Recognizing boolean closed A-tree languages with membership conditional rewriting mechanism

Authors:
Hitoshi Ohsaki;Hiroyuki Seki;Toshinori Takai
Affiliations:
PRESTO “Information and Systems” Japan Science and Technology Corporation and National Institute of Advanced Industrial Science and Technology, Amagasaki, Japan;Nara Institute of Science and Technology, Ikoma, Japan;National Institute of Advanced Industrial Science and Technology, Amagasaki, Japan
Venue:
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Year:
2003

Citing 9
Cited 10

Associative path orderings

Proc. of the first international conference on Rewriting techniques and applications
Nondeterministic space is closed under complementation

SIAM Journal on Computing
Aspects of classical language theory

Handbook of formal languages, vol. 1
Tree languages

Handbook of formal languages, vol. 3
Term rewriting and all that

Term rewriting and all that
Well-structured transition systems everywhere!

Theoretical Computer Science
The Reachability Problem for Ground TRS and Some Extensions

TAPSOFT '89/CAAP '89 Proceedings of the International Joint Conference on Theory and Practice of Software Development, Volume 1: Advanced Seminar on Foundations of Innovative Software Development I and Colloquium on Trees in Algebra and Programming
Decidability and Closure Properties of Equational Tree Languages

RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Recognizing boolean