Formal Software Specification with Refinements and Modules of Typed Graph Transformation Systems

The domain of transformation systems has been introduced to provide a general integration framework for formal specifications. In this chapter an application of the integration approach to less formal software specifications is discussed. For that purpose models given in the Unified Modeling Language (UML) are considered: class diagrams for the specification of the structure and architecture of the system, and statechart and sequence diagrams for the specification of its behaviour. Analogous to the applications to specification formalisms presented in the previous chapters, the basic idea here is to interpret specifications semantically by sets of transformation systems, exhibit their correspondences, and thereby to check whether a common interpretation of all considered specifications is possible. As opposed to the former examples, however, the investigation cannot be completely formal, since the semantics of the given UML languages is not formally defined. That means the correctness of the transformation system semantics cannot be formally proved. To cope with this situation the interpretation will be open w.r.t. certain semantic decisions, which is then treated as parameters of possible admissible interpretations. On the other hand, the interpretation in the transformation system reference model provides the means for the formalisation and thus precision of the considered software specification languages.KeywordsState MachineUnify Modeling LanguageClass DiagramSequence DiagramClass GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This report gives an overview of the current status and plans to construct a prototype environment of advanced tools for software and hardware development based on the use of wide-spectrum languages. The wide-spectrum languages include Anna (ANNotated Ada), and TSL (Task Sequencing Language). The tools described here provide interactive aid at all stages in the system development process. Special emphasis is placed on distributed computing, both in providing tools for handling parallelism in the subject system, and in designing tools that utilize parallelism in the programming environment. Applications of these tools include requirements analysis, formal specification, rapid prototyping, testing, formal verfication and construction of self-testing Ada software for multi-processor systems.The report describes an existing environment of prototype tools supporting applications of Anna and TSL to formal specification and testing of Ada software. The new environment tools will be based on component tools already developed at Stanford and proven to be portable to various Ada environments. All tools are implemented in Ada and are intended to interface with standard components of Ada programming environments.

High quality software components require a representation that allows the implementation-independent description of the structure and behavior of software components. Hence, the static as well as the dynamic structure of the system has to be represented in a structured way. Graph transformation systems support static and dynamic modeling through a single computational framework for the sake of correctness, maintainability, and integrity. The framework introduced along with the corresponding tool, UPGraDE (Universal Programmed Graph Grammar Development Environment), which is based on the universal graph language GRASP (GRAph grammar with Set Productions). Any type of system can be specified through a minimal set of operations (syntax) and rules to specify the behavior of any type of software (semantics). The UPGraDE Environment, consisting of several totally transparent interconnected modules, performing well defined tasks, is a highly modular and extensible environment suited for nearly every GRASP development purpose.

The main idea of graph grammars and graph transformation is the rule-based graph rewriting, where the application of every rule graph rule leads to a graph transformation step. Graph grammars can be used to generate graph languages which is similar to Chomsky grammars in formal language theory. Moreover, graphs can be used to model the states of all kinds of systems, which allows one to use graph transformation to model state changes in these systems. A rule-based transformation system may show two kinds of nondeterminism: (1) for each rule can exist several matches, and (2) several rules can be applicable. This paper concentrates on the second non-determinism, studying a method to detect the rules which are not applicable in graph transformation systems, proposing a backward graph transformation conflict detecting algorithm. At first the computation of conflict and dependency of two rules is available by use of AGG . Secondly the set of dependencies has to be tested by Warshall algorithm and the set of conflicts has to be computed by backward algorithm. At last, the termination of graph transformation systems and validity of rules can be detected as well.

A recent method combines model checkers with specifica- tion-based mutation analysis to generate test cases from formal software specifications. However high-level software specifications usually must be reduced to make analysis with a model checker feasible.

On translating UML models into graph transformation systems

In this work we show that the reachability problem for graph transformation systems is in the complexity class XP when parameterized with respect to the depth of derivations and the cutwidth of the source graph. More precisely, we show that for any set \(\mathcal {R}\) of graph transformation rules, one can determine in time \(f(c,d)\cdot |G|\cdot |H|^{g(c,d)}\) whether a graph G of cutwidth c can be transformed into a graph H in depth at most d by the application of graph transformation rules from \(\mathcal {R}\). In particular, our algorithm runs in polynomial time when c and d are constants. On the other hand, we show that the problem becomes NP-hard if we allow \(c=O(|G|)\) and \(d=5\). In the case in which all transformation rules are monotone we get an algorithm running in time \(f(c,d)\cdot |G|^{O(c)}\cdot |H|\). To prove our main theorems we will establish an interesting connection between graph transformation systems and regular slice languages. More precisely, we show that if \(\mathcal {A}\) is a slice automaton representing a set \({\mathcal {L}}_{{\mathcal {G}}}(\mathcal {A})\) of graphs, then one can construct in time linear in \(|\mathcal {A}|\) a slice automaton \(\mathcal {N}(\mathcal {A})\) representing the set of all graphs that can be obtained from graphs in \({\mathcal {L}}_{{\mathcal {G}}}(\mathcal {A})\) by the application of one layer of transformation rules in \(\mathcal {R}\).

