Concurrent systems such as communication protocols, industrial control systems, discrete-event systems, flexible manufacturing systems (FMS), etc. employ multiple processors to speed up the execution, automate the process, and increase the throughput. PNs have been used for modeling and analyzing concurrent systems. The net behavior can be obtained with reachability analysis. The size of reachability graph depends not only on the structure of the net but also on the initial marking.

As a result, the size of Petri nets in the literature over the last two decades is limited. It is interesting to explore the mathematical theory that can deal with very (infinitely) large nets. For instance, the mathematical tool of integer linear programming programs has been successful in synthesizing optimal supervisors for FMS. However, it is an NP-complete problem and the time and memory required grow explosively with the size of the system. Later on, the same problem is reduced to solve linear systems of equations via clever mathematics. Furthermore, for special subclass of nets, closed-form solutions exist, essentially extending the solution to super-large systems, while being even much faster.

This special issue solicits papers that deal with closed-form mathematical problems for more complicated classes of nets or more advanced mathematical theory. Papers dealing with mathematical (such as dynamic or mixed integer programming, stochastic Monte Carlo methods, numerical methods and simulation operation research, etc.) problems and solutions in these areas are also welcomed.

Potential topics include, but are not limited to:

• High assurance systems
• Software design and systems
• Real time systems
• E-commerce
• SOA
• Web-service
• Biological systems
• Distributed systems
• Parallel and distributed programming
• Logical controller design
• Formal specification, specification validation, and testing
• Fault-tolerant systems
• Multiagent systems
• Workflow management
• Model checking