Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Computer Science

Supervisor

Dr. Steven beauchemin

2nd Supervisor

Dr. John Barron

Joint Supervisor

Abstract

Workflow-nets are mathematical frameworks that are used to formally describe, model and implement workflows. First, we propose critical section workflow nets (abbreviated WFCSnet). This framework allows feedbacks in workflow systems while ensuring the soundness of the workflow. Feedback is generally not recommended in workflow systems as they threaten the soundness of the system. The proposed WFCSnet allows safe feedback and limits the maximum number of activities per workflow as required. A theorem for soundness of WFCSnet is presented. Serializability, Separability, Quasi-liveness and CS-Properties of WFCSnet are examined and some theorems and lemmas are proposed to mathematically formalize them. In this thesis, we define some formal constructs that we then build upon. We define the smallest formal sub-workflow that we call a unit. We propose some mathematical characteristics for the unit and show how it can be used. We study similarities between units and whether two units can be used interchangeably or not. We then use composites out of simple units to build more complex constructs and we study their properties. We define the concept of cooperation and propose a mathematical definition of the concept. We discuss the concept of task coverage and how it affects cooperation. We claim that task coverage is necessary for any task to be achieved and therefore, a necessity for cooperation. We use mathematical methods to determine the task coverage and the candidate cooperative partners based on their capabilities that can contribute to the desired task. Workflow-net based cooperative behaviour among agents is proposed. First, we propose a cooperative algebra, which takes the desired objective of cooperation as a plan and then transforms this plan into a workflow-net structure describing dependencies and concurrency among sub-workflow elements constituting the overall plan. Our proposed cooperative algebra converts the plan into a set of matrices that model the cooperative workflow among agents. We then propose a cooperative framework with operators that assign tasks to agents based on their capabilities to achieve the required task.

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