Formal methods are mathematically-based techniques for specifying, developing and verifying a component or system for increasing the confidence regarding the reliability and robustness of the target. It can be used at different levels with different techniques, and one approach is to use model-oriented formal languages such as VDM languages in writing specifications. During model development, we can test executable specifications in VDM-SL and VDM++. In a lightweight formal approach, we test formal specifications to increase our confidence as we do in implementing software code with conventional programming languages. For this purpose, millions of tests may be conducted in developing highly reliable mission-critical software in a lightweight formal approach. In this paper, we introduce our approach to supporting a large volume of testing for executable formal specifications using Hadoop, an implementation of the MapReduce programming model. We are able to automatically distribute an interpretation of specifications in VDM languages by using Hadoop. We also apply a property-based data-driven testing tool, , over MapReduce so that specifications can be checked with thousands of tests that would be infeasible to write by hand, often uncovering subtle corner cases that wouldn't be found otherwise. We observed effect to coverage and evaluated scalability in testing large amounts of data for executable specifications in our approaches.

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Formal methods are mathematically-based techniques for specifying, developing and verifying a component or system for increasing the confidence regarding the reliability and robustness of the target. It can be used at different levels with different techniques, and one approach is to use model-oriented formal languages such as VDM languages in writing specifications. During model development, we can test executable specifications in VDM-SL and VDM++. In a lightweight formal approach, we test formal specifications to increase our confidence as we do in implementing software code with conventional programming languages. For this purpose, millions of tests may be conducted in developing highly reliable mission-critical software in a lightweight formal approach. In this paper, we introduce our approach to supporting a large volume of testing for executable formal specifications using Hadoop, an implementation of the MapReduce programming model. We are able to automatically distribute an interpretation of specifications in VDM languages by using Hadoop. We also apply a property-based data-driven testing tool, , over MapReduce so that specifications can be checked with thousands of tests that would be infeasible to write by hand, often uncovering subtle corner cases that wouldn't be found otherwise. We observed effect to coverage and evaluated scalability in testing large amounts of data for executable specifications in our approaches.

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An automotive control system is a typical safety-critical embedded software, which requires extensive verification and validation (V&V) activities. This article introduces a toolset for automated V&V of automotive control system, including a test generator for automotive operating systems, a task simulator for validating task design of control software, and an API-call constraint checker to check emergent properties when composing control software with its underlying operating system. To the best of our knowledge, it is the first integrated toolset that supports V&V activities for both control software and operating systems in the same framework.

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We try to use a computer algebra system Mathematica as a test case generation system. In test case generation, we generally need to solve equations and inequalities. The main reason why we take Mathematica is because it has a built-in function to solve equations and inequalities. In this paper, we deal with both black-box testing and white-box testing. First, we show two black-box test case generation procedures described in Mathematica. The first one is based on equivalence partitioning. Mathematica explicitly shows a case that test cases do no exist. This is an advantage in using Mathematica. The second procedure is a modification of the first one adopting boundary value analysis. For implementation of boundary value analysis, we give a formalization for it. Next, we show a white-box test case generation procedure. For this purpose, we also give a model for source programs. It is like a control flow graph model. The proposed procedure analyzes a model description of a program.

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