### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 1102-1114 |

Number of pages | 13 |

Journal | Lecture Notes in Computer Science |

Volume | 3580 |

State | Published - Oct 19 2005 |

Event | 32nd International Colloquium on Automata, Languages and Programming, ICALP 2005 - Lisbon, Portugal Duration: Jul 11 2005 → Jul 15 2005 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science*,

*3580*, 1102-1114.

**Congruences for visibly pushdown languages.** / Alur, Rajeev; Kumar, Viraj; Parthasarathy, Madhusudan; Viswanathan, Mahesh.

Research output: Contribution to journal › Conference article

*Lecture Notes in Computer Science*, vol. 3580, pp. 1102-1114.

}

TY - JOUR

T1 - Congruences for visibly pushdown languages

AU - Alur, Rajeev

AU - Kumar, Viraj

AU - Parthasarathy, Madhusudan

AU - Viswanathan, Mahesh

PY - 2005/10/19

Y1 - 2005/10/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=26444446962&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26444446962&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:26444446962

VL - 3580

SP - 1102

EP - 1114

JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SN - 0302-9743

ER -