Lexicographical Generations of Combined Traces

Combined traces are intrinsic mathematical model for studying concurrent systems behaviors. They can be used to describe and investigate processes of elementary net systems with inhibitor arcs and allow to describe weak causality and simultaneity of actions. We provide several algorithms for manipulating combined traces using their language theoretic representations. In particular, we propose two methods of enumeration related to combined traces, supported by a collection of auxiliary procedures. First, for a specified combined trace we iterate the set of all its representatives (namely step sequences). Next, we use the lexicographical order on step sequences to list all combined traces of a fixed size. We also discuss the time complexity of all presented algorithms.