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Summary: Congruences for Visibly Pushdown Languages
Rajeev Alur1
, Viraj Kumar2
, P. Madhusudan2
, and Mahesh Viswanathan2
1
University of Pennsylvania, Philadelphia, PA, USA,
alur@cis.upenn.edu
2
University of Illinois at Urbana-Champaign, Urbana, IL, USA,
{kumar,madhu,vmahesh}@cs.uiuc.edu
Abstract. 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 parame-
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