Visibly Pushdown Automata

Abstract. Visibly pushdown automata are special pushdown automata whose stack behavior is driven by the input symbols according to a partition of the alphabet. We show that it is decidable for a given visibly pushdown automaton whether it is equivalent to a visibly counter automaton, i.e. an automaton that uses its stack only as counter. In particular, this allows to decide whether a given visibly pushdown language is a regular restriction of the set of well-matched words, meaning that the language can be accepted by a finite automaton if only well-matched words are considered as input. 1

We extend the Expressionist project, and thereby the re-emerging area of grammar-based text generation, by applying a technique from software verification to a critical search problem related to content generation from grammars. In Expressionist, authors attach tags (corresponding to pertinent meanings) to nonterminal symbols in a context-free grammar , which enables the targeted generation of content that expresses requested meanings (i.e., has the requested tags). While previous work has demonstrated methods for requesting content with a single required tag, requests for multiple tags yields a search task over domains that may realistically span quintillions or more elements. In this paper, we reduce Expressionist grammars to symbolic visibly pushdown automata, which allows us to locate in massive search spaces generable outputs that satisfy moderately complex criteria related to tags. While the satisficing of more complex tag criteria is still not feasible using this technique, we forecast a number of opportunities for future directions.