"Congruences for Visibly Pushdown Languages" by Rajeev Alur, Viraj Kumar et al.

Departmental Papers (CIS)

Title

Congruences for Visibly Pushdown Languages

Author(s)

Rajeev Alur, University of Pennsylvania
Viraj Kumar, University of Illinois
P. Madhusudan, University of Illinois
Mahesh Viswanathan, University of Illinois

Document Type

Conference Paper

Date of this Version

July 2005

Comments

Postprint version. Published in Lecture Notes in Computer Science, Volume 3580, 32nd International Colloqium on Automata, Languages, and Programming, (ICALP 2005), pages 1102-1114.
Publisher URL: http://dx.doi.org/10.1007/11523468_89

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 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.