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We study congruences on words in order to characterize the class of visibly pushdown languages (Vpl), a subclass of context-free languages. For any language L, we define a natural congruence on words that resembles the syntactic congruence for regular languages, such that this congruence is of finite index if, and only if, L is a Vpl. We then study the(More)
Boolean programs with recursion are convenient abstractions of sequential imperative programs, and can be represented as recursive state machines (RSMs) or pushdown automata. Motivated by the special structure of RSMs, we define a notion of modular visibly pushdown au-tomata (modular VPA) and show that for the class of languages accepted by such automata,(More)
Students in the developing world are frequently cited as being among the most important beneficiaries of online education initiatives such as massive open online courses (MOOCs). While some predict that online classrooms will replace physical classrooms, our experience suggests that blending online and in-person instruction is more likely to succeed in(More)