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 kmodule 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. Comments From the 32nd International Colloquium, ICALP 2005, Lisbon, Portugal, July 11-15, 2005. This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/cis_papers/187 Congruences for Visibly Pushdown Languages Rajeev Alur, Viraj Kumar, P. Madhusudan, and Mahesh Viswanathan 1 University of Pennsylvania, Philadelphia, PA, USA, [email protected] 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 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. 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.