Formal specification of semantics of UML 2.0 activity diagrams by using Graph Transformation Systems Somayeh Azizi 1, Vahid Panahi 2 Computer science department, Sama Technical and vocational, Training School, Islamic university, Arak Branch Arak, Iran, s.azizi2011@gmail.com 2 Arak, Iran,v.p1386@gmail.com Abstract - Graphical structures of various kinds (like graphs, diagrams, visual sentences) are very useful to describe complex structures and systems. The field of Graph transformation and Abstract State Machine has been widely used for modeling. Graphs are well suited to describe the underlying structures of models. They provide a good method to carry out the analysis and verification activities and use from the AGG (Attributed Graph Grammar) tools for design them. So the Abstract State Machine (ASM) is a modern computation model. ASM based tools are used in academia and industry, albeit on a modest scale. They allow you to give high-level operational semantics to computer artifacts and to write executable specifications of software and hardware at the desired abstraction level. Keywords: Graph Transformation, Abstract state machine, Activity Diagram, Semantics, Verification and Validation I. INTRODUCTION Recently modeling is significant department of activities that it available introduction a proper software for security user requirement. Select proper model is base of modeling. For complete understanding of systems and specific relation between different stages of them, they should model. They are some approach for modeling such as: Unified modeling language(uml) Petri Nets The token flow semantics of UML2.0 activity diagrams is formally defined using Abstract State Machines and Graph Transformation System. The state of the art in semantics for UML 2.0 activity diagrams covers three distinct approaches: mapping to Petri-nets, using graph transformation rules, or providing pseudo-code. ASM using pseudo- code and graph transformation system using graph transformation rules for determine semantics. A major goal of this paper is ability to determine the correctness behavior and formal semantics of UML2.0 activity diagram by Graph Transformation System and Abstract state machine Graph Transformation system (GTS) Process Algebra State Diagrams The Unified Modeling Language (UML) is a graphical language for visualizing, specifying, constructing, and documenting the artifacts of a software system. UML Activity diagram is a visual representation of any system's activities and flows of data or control between activities. They describe the workflow behavior of a system. Activity diagrams are similar to state diagrams because activities are the state of doing something. The diagrams describe the state of activities by showing the sequence of activities performed. State diagram and activity diagrams both describe state transitions and share many of the same elements. The main reason to use activity diagrams is to model the workflows. Activity Diagrams are also useful for analyzing a use case by describing what actions need to take place and when they should occur. Currently, the UML semantics is informally defined in plain text and it is often unclear, ambiguous or it contains contradictory assertions. It is difficult to present the precise semantics which are taken as important in workflow system with the guide provided by OMG to the UML activity diagram. In this paper, the alternative approach of using Abstract State Machines and Graph Transformation System to formalize UML activity diagrams is presented. We propose the workflow modeling methodology by applying ASM and GTS semantics to the activity diagram. Through the exact definition to formal semantics based on ASM and GTS, it is possible to effectively model the workflow. II. RELATED WORK There is research done about formal specification semantics of uml2.0 activity diagram using different formal language. Harel defines state diagrams to model activities behavior in STATEMENT structured analysis notation. In resumption Eshuis used this method to describe the behavior of UML1.5 activity diagram. He defines concept of strong fairness that based on model should not be indefinite loops. He also indicated modeled in two levels: Requirement level semantics: This level is easy for analysis. Implementation-level semantics: This level is difficult for analysis but it provides a real vision of system Bogor used abstract state machine to describe UML2.0 activity diagrams. This method is based on event and per state is algebra. In ASM transition from one status to another status is done by rule if- then. Hausmann defines concept Dynamic Meta Modeling (DMM) using graph transformation systems. He developed the old graph rules by defining a new concept named rule invocation. In DMM there are two types of rules: big-step and small-step rules. Big-step rules act as traditional rules but small-step rules should be invoked by big-step rules. Haussmann then defines
semantics for Activity diagrams using concept of DMM. Engels use DMM and semantics defined by Haussmann for modeling and verification of workflows. For verification, he use GROOVE but as GROOVE does not support attributed typed graphs and rule invocation, they change the rules to be verifiable by GROOVE they check deadlock freeness and action reach ability properties on the modeled workflows. In contrast to this work, our approach has more flexibility to support user defined properties. Furthermore, event and exception modeling can be supported by our approach. Additionally, the extension defined by Haussmann (small/big step rules and rule invocation) cannot be modeled directly in existing graph transformation tools; hence it is not so easy for designers to use this approach. III. ACTIVITY DIAGRAM UML2.0 Activity Diagram modeling behavior aspect of software systems particular Data Flow and control Flow. Data