There are only very few natural ways in which arbitrary functions can be combined. One composition operator is override: for arbitrary functions f and g, f g is the). Another operator is update: f [g] has the same domain as f , behaves like f on dom( f ) \ dom(g), and like g on dom( f ) ∩ dom(g). These operators are widely used, especially within computer science, where for instance f [g] may denote the new statethat results when in state f the updates given as g are applied. It is therefore surprising that thus far no axiomatization of these operators has been proposed in the literature.As an auxiliary operator we consider the minus operator: f − g is the restriction of f to the domain dom( f ) \ dom(g). The update operator can be defined in terms of override and minus. We present five equations that together constitute a sound and complete axiomatization of override and minus. As part of our completeness proof, we infer a large number of useful derived laws using the proof assistant Isabelle. With the help of the SMT solver Yices, we establish independence of the axioms. Thus, our axiomatization is also minimal. Finally, we establish that override and minus are functionally complete in the sense that any operation on general functions that corresponds to a valid coloring of a Venn diagram can be described using just these two operations.

Abstract. Model-based testing is a promising software testing technique for the automation of test generation and test execution. One obstacle to its adoption is the difficulty of developing models. Learning techniques provide tools to automatically derive automata-based models. Automation is obtained at the cost of time and unreadability of the models. We propose an abstraction technique to reduce the alphabet and large data sets. Our idea is to extract a priori knowledge about the teacher and use this knowledge to define equivalence classes. The latter are then used to define a new and reduced alphabet. The a priori knowledge can be obtained from informal documentation or requirements. We formally prove soundness of our approach. We demonstrate the practical feasibility of our technique by learning a model of the new biometric passport. Our automatically learned model is of comparable size and complexity of a previous model manually developed in the context of testing a passport implementation. Our model can be learned within one hour and slightly refines the previous model.

Abstract. The Dutch company Chess develops a wireless sensor network (WSN) platform using an epidemic communication model. One of the greatest challenges in the design is to find suitable mechanisms for clock synchronization. In this paper, we study a proposed clock synchronization protocol for the Chess platform. First, we model the protocol as a network of timed automata and verify various instances using the Uppaal model checker. Next, we present a full parametric analysis of the protocol for the special case of cliques (networks with full connectivity), that is, we give constraints on the parameters that are both necessary and sufficient for correctness. These results have been checked using the proof assistant Isabelle. Finally, we present a negative result for the special case of line topologies: for any instantiation of the parameters, the protocol will eventually fail if the network grows.

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This paper contains supplementary material to the IEEE TPDS paper entitled "On necessary and sufficient conditions for deadlock-free routing in wormhole networks". In Section 1, we prove that deciding deadlock freedom of wormhole networks is co-NP-complete. In Section 2, we provide a counter example to a polynomial algorithm for this decision problem.

International audienc

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