Graph Transformation Systems (GTSs) provide visual and explicit semantics for dynamically evolving multi-process systems such as network programs and communication protocols. Existing symmetry reduction techniques that generate a reduced, bisimilar model for alleviating state explosion in model checking are not applicable to dynamic models such as those given by GTSs. We develop symmetry reduction techniques applicable to evolving GTS models and the programs that generate them. We also provide an on-the-fly algorithm for generating a symmetry-reduced quotient model directly from a set of graph transformation rules. The generated quotient model is GTS-bisimilar to the model under verification and may be exponentially smaller than that model. Thus, analysis of the system model can be performed by checking the smaller GTS-bisimilar model.

Non-functional requirements like performance and reliability play a prominent role in distributed and dynamic systems. To measure and predict such properties using stochastic formal methods is crucial. At the same time, graph transformation systems are a suitable formalism to formally model distributed and dynamic systems. Already, to address these two issues, Stochastic Graph Transformation Systems (SGTS) have been introduced to model dynamic distributed systems. But most of the researches so far are concentrated on SGTS as a modeling means without considering the need for suitable analysis tools. In this paper, we present an approach to verify this kind of graph transformation systems using PRISM (a stochastic model checker). We translate the SGTS to the input language of PRISM and then PRISM performs the model checking and returns the results back to the designers.

This paper proposes a methodology to analyze graph transformation systems by means of Alloy and its supporting tools. Alloy is a simple structural modeling language, based on first-order logic, that allows the user to produce models of software systems by abstracting their key characteristics. The tools can generate instances of invariants, and check properties of models, on user-constrained representations of the world under analysis. The paper describes how to render a graph transformation system —specified using AGG— as an Alloy model and how to exploit its tools to prove significant properties of the system. Specifically, it allows the user to decide whether a given configuration (graph) can be obtained through a finite and bounded sequence of steps (invocation of rules), whether a given sequence of rules can be applied on an initial graph, and, given an initial graph and an integer n, which are the configurations that can be obtained by applying a sequence of n (particular) rules.

The paper presents a conceptual framework for a module concept for graph transformation systems from a software engineering as well as from a theoretical point of view. The basic idea is to reuse concepts, which are known within or without the graph grammar field, to structure large specifications. These are the concept of distributed graph transformation systems, the concept of inheritance of specifications, and the import-export-interface concept. All these concepts are presented in a uniform framework based on the syntactical notion of a graph class specification and its semantics given by a graph transformation system. This is the basis for an explicit integration of these concepts and a corresponding specification language, to be discussed in a subsequent paper.

Agent systems demand from graph transformation systems not only an effectiveness of parsing but also supporting of the online derivation control (in order to visualize or control of their development). The way of the effective realization Derivation Control Environment for the distributed systems is presented. Finally, the computational effectiveness of the parsing, membership problems of the full graph transformation system is discussed.

Today, software system development (especially safety critical systems) is a complex task. Any bug in these systems may cause serious and costly problems. In this paper, we propose a formal and automatic approach to refinement of platform independent models to more platform specific ones. Using graph transformation systems as background formalism, we can validate the approach. For each level of abstraction, using the designed formal styles, we define proper graph rules to refine the models. Compared to the existing approaches which only consider the structural parts of the model, our proposed approach considers the behavioral parts of the models for refinement.

A rich concurrent semantics has been developed along the years for graph transformation systems, often generalizing in non-trivial ways concepts and results fist introduced for Petri nets. Besides the theoretical elegance, the concurrent semantic has potential applications in verification, e.g. in partial order reduction or in the use of finite prefixes of the unfolding for model checking. In practice (graph) transformation systems are often equipped with Negative Application Conditions, that describe forbidden contexts for the application of a rule. The talk will summarize some recent results showing that if the NACs are sufficiently simple (“incremental”) the concurrent semantics lifts smoothly to systems with NACs, but the general case requires original definitions and intuitions. Joint work with Reiko Heckel, Frank Hermann, Susann Gottmann and Nico Nachtigall

A heuristic solution for model checking graph transformation systems