Nested Tracking Graphs

Nested Tracking Graphs

Nested Term Graphs

We report on work in progress on ‘nested term graphs’ for formalizing higher-order terms (e.g. finite or infinite λ -terms), including those expressing recursion (e.g. terms in the λ -calculus with letrec). The idea is to represent the nested scope structure of a higher-order term by a nested structure of term graphs. Based on a signature that is partitioned into atomic and nested function symb...

Positive Nested Conceptual Graphs

This paper deals with positive (i.e. without negation) nested conceptual graphs (NCGs). We first give a general framework graphs of graphs provided with morphism for defining classes of NCGs. Then we define a new class of NCGs typed NCGs and we show that known kinds of NCGs can be described very simply as classes of the general framework. All NCG models considered generalize the simple CG model...

Nested colorings of graphs

We develop a new upper bound, called the nested chromatic number, for the chromatic number of a finite simple graph. This new invariant can be computed in polynomial time, unlike the standard chromatic number which is NP -hard. We further develop multiple distinct bounds on the nested chromatic number using common properties of graphs. We also determine the behavior of the nested chromatic numb...

Nested Dynamic Condition Response Graphs

We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner Exformatics, a danish provider of case and workflow management systems. We formalize the semantics by giv...