A deductive system for proving workflow models from operational procedures

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Abstract

Many modern business environments employ software to automate the delivery of workflows; whereas, workflow design and generation remains a laborious technical task for domain specialists. Several different approaches have been proposed for deriving workflow models. Some approaches rely on process data mining approaches, whereas others have proposed derivations of workflow models from operational structures, domain specific knowledge or workflow model compositions from knowledge-bases. Many approaches draw on principles from automatic planning, but conceptual in context and lack mathematical justification. In this paper we present a mathematical framework for deducing tasks in workflow models from plans in mechanistic or strongly controlled work environments, with a focus around automatic plan generations. In addition, we prove an associative composition operator that permits crisp hierarchical task compositions for workflow models through a set of mathematical deduction rules. The result is a logical framework that can be used to prove tasks in workflow hierarchies from operational information about work processes and machine configurations in controlled or mechanistic work environments.

Highlights

► A k-dimensional Petri net (called a k-PN) presented in Section 2.2 and Definition 4. ► Functions to map actions involving pre and post conditions to k-PN in Section 4.1. ► In Section 4.2, a functional form of k-PN called a k-PN template was presented. ► Associative serial combination operator () for k-PN templates followed by proofs. ► Efficient hierarchical composition and query methods for action k-PN templates.

Introduction

In structured business environments formalisms may be applied to inform  workflow management. In modern environments, many organisations already manage workflow through computer programs known as workflow management systems (WfMS). WfMS emerged in the mid 90s when Van der Aalst et al. argued in [1] in favour of conceptual formalisms for workflow management systems, which lead to an initiative (see [2]) to catalogue workflow patterns towards formalising WfMS called the Workflow Patterns Initiative.1

An outcome of the Pattern Initiative was YAWL (Yet Another Workflow Language), which is a formal language that has been developed around state-transition systems called Petri nets, to define control procedures in workflow management [3]. In the same context as other workflow languages such as the Business Process Execution Language (BPEL) [4] or scientific workflow languages such as Simple Conceptual Unified Flow Language (SCUFL) that is executable on the Taverna or myGrid software tools [5], YAWL is a model definition language that can be executed on the YAWL engine [6]. The YAWL engine, which has been developed from surveys of other reputable WfMS [2], [7], involves an editor that permits users to create workflow model diagrams as annotated and directed networks of motifs, where each motif represents a control rule in the YAWL language. In delivery of workflow signals, the YAWL engine can convert workflow model diagrams to Petri-net based state machines that inform control signals and data exchanges through network interfaces with workflow events. In summary, this style of WfMS automates workflow through formally specified programs. The benefit of this style of WfMS is certainly workflow automation; however at the horizon of this automation, workflow language experts are still required for workflow model development. With that summary we arrive at the problem for this paper, which is how tasks in workflow models can be algebraically defined and applied to extend the horizon of automation for WfMS.

In controlled work environments, problems of workflow modelling may be sufficiently consistent to be solved with mathematical methods. An example can be seen in [8] with the problem of work allocations and peak load management for cloud servers, where the problems could be solved as constraint satisfaction problems. Even systems based on semantics and conceptual conventions such as web ontologies can have support for concrete knowledge systems improved with mathematical deduction and predicate logic [9], which could conceivably be applied to workflow systems. The need for mathematical systems to solve workflow modelling problems can be further seen where the analysis and deduction of workflows have been done in agent-based model simulations. In [10], very precise details of the actions and events have been mathematically defined for a set of workflow agents and logical systems of deduction and induction, such as the ProM process mining tool (see [11]), were applied to recover workflow models for analysis. In this paper we present an approach using mathematical deduction to algebraically derive tasks for workflow models from resource data in work environments that may be characterised as mechanistic or involving sufficiently detailed tasks for a logical deductive approach. This approach can avoid some of the errors that probabilistic process mining methods can introduce to derived workflow models. Moreover, the deductive process we present here operate on templates of tasks, where those templates can be transported to and mathematically tested in different work environments, which permits efficient reuse of task templates.

Many authors have considered the problem of automatic workflow generation or process mining for workflow models. In addition to ProM and other process mining approaches in [11], van der Aalst in [12] proposed that Bills-of-Materials (BOMs) could be used to establish a template for workflow. In this context, a BOM is a hierarchically ordered set of materials that must be assembled in order to create a product, where the assembly steps characterise the work that must be done in a workflow. In this paper, we have developed a mathematical framework that can be applied to hierarchically deduce task templates for workflow models from operational level attributes. Our framework addresses several problems associated with current approaches. Process mining that relies on probabilistic approaches can involve errors that can be avoided in cases where workflow tasks can be derived algebraically. The transplanting of workflow models to different work environments can involve additional tailoring of the model, where the task templates defined in our systems can be efficiently tested for inclusion into different work environments and thus can be used to minimise workflow tailoring processes. In addition, our framework addresses the problem of deducing high-level task templates from plans, derived through automatic planning algorithms such as STRIPS, that can be tested in other work environments. In our framework, we have formalised a template construct about Petri nets that allows rapid testing and automatic recombinations and deductions of workflow tasks. In arriving at the particular details for our framework, Section 2 provides a summary of Petri nets and Petri-net based WfMS along with a multidimensional form of Petri nets called k-PN underpinning our framework; Section 3 visits automatic planning through discussion about STRIPS as a conduit for algebraic workflow deduction; Section 4 develops an isomorphism between logical operators used in automatic planning and additive operators defined for a class of k-PN; in addition, this section extends k-PNs to templates isomorphic to action operators used in STRIPS, provides and proves a serial combination operator for these templates and proves the associativity of this operator for hierarchical compositions; Section 5 looks at some practical applications and consequences for our framework; Section 6 gives a summary of the framework and its applications to discuss additional problems and further work.

Section snippets

Workflow management systems

YAWL is a very expressive workflow language based on rigorous analyses of existing workflow management systems and workflow languages [3], [13]. The Workflow Pattern Initiative has evaluated several workflow products and have found considerable differences in their expressive powers. YAWL is a workflow language that has evolved around a class of state-transition systems called Petri nets for their suitable levels of expressivity in representing workflows.

Automatic planning

Workflow management systems that rely on workflow languages also rely on human input to encode workflow models. Human encoding implies a level of expertise that may be required many times in optimising a workflow; whereas, some kind of automation for this process could reduce or eliminate cost. Towards that end, this section looks at automatic planning as a candidate approach for algebraic workflow deduction.

Automatic planning deals with knowledge representations for actions and the problem of

A k-PN template for action operators

In a k predicate world, an action operation may be modelled using a k-PN that involves single input and output places configured with vectors that represent the input and output models of action operations; we will call such a k-PN an action k-PN. In this context, we will continue to use the definitions for model and model to set function ϕ from Section 3.1. We have chosen an arrangement for action k-PN where the vector elements have a one-to-one correspondence with the k predicates and each

A system of workflow model deductions

At operational levels of a business, tasks are physically constrained by space and time to a finite set of atomic actions over a finite and discrete set of resources. Even in a business context where jobs may enter production with irregular specifications, the list of known actions over a set of resources given the set of jobs to date, will be always be finite and discrete. This property ensures that the known list of atomic actions for each resource will be finite and enumerable. In many

Conclusion and further work

In this paper we have proven a deductive system that can be used to associate and transform information gathered from the operational levels of businesses for different levels of management. We envisage business environments where section supervisors would maintain data about production units in information systems, in the form of action operators and action k-PN templates. Different levels of management could benefit from queries involving the combination operator () and associative

Rune Rasmussen is a Research Associate in the Mathematical, Information and Physical Sciences (MIPS) discipline at the Queensland University of Technology in Australia. In 2008, Rune completed his Ph.D. thesis, which dealt with an intractable problem of solving a board game called Hex. Rune is currently involved with the Australian Smart Services CRC on projects that aim to inform business process management through simulation. Broadly, his research activities can be best categorised as:

  • 1.

References (20)

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Cited by (3)

Rune Rasmussen is a Research Associate in the Mathematical, Information and Physical Sciences (MIPS) discipline at the Queensland University of Technology in Australia. In 2008, Rune completed his Ph.D. thesis, which dealt with an intractable problem of solving a board game called Hex. Rune is currently involved with the Australian Smart Services CRC on projects that aim to inform business process management through simulation. Broadly, his research activities can be best categorised as:

  • 1.

    Business Process Simulation (including 3D virtual world)

  • 2.

    Computational Statistics

  • 3.

    Statistical Ecology and Modelling

  • 4.

    Artificial Intelligence and Machine Learning

  • 5.

    Combinatorial Game Theory

Ross Brown is a Senior Lecturer with the Faculty of Science and Technology, in the Bachelor of Games and Interactive Entertainment degree. He is also a member of the QUT Business Process Management (BPM) Research Group.

Ross does research in the application of 3D games technology to other research domains. In particular, his research involves the development of virtual world technology for representing BPM information. Executable workflows embedded in virtual environments, collaborative 3D process modelling and the 3D spatial visualisation of process models. The Smart Services Collaborative Research Centre in Australia financially supports a number of his research projects.

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