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Language equivalence can be checked coinductively by establishing a bisimulation on suitable deterministic automata. We improve and extend this technique with bisimulation-up-to, which is an enhancement of the bisimulation proof method. First, we focus on the regular operations of union, concatenation and Kleene star, and illustrate our method with new proofs of classical results such as Arden’s rule. Then we extend our enhanced proof method to incorporate language complement and intersection. Finally we define a general format of behavioural differential equations, in which one can define operations on languages for which bisimulation-up-to is a sound proof technique.

The Matlab/Simulink language has become the standard formalism for modeling and implementing control software in areas like avionics, automotive, railway, and process automation. Such software is often safety critical, and bugs have potentially disastrous consequences for people and material involved. We define a verification methodology to assess the correctness of Simulink programs by means of automated test-case generation. In the style of fault- and mutation-based testing, the coverage of a Simulink program by a test suite is defined in terms of the detection of injected faults. Using bounded model checking techniques, we are able to effectively and automatically compute test suites for given fault models. Several optimisations are discussed to make the approach practical for realistic Simulink programs and fault models, and to obtain accurate coverage measures.