This article proposes EduTalk, an out-of-the-box Internet of Things (IoT)-based smart learning environment for programming education. In particular, EduTalk enables the students to write VPython programs that render 3-D animations in the browser without installing extra software or using any specific (and typically expensive) hardware. EduTalk takes the user’s smartphone as a controller for cyber–physical interaction, which nicely integrates with learning of other core courses such as physics and mathematics. EduTalk allows building science exhibition projects by writing VPython programs to show 3-D animation, where the cost for EduTalk’s cyber–physical interaction is low and is almost maintenance free. The major contribution of this article is the IoT-based EduTalk proposal that subtly utilizes an IoT platform IoTtalk to conveniently generate cyber–physical interaction for learning how to program as well as learning core courses such as physics. The programming exercises can be easily extended to science exhibition projects and then the development of digital twin applications. A mechanism is provided to easily integrate GlowScript animation demos with EduTalk, which significantly simplifies the effort for teachers to prepare the lecturers. Finally, we show how data collected from EduTalk can be analyzed to improve learning design for cyber–physical interactive animation.

Graphical Internet of Things (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 that 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.

A subgroup permutation code is a set of permutations onnsymbols with the property that its elements are closed under the operation of composition. In this paper, we give inapproximability results for the minimum and maximum weight problems of subgroup permutation codes under several well-known metrics. Based on previous works, we prove that under Hamming, Lee, Cayley, Kendall's tau, Ulam's, andlpdistance metrics, 1) there is no polynomial-time 2log1-εn-approximation algorithm for the minimum weight problem for any constant ε >; 0 unless NP ⊆ DTIME(2polylog(n)) (quasi-polynomial time), and 2) there is no polynomial-timer-approximation algorithm for the minimum weight problem for any constantr>; 1 unless P = NP. Underl∞-metric, we prove that it is NP-hard to approximate the minimum weight problem within factor 2-ε for any constant ε >; 0. We also prove that for any constant ε >; 0, it is NP-hard to approximate the maximum weight withinp√{[ 3/ 2]}-ε under ℓpdistance metric, and within [ 3/ 2]-ε under Hamming, Lee, Cayley, Kendall's tau, and Ulam's distance metrics.

Let Sλnbe the set of all permutations over the multiset {1,...,1,...,m,...,m} where n = mλ. A frequency permutation array (FPA) of minimum distance d is a subset of Sλnin which every two elements have distance at least d. FPAs have many applications related to error correcting codes. In coding theory, the Gilbert-Varshamov bound and the sphere-packing bound are derived from the size of balls of certain radii. We propose two efficient algorithms that compute the ball size of frequency permutations under Chebyshev distance. Both methods extend previous known results. The first one runs in O((2dλdλ)2.376log n) time and O ((2dλdλ)2)space. The second one runs in O ((2dλdλ)((dλ+λ)/λ)n/λ) time and O ((2dλdλ)) space. For small constants λ and d, both are efficient in time and use constant storage space.

Permutation codes of length n and distance d is a set of permutations on n symbols, where the distance between any two elements in the set is at least d. Subgroup permutation codes are permutation codes with the property that the elements are closed under the operation of composition. In this paper, under the distance metric ℓ∞-norm, we prove that finding the minimum weight codeword for subgroup permutation code is NP-complete. Moreover, we show that it is NP-hard to approximate the minimum weight within the factor 7 over 6 - ∈ for any ∈ > 0.

A frequency permutation array (FPA) of lengthn=mλ and distancedis a set of permutations on a multiset overmsymbols, where each symbol appears exactly λ times and the distance between any two elements in the array is at leastd. 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 λ+1 symbols, which has an interesting application to private information retrieval.

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