Formalization of workflows and correctness issues in the presence of concurrency

In this paper, main components of a workflow system that are relevant to the correctness in the presence of concurrency are formalized based on set theory and graph theory. The formalization which constitutes the theoretical basis of the correctness criterion provided can be summarized as follows: Activities of a workflow are represented through a notation based on set theory to make it possible to formalize the conceptual grouping of activities. Control-flow is represented as a special graph based on this set definition, and it includes serial composition, parallel composition, conditional branching, and nesting of individual activities and conceptual activities themselves. Data-flow is represented as a directed acyclic graph in conformance with the control-flow graph. The formalization of correctness of concurrently executing workflow instances is based on this framework by defining two categories of constraints on the workflow environment with which the workflow instances and their activities interact. These categories are: Basic constraints that specify the correct states of a workflow environment. Inter-activity constraints that define the semantic dependencies among activities such as an activity requiring the validity of a constraint that is set or verified by a preceding activity. Basic constraints graph and inter-activity constraints graph which are in conformance with the control-flow and data-flow graphs are then defined to represent these constraints. These graphs are used in formalizing the intervals among activities where an inter-activity constraint should be maintained and the intervals where a basic constraint remains invalid. A correctness criterion is defined for an interleaved execution of workflow instances using the constraints graphs. A concurrency control mechanism, namely Constraint Based Concurrency Control technique is developed based on the correctness criterion. The performance analysis shows the superiority of the proposed technique. Other possible approaches to the problem are also presented.