Congruences for Visibly Pushdown Languages
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 problem of finding canonical minimal deterministic automata for VPLs. Though VPLs in general do not have unique minimal automata, we consider a subclass of VPAs called k-module single-entry VPAs that correspond to programs with recursive procedures without input parameters, and show that the class of well-matched VPLs do indeed have unique minimal k-module single-entry automata. We also give a polynomial time algorithm that minimizes such k-module single-entry VPAs.
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<br>Postprint version. Published in <i>Lecture Notes in Computer Science</i>, 32nd International Colloqium on Automata, Languages, and Programming, 2005.<br><p>