Abstract
Embedded real-time systems generate state sequences where time elapses between state changes. Ensuring that such systems adhere to a provided specification of admissible or desired behavior is essential. Formal model-based testing is often a suitable cost-effective approach. We introduce an extended version of the formalism of symbolic graphs, which encompasses types as well as attributes, for representing states of dynamic systems. Relying on this extension of symbolic graphs, we present a novel formalism of timed graph transformation systems (TGTSs) that supports the model-based development of dynamic real-time systems at an abstract level where possible state changes and delays are specified by graph transformation rules. We then introduce an extended form of the metric temporal graph logic (MTGL) with increased expressiveness to improve the applicability of MTGL for the specification of timed graph sequences generated by a TGTS. Based on the metric temporal operators of MTGL and its built-in graph binding mechanics, we express properties on the structure and attributes of graphs as well as on the occurrence of graphs over time that are related by their inner structure. We provide formal support for checking whether a single generated timed graph sequence adheres to a provided MTGL specification. Relying on this logical foundation, we develop a testing framework for TGTSs that are specified using MTGL. Lastly, we apply this testing framework to a running example by using our prototypical implementation in the tool AutoGraph.
Highlights
Software has become an intrinsic part of parallel embedded real-time systems, which need to realize increasingly advanced functionality with complex coordination behavior
Step 3 (Check satisfaction for timed graph sequences (TGSs) given by GH): We check in the node marked 3 whether the current graph with history represented by m : Gi GHi satisfies the encoded metric temporal graph conditions (MTGCs) ψ in the form of the basic graph conditions (BGCs) φ
To improve available support for model-based development of a wide variety of systems that must adhere to a given specification, we introduced a test-based approach for the modeling formalism of timed graph transformation systems (TGTSs)
Summary
Software has become an intrinsic part of parallel embedded real-time systems, which need to realize increasingly advanced functionality with complex coordination behavior. Ing the applicability by allowing to discard parts of matches using contexts, (d) the extension/adaptation of MTGL from [38,81] described above that permits to express more complex metric temporal properties, and (e) the prototypical implementation of all notions and constructions relevant to our formal testing approach in the tool AutoGraph. We envision to improve upon the following aspects of the introduced approach: (a) its effectiveness, by considering suitable additional operators, (b) its efficiency, by applying incremental pattern matching techniques for the generation of timed graph sequences from the TGTS at hand as well as for checking the satisfaction of conditions of MTGL, and (c) its applicability, by developing new means for presenting violations and for filtering definite and potential violations. Note the glossary on page 73 covering most symbols introduced throughout the paper
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