Flow specific data transform from source path to destination and Control Flow specific existing paths for data transform an activity is operation sequence from start to end the system done and per activity can be transaction on data or process. A. Kind Of Activity Nodes 1. Action Node: An action node is a atomic stage in activity such as math function that they can manipulate data 2. Control Nodes: A control node is Responsible for routing of tokens. They routing based on decision node, fork node and join node. The tokens are production and consumption. B. Kind Of Control Nodes 1. Initial Node: An initial node Defines start of activity. This node has no input edge and it has only output edge. 2. Decision Node: A decision node has an input edge and more than one output edge. Input tokens are moving based on constraints on one of the output edges. The node will select different outputs based on a given Boolean expression. 3. Merge Node: A merge node have more than one input edges and only one output edge. This node each token to pass to side its output edge and they lead several workflow activities to a flow activity. 4. Fork Node: A fork node has only one input edge and more than output edge. Each input token is copied and passes through all the output edges. They are divided a flow to multiple simultaneous flow in an activity. 5. Join Node: A join node has more than input edge and only one output edge. If all incoming edges carry tokens In this case these nodes are used as a synchronization point. 6. Final Node Activity Final: An activity final node has one or more Than one input edge. If the first token to reach the node then sequence of all tokens immediately across the activity can be used and enforcement activity will stop. Flow Final: A flow final node has one or more than one input edge. This node uses each token entered and Lead to a path is ending. IV. Figure 1 Kind Of Action Nodes Figure 2 Kind Of Control Nodes GRAPH TRANSFORMATION Graph transformation is applied for simulating the behavior of models. It consists of three set: (i) type graph,(ii) host graph,(iii) rules. Hence per Graph transformation represents formally with triple AGT (TG, HG, R). The type graph (Meta model) defines the abstract syntax of a modeling language. Formally, it can be represented by a type graph (TG). Nodes in it called classes. Per class have attributes and functions. A host graph (Instance Models) describes the system define in modeling language. In fact it is a wellformed instance of the Meta model. A graph transformation rule describes dynamic behavior of graph transformation. Formally, A graph Transformation rule p = (L,R,N) consists of: a graph L being the left hand side (LHS) of the rule a graph R being the right hand side (RHS) of the rule; a set of graphs N being the negative application conditions (NACs). The application of a graph transformation rule transforms a graph G, the source graph, into a graph H, the target graph, by looking for an occurrence of L in G and then replacing that occurrence of L with R, resulting in H. The role of the NACs is that they can still prevent application of the rule when an occurrence of the LHS has been found, namely if there is an occurrence of some N N in G that extends th the candidate occurrence of L. [1,3] V. ABSTRACT STATE MACHINE The Abstract State Machine (ASM) Project (formerly known as the Evolving Algebras Project) was started by Yuri Gurevich as an attempt to bridge the gap between
formal models of computation and practical specification methods. A sequential ASM is defined as a set of transition rules of form : { If Condition then Updates },which transform first-order structures (the states of the machine), where the guard Condition, which has to be satisfied for a rule to be applicable, is a variable free firstorder formula, and Updates is a finite set of function updates (containing only variable free terms) of form: f (t1,...,tn):= t. The execution of these rules is understood as updating, in the given state and in the indicated way, the value of the function f at the indicated parameters, leaving everything else unchanged. (This proviso avoids the frame problem of declarative approaches.) In every state, all the rules which are applicable are simultaneously applied (if the updates are consistent) to produce the next state. If desired or useful, declarative features can be built into an ASM by integrity constraints and by assumptions on the state, on the environment, and on the applicability of rules. The ASM is formal and can therefore serve as a foundation for the implementation of tools. Finally, it helps to ensure that the specified behavior meets the intuition of the modeler. Abstract State Machine has a main rule that computation transition and uses from it for determine token flow semantics. The semantics of activity diagram determine base token flow. When token available in initial, object and action nodes then calling transition of rule. if guards evaluation true then token move toward destination nodes. [2] VI. WORKFLOW MODELING The modeling of workflow should treat of each element of the activity diagram was determined uses each node in activity diagram is equivalent to a class in this method. Each class consists of three parts, the class name, attributes and functions. Class name is equivalent to the node name and attributes of each class determine according to class name and action it. In the proposed method of functions are obtained from pseudo-code of state machine abstraction and attributes are Combination of characteristics in the graph transformation system and abstract state machine. In UMl2.0 semantic specification is based tokens. These diagrams explain each activity and its interactions in detail, including how it is triggered, what resources are needed and what deliverables will be created. This knowledge will enable you to discover and address any unstated requirements prior to finalizing the project plan. These workflow diagrams are key to effective analysis and communications. to model workflows we consider these parts of Activity diagrams: Init node, Final node, Action node, Fork node, Join node, Merge Figure 3 rules showing the semantics of Decision node
