled transition systems where the state space is not necessarily discrete, it could be the reals, for example. We assume that it is a Polish space (the underlying topological space for a complete separable metric space)...

We describe a class of C∗-algebras which simultaneously generalise the ultragraph algebras of Tomforde and the shift space C∗-algebras of Matsumoto. In doing so we shed some new light on the different C∗-algebras that may be associated to a shift space. Finally, we show how to associate a simple C∗-algebra to an irreducible sofic shift. keywords: C∗-algebras, labelled graph, ultragraph, Matsumo...