A cryptarithm is a mathematical and logical puzzle in which words form an equation where the letters represent numbers to be determined in a given base. This problem is popular in recreational mathematics, education, and constraint programming. We propose a general, efficient and easy-to-use approach to solve this NP-Complete problem, as well as a hierarchical approach for their generation. The experimental evaluation has generated a large, diverse, and remarkable collection of new cryptarithms.

Situational awareness and decision support tools such as procedures and alarm systems are vital for effective interaction among control room operators, especially in safety-critical situations. In safety-critical environments such as process plants, there remains a gap in evaluating specific tools during actual operations, or ”work-as-done.” Additionally, the underlying factors that might impact operators’ cognitive states and performance concerning safety have not been thoroughly explored. The need for such an evaluation is further bolstered by current interaction configurations where operators are more passive than active, thus reducing their cognitive performance. Therefore, this experimental study addresses the highlighted evaluation gap by introducing and comparing three human system interfaces/decision support tools in four human-in-the-loop configurations. The supports include two alarm design formats (prioritized vs. non-prioritized) and three procedure representation formats (paper, screen-based digitized, and an AI-based support system built with an integrated Bayesian network and reinforcement learning model). Ninety-two people (n = 92) participated voluntarily in the test. They were divided equally into four groups. Each group tested three safety-related events in a simulated formaldehyde production facility. Individuals belonging to the group with prioritized alarms and utilized paper procedures rated procedural support slightly higher on average than others in different groups. Unlike the other groups, their assessment of alarm prioritization support remained consistent across all scenarios. Further analysis of the impact of the setup on cognitive states and actual performance will be performed.

Specifying and implementing a proof system from scratch requires significant effort. Logical Frameworks and Higher Order Logic Programming Languages provide dedicated, high-level meta languages to facilitate this task in two ways: 1) variable binding and substitution are for free when meta language binders represent object logic ones; 2) proof construction, and proof search, are greatly simplified by leveraging the unification procedure provided by the meta language. Notable examples of meta languages are Elf [21], Twelf [23], λ Prolog [16], Beluga [24], Abella [8] and Isabelle [31] which have been used to implement or specify many formal systems such as First Order Logic [5], Set Theory [20], Higher Order Logic [19], and the Calculus of Constructions [4].