Petri Net Synthesis for Conflict Free Resource Allocation in Discrete State Systems

The theory of Petri nets that was conceived to model the interactions between asynchronous concurrent processes, can be extended to explore conflicts and delineate the options available to resolve such conflicts in such processes. To this end we define the property of essentially decision free places (EDF places) in Petri nets to represent the absence of conflicts in resource allocations. Using the theory of net invariants we develop a procedure for identifying non-EDF places in the synthesized logic. Furthermore, we outline a technique of resolving such contlicts with the use of ’NOT’ arcs in the Petri net. Some results in the synthesis of Petri net models of discrete state systems are provided as a prelude to the theory of EDF-ness. Acknowledgements The completion of this dissertation would not be possible but for the hearty indulgence of many individuals. Special recognition must go to my advisor Prof. Bruce H. Krogh, who suggested this topic, provided able guidance, encouragement, and valuable suggestions throughout the course of this work; his insightful attention to detail was an important influence in this dissertation. I also wish to thank the rest of my thesis committee composed of Prof. Ram Akella, and Prof. Jose Moura. With a deep sense of gratitude I wish to express my thanks to my parents, Prof. and Mrs. Ramji Rao, for their constant affection, encouragement and interest in my academic career. To them I dedicate this dissertation. My thanks are due to my many teachers, without whose benediction I would not be what I am today. I also wish to thank the indian student community at the Carnegie-Mellon University, for putting me up for the first few weeks of my arrival at Pittsburgh. Particularly, I would like to thank Shyam and Raj for mitigating my painful transition from FORTRAN to C. My fellow students deserve my appreciation, particularly Pete, Dai, Chris, Jay, and the rest of the Porter Hall flock for the many hours of interesting intellectual company.