Formalization of Workflows and Their Correctness Issues 31

In this paper, main components of a workkow system that are relevant to the cor-rectness 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 workkow are represented through a notation based on set theory to make it possible to formalize the conceptual grouping of activities. Control-ow is represented as a special graph based on this set deenition, and it includes serial composition, parallel composition, conditional branching, and nesting of individual activities and conceptual activities themselves. Data-ow is represented as a directed acyclic graph in conformance with the control-ow graph. The formalization of correctness of concurrently executing workkow instances is based on this framework by deening two categories of constraints on the workkow environment with which the workkow instances and their activities interact. These categories are: Basic constraints that specify the correct states of a workkow environment. Inter-activity constraints that deene the semantic dependencies among activities such as an activity requiring the validity of a constraint that is set or veriied by a preceding activity. Basic constraints graph and inter-activity constraints graph which are in conformance with the control-ow and data-ow graphs are then deened 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 deened for an interleaved execution of workkow 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.