Advanced Branching and Synchronization Patterns Description Using Pi-Calculus

2.1 Related Work

A Ph.D. thesis by Twan Basten researches basic process algebra and Petri nets (Basten, 1998) . A more practical approach of using CCS (Milner R., 1999) to formalize web service choreography can be found in (Brogi A. C., 2004). Another approach of giving a detailed representation of the workflow patterns has been made with YAWL (van der Aalst W. t., 2003). The only approach known to the authors on the use of the Pi-calculus for workflow definitions is from Yang Dong and Zhang Shen-Sheng and centers on basic control flow constructs and the definition of activities (Dong & Dadam, 2003).Pi-calculus and Petri nets provide theoretical support for most business process standard (Gang Xue, 2008). Recently, Pi-calculus is also used to formalize web service interactions. Reference (Decker G. F., 2006) describes and formalizes web services using Pi-calculus, and the model described has been verified (Decker G. F., 2006).

2.2 Advanced Branching and Synchronization Patterns

The Workflow Patterns Initiative was established with the aim of delineating the fundamental requirements that arise during business process modeling on a recurring basis and describe them in an imperative way. There are eight kinds of the workflow patterns. They are as follows (Russell N. A., 2006): Basic Control Flow Patterns, Advanced Branching and Synchronization Patterns, Multiple Instance Patterns, State-based Patterns, Cancellation and Force Completion Patterns, Iteration Patterns, Termination Patterns, Trigger Patterns. Advanced Branching and Synchronization Patterns presents a series of patterns which characterize more complex branching and merging concepts which arise in business processes .This kind of patterns contains the most pattern and changes in various forms. This paper is mainly used to describe the kind of Advanced Branching and Synchronization Patterns using Pi-calculus.

2.3 Pi- Calculus

The Pi-calculus is a modern process algebra that describes mobile systems in a broader sense (Milner R. J., 1990). We give a brief presentation of the syntax and semantics of the Pi-calculus in this section. The syntax of Pi-calculus is given below by the following equation (Milner R. J., 1990).

This paper will use the concept of the counter built using the pi-calculus. Counter is defined as follows (Milner R., 1999): and . is used to increase the counter and is used to reduce the counter until the counter is 0.