A frequency permutation array (FPA) of length = and distance is a set of permutations on a multiset over symbols, where each symbol appears exactly times and the distance between any two elements in the array is at least . FPA generalizes the notion of permutation array. In this paper, under the Chebyshev distance, we first prove lower and upper bounds on the size of FPA. Then we give several constructions of FPAs, and some of them come with efficient encoding and decoding capabilities. Moreover, we show one of our designs is locally decodable, i.e., we can decode a message bit by reading at most + 1 symbols, which has an interesting application to private information retrieval.

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Graphical IoT device management platforms, such as IoTtalk, make it easy to describe interactions between IoT devices. Applications are defined by dragging-and-dropping devices and specifying how they are connected, e.g. a door sensor controlling a light. While this allows simple and rapid development, it remains possible to specify unwanted device configurations -such as using the same device to drive a motor up and down simultaneously, risking damaging the motor.We propose BigraphTalk, a verification framework for IoTtalk that utilizes formal techniques, based on bigraphs, to statically guarantee that unwanted configurations do not arise. In particular, we check for invalid connections between devices, as well as type errors, e.g. passing a float to a boolean switch. To the best of our knowledge, BigraphTalk is the first platform to support the graphical specification of correct-by-design IoT applications.BigraphTalk provides fully automated verification and feedback without end-users ever needing to specify a bigraph. This means any application, specifiable in IoTtalk, is guaranteed, so long as verification succeeds, not to violate the given configuration constraints when deployed; with no extra cost to the user.

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