Edit distance modulo bisimulation

Abstract

When a user learns to use a new device, her understanding of it evolves. A progressive comparison of the evolving user models towards the device target model, for analysing learning, involves determining the behavioral proximity between them. To quantify the gap between a user model and a target model, we introduce an edit distance metric for measuring their behavioral proximity using a bisimulation-based equivalence relation. We define edit distance to be the minimum number of edges and states with incident edges required to be deleted from and/or added to a user model to make it bisimilar to the target model. We propose an algorithm to compute edit distance between two models and employ the heuristic procedure on experimental data for computing edit distance between target and user models. The data is organised into two experiments depending on the device the user interacted with: (a) a simple device resembling a vending machine and (b) a close to real-world vehicle transmission model. The results validate our proposed metric as edit distance converges with progressive user learning, increases for erroneous learning, and remains unchanged indicating no learning.