An algebra of Petri nets with arc-based timing restrictions
Human beings from the moment they understood the power of their brain tried to create things to make their life easier and satisfy their needs either physical or mental. Inventions became more and more complicated, covering almost every aspect of human life and satisfying the never ending human curiosity. One of the reasons for this complexity is that an increasing number of systems exhibit concurrency. The development of concurrent systems is generally challenging since it is more difficult to fully understand their exact behaviour. In this thesis We present and investigate two of the most widely used and well studied theories to capture concurrent behaviour. Based on the results of PBC, we develop two algebras, one based on term re-writing and the other on Petri nets, aimed at the Specification and analysis of concurrent systems with timing information. The former is based on process expressions (at-expressions) and employs a set of SOS rules providing their operational semantics. The latter is based on a class of Petri nets with time restrictions associated with their arcs, called at-boxes, and the corresponding transition firing rule. We relate the two algebras through a compositionally defined mapping which for a given at-expression returns an at- box with behaviourally equivalent transition system. The resulting framework consisting of the two algebras is called the Timed-Arc Petri Box Calculus, or atPBC.