Abstract
This paper proposes a calculational approach to prove properties of two well-known binary trees used to enumerate the rational numbers: the Stern-Brocot tree and the Eisenstein-Stern tree (also known as Calkin-Wilf tree). The calculational style of reasoning is enabled by a matrix formulation that is well-suited to naturally formulate path-based properties, since it provides a natural way to refer to paths in the trees. Three new properties are presented. First, we show that nodes with palindromic paths contain the same rational in both the Stern-Brocot and Eisenstein-Stern trees. Second, we show how certain numerators and denominators in these trees can be written as the sum of two squares x(2) and y(2), with the rational x/y appearing in specific paths. Finally, we show how we can construct Sierpifiski's triangle from these trees of rationals. (C) 2015 Published by Elsevier Inc.

Abstract
We describe our experience using magic card tricks to teach algorithmic skills to first-year Computer Science undergraduates. We illustrate our approach with a detailed discussion on a card trick that is typically presented as a test to the psychic abilities of an audience. We use the trick to discuss concepts like problem decomposition, pre- and post-conditions, and invariants. We discuss pedagogical issues and analyse feedback collected from students. The feedback has been very positive and encouraging. © 2014 ACM.

Abstract
Despite great advances in computer-assisted proof systems, writing formal proofs using a traditional computer is still challenging due to mouse-and-keyboard interaction. This leads to scientists often resorting to pen and paper to write their proofs. However, when handwriting a proof, there is no formal guarantee that the proof is correct. In this paper we address this issue and present the initial steps towards a system that allows users to handwrite proofs using a pen-based device and that communicates with an external theorem prover to support the users throughout the proof writing process. We focus on calculational proofs, whereby a theorem is proved by a chain of formulae, each transformed in some way into the next. We present the implementation of a proof-of-concept prototype that can formally verify handwritten calculational proofs without the need to learn the specific syntax of theorem provers.

Abstract
Large-scale password data breaches are becoming increasingly commonplace, which has enabled researchers to produce a substantial body of password security research utilising real-world password datasets, which often contain numbers of records in the tens or even hundreds of millions. While much study has been conducted on how password composition policies-sets of rules that a user must abide by when creating a password-influence the distribution of user-chosen passwords on a system, much less research has been done on inferring the password composition policy that a given set of user-chosen passwords was created under. In this paper, we state the problem with the naive approach to this challenge, and suggest a simple approach that produces more reliable results. We also present pol-infer, a tool that implements this approach, and demonstrates its use in inferring password composition policies. © 2019 IEEE.

Abstract
This paper shows by examples how the Theory of Programming can be taught to first-year CS undergraduates. The only prerequisite is their High School acquaintance with algebra, geometry, and propositional calculus. The main purpose of teaching the subject is to support practical programming assignments and projects throughout the degree course. The aims would be to increase the student’s enjoyment of programming, reduce the workload, and increase the prospect of success. © 2019, Springer Nature Switzerland AG.

Abstract
The choice of password composition policy to enforce on a password-protected system represents a critical security decision, and has been shown to significantly affect the vulnerability of user-chosen passwords to guessing attacks. In practice, however, this choice is not usually rigorous or justifiable, with a tendency for system administrators to choose password composition policies based on intuition alone. In this work, we propose a novel methodology that draws on password probability distributions constructed from large sets of real-world password data which have been filtered according to various password composition policies. Password probabilities are then redistributed to simulate different user password reselection behaviours in order to automatically determine the password composition policy that will induce the distribution of user-chosen passwords with the greatest uniformity, a metric which we show to be a useful proxy to measure overall resistance to password guessing attacks. Further, we show that by fitting power-law equations to the password probability distributions we generate, we can justify our choice of password composition policy without any direct access to user password data. Finally, we present Skeptic - -a software toolkit that implements this methodology, including a DSL to enable system administrators with no background in password security to compare and rank password composition policies without resorting to expensive and time-consuming user studies. Drawing on 205,176,321 passwords across 3 datasets, we lend validity to our approach by demonstrating that the results we obtain align closely with findings from a previous empirical study into password composition policy effectiveness. © 2020 ACM.