Figure 4 A sample activity diagram Figure 5 The sample activity diagram in fig3 as host graph with ASM and GTS node, Decision node We will use token-flow semantics in our graphs. In this paper we show determine semantics of decision node with ASM and GTS. Decision node: pseudo-code of decision node forall I with 1 I accepting Edges do t( I ) := new(token Offer) seq forall I with 1 I accepting Edges do t(i).offered Token := t. offered Token t(i).paths := {p element At(accepting Edges, i) p t. path } t(i).exclude := t. exclude {t(j) 1 j accepting Edges I j} t(i).include := t. include {t} add t(i) to offers (element At(accepting Edges, I ) In Figure3: The NAC of this rule states that both of the following nodes should not be Join or Merge nodes, because these nodes have several output edge, but
decision node chooses the output of a edge between its output edges. This restriction is implemented by the function Exclude. This function cause the tokens do, not clash together. We have different rules for cases that the following nodes are Join or Merge nodes. The LHS shows the precondition of this rule. If Decision node has the token and both of the following nodes have not any token, then this rule can be applied on the model and token will be routed to only one of the following nodes. Thus offer token entered into decision node and the value of the attribute inequality is false. Yet offers token not enter within nodes that they are outputs decision nodes. Guard adjective in one of the output nodes is True and order output node Labeled with else. As it is shown, the RHS says that offer token must be routed to only one of the following Nodes. Thus Is offer token out of the decision node and based on current conditions enter one of the output nodes. We will use Activity diagram of figure 3 as a running example for the rest of this paper. It describes the processing of orders in a company. Figure4 represent a workflow modeled with activity diagram.this activity can be image as host graph in graph transformation system. For each node in activity diagram, there is a node (class) in host graph.class diagrams have three parts: (i) class name, (ii) attributes, (iii) functions. Class name is name of node and one of attribute for node is token offer attribute. Token offers computation in initial node and this attribute values in initial node is not null and other nodes is null. By moving token in path and inter it at a node, calling functions and computation token offer it. When token arrives final node, the token offer attribute for preview nodes is null and for final node is not null. Therefore when token flow will be terminated that token arrives final node or there is not any path for token to be routed. VII. VERIFICATION AND VALIDATION The use of formal verification methods is essential in the design process of dependable computer controlled systems. The efficiency of applying these formal methods will be highly increased if the underlying mathematical background is hidden from the designer in such an integrated system effective techniques are needed to transform the system model to different sort of mathematical models supporting the assessment of system characteristics. To verification of activities must be design an approach. The theory and application of visual languages is also based on the strong paradigm of graph transformation. Therefore For analyze designed activities, graph transformation system (type graph, host graph, rules) and properties gets as input of verification approach. Graph transformation system must be design in AGG; also properties define by special rules. If designers are expert in graph transformation, they can directly to model workflows by using graph transformation system. In this approach designers do not need to learn of formal method. In other case, they can model workflows by UML2.0 activity diagram, then by transformer, designed activities in UML transformed to graph transformation. In this approach verification done automatically and designers do not need to define of rules for verification. VIATRA (Visual Automated Transformations) is a model transformation framework developed mainly for the formal dependability analysis of UML models. In VIATRA, Meta modeling is conceived specially: the instantiation is based on mathematical formalisms and called Visual Precise Meta modeling. The attribute transformation is performed by abstract state machine statements, and there is built-in support for attributes of basic Java types. The model constraints can be expressed by graph patterns with arbitrary levels of negation. The rule constraints are also specified by graph patterns. VIATRA uses abstract state machines (ASM) to define the control flow of the system.[1,3] VIII. CONCLUSION This paper proposes a formal approach base compose Graph Transformation Systems (GTS) and Abstract State Machine (ASM). This approach determines behavior of UML2.0 activity diagrams base token flow. Rules of ASM that define with pseudo-code, display by fundamental element of GTS (LHS, RHS, NAC). REFERENCES [1] Vahid Rafe, Adel T. Rahmani, Formal Analysis of Workflows Using UML 2.0 Activities and Graph Transformation Systems ICTAC 2008, LNCS 5160, pages. 305 318, 2008. [2] Stefan Sarstedt, Walter Guttmann, An ASM Semantics of Token Flow in UML2.0 Activity Diagrams, 2008. [3] Laszlo Lengyel, Tihamer Levendovszky, Gergely Mezei and Hassan Charaf, Model Transformation with a Visual Control Flow Language, International Journal of Computer Science Volume1 Number 1, 2005.