BPMN and Beyond Business process modelling notation, workflow ...

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4 Bernhard Thalheim and Klaus-Dieter Schewe In order to develop usable websites the story of the application has to be neatly supported [9, 12, 10, 14]. Interaction modelling include modelling of environments, tasks and actors beside modelling of interaction flow, interaction content and interaction form [7]. 1.4 Achievements of the ASM Approach The abstract state machine (ASM) method nicely supports high-level design, analysis, validation and verification of computing systems: – ASM-based specification improves industrial practice by proper orchestration of all phases of software development, by supporting a high-level modelling at any level of abstraction, and by providing a scientific and formal foundation for systems engineering. All other specification frameworks known so far only provide a loose coupling of notions, techniques, and notations used at various levels of abstraction. By using the ASM method, a system engineer can derive a general applicationoriented understanding, can base the specification on a uniform algorithmic view, and can refine the model until the implementation level is achieved. The three ingredients to achieve this generality are the notion of the ASM itself, the ground model techniques, and the proper treatment of refinement. – Abstract state machines entirely capture the four principles [16] of computer science: structuring, evolution, collaboration, and abstraction. communication cooperation coordination state ❍✟ architecture modelling mapping refinement ❍❍ ✟✟ structuring ❍❍ ✟✟ collaboration ❍❍ interaction distribution ❍ agents systems ✁ ✁✁ ❆ ❆ ❆ evolution ❆ ✁ ❍❍ evolvement ✟ temporal development ❍ integration rules migration ❆❆ ✁ ✁ conservative component abstraction ✘✘ abstraction abstraction ✟✟ ❍❍ ❍❍ localisation abstraction approximation implementation abstraction Fig. 1. The four principles of Computer Science This coverage of all principles has not been achieved in any other approach of any other discipline of computer science. Due to this coverage, the ASM method underpins computer science as a whole. We observe the following by comparing current techniques and technologies and ASM methods: ASM are running in parallel. Collaboration is currently mainly discussed at the logical or physical level. Evolution of systems is currently considered to be a hot but difficult topic. Architecture of systems has not yet been systematically developed. – The ASM method is clearly based on a number of postulates restricting evolution of systems. For instance, sequential computation is based on the postulate of sequential time, the postulate of abstract state, and the postulate of bounded exploration of the state space. These postulates may be
ASM Foundations of Database Management 5 extended to postulates for parallel and concurrent computation, e.g., by extending the last postulate to the postulate of finite exploration. 2 ASM Specification of Database Systems Database systems are designed to operate in parallel. Operating of databases systems can be understood in a state-based approach. 2.1 ASM Specification of Databases and Database Structuring The abstract state machine approach allows simple and refinable specification of parallel processes based on states and transitions. The ASM signature S is a finite collection of function names. – Each function name f has an arity, a non-negative integer. – Nullary function names are called constants. – Function names can be static or dynamic. – Every ASM signature contains the static constants undef, true, false. A database schema may be based on a collection of (predicative) functions representing the structures of the database. Typically such functions are dynamic. Static functions are those functions that do not change over time. Most generic database computation functions such as the aggregation functions can considered to be static. They are defined as static higher-order functions. Their concretisation to database functions may lead to a dynamic functions or may still be static. Database state functions are however dynamic. The signature S is the main component of alphabet for the logical language L S . We assume that this language is specified in the canonical way used in predicate logics. An ASM database schema S is given by a signature S and by a finite set Σ of formulas from L S . We restrict the consideration in this paper to the tuple (or product) constructor. The set, list, multiset, disjoint union, labelling and naming constructors can be treated in a similar way. A database state DB (or database instance) for the signature S is a nonempty set V al called the superuniverse of DB, together with an interpretation f DB of each function name f in S. – If f is an n-ary function name of S, then f DB : V al n → V al. – If c is a constant of S, then c DB ∈ V al. – The superuniverse V al of the state DB is denoted by V al(DB). Relations are functions that have the value true, false, undef (ā ∈ R iff R(ā) = true). dom(f DB ) = {(a 1 , ..., a n ) ∈ V al(DB) n | f DB (a 1 , ..., a n ) ≠ undef } rel(f DB ) = {(a 1 , ..., a n ) ∈ V al(DB) n | f DB (a 1 , ..., a n ) = true} The superuniverse can be divided into subuniverses represented by unary relations. These unary relations form the basic data types under consideration. A
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BPMN and Beyond Business process mo
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[Tha00] B. Thalheim. Entity-relatio
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can be defined elementwise, constru
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Our target reader is either knowled
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3 Framework for BPMN Execution Mode
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is usually required to be an atomic
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workflow designer to define in a si
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AndJoinGateTransition(node) = Workf
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that it does not depend only on the
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elow, an instance of WorkflowTransi
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as they arrive” [15, Sect.9.3.3 p
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to whose boundary e is attached and
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if active(targetAct(e)) then Consum
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. . . with the assistance of a soft
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