This article presents novel results on automated test generation for hybrid control systems. In contrast to test automation techniques for purely discrete controllers this involves the generation of both discrete and real-valued, potentially time-continuous, input data to the system under test. To this end, the test automation techniques introduced here are allocated in two-layers: The upper layer contains a symbolic test case generator constructing test cases as paths through an abstracted representation of the transition graph specifying the system under test. Different test strategies designed to pursue various quality objectives lead to different selections of symbolic test cases. Symbolic test cases are transformed into feasible, i. e., executable, test cases by constructing concrete sequences of input data, allowing the execution of the pre-planned transition sequence. The input data construction is performed by the lower layer consisting of a constraint solver. This component applies interval analysis techniques identifying the domains from where to pick the appropriate test data. The well known complexity problems of the various paving algorithms used in interval analysis are circumvented by three main concepts: First, sequences of constraints, each element representing a conjunct of a larger * Work of the authors situated at Oldenburg has been partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center "Automatic Verification and Analysis of Complex Systems" (SFB/TR 14 AVACS, http://www.avacs.org). † Partly supported by the Deutsche Forschungsgemeinschaft DFG as part of the priority programme SPP 1064 on Software Specification -Integration of Software Specification Techniques for Applications in Engineering (SPP 1064, HY-BRIS, http://www.tzi.de/agbs/projects/hybris). This is the extended version of an article to appear in the Proceedings of the SOQUA'06, November 6, 2006, Portland, OR, USA. global constraint, are processed separately, thereby keeping the dimension of the local constraint problems involved at an acceptable level. Second, interval vectors containing the global solution set are contracted using forward-backward interval constraint propagation. Third, both symbolic test case generator and constraint solver learn to avoid symbolic transition sequences whose prefixes are already known to be infeasible and to avoid interval solutions for local constraints which are known to be in conflict with other local constraints to be satisfied for the same symbolic test case, respectively.
We prove the correctness of a sliding window protocol with an arbitrary finite window size n and sequence numbers modulo 2 n . The correctness consists of showing that the sliding window protocol is branching bisimilar to a queue of capacity 2 n . The proof is given entirely on the basis of an axiomatic theory, and has been checked in the theorem prover PVS.
C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a Software ENgineeringVerifying a Sliding Window Protocol in mCRL W.J. Fokkink, J.F. Groote, J. Pang, B. Badban, J.C. van Improving the quality of embedded systems using formal design and systematic testing.
We present GDPLL, a generalization of the DPLL procedure. It solves the satisfiability problem for decidable fragments of quantifier-free first-order logic. Sufficient conditions are identified for proving soundness, termination and completeness of GDPLL. We show how the original DPLL procedure is an instance. Subsequently the GDPLL instances for equality logic, and the logic of equality over infinite ground term algebras are presented. Based on this, we implemented a decision procedure for inductive datatypes. We provide some new benchmarks, in order to compare variant
We present an approach to automatically generating invariants for timed automata models. The CIPM algorithm that we propose first computes new invariants for timed automata control locations taking their originally defined invariants as well as the constrains on clock variables imposed by incoming state transitions into account. In doing so the CIPM algorithm also prunes idle transitions, which are transitions that can never be taken, from the automaton. We discsuss a prototype implementation of the CIPM algorithm as well as some initial experimental results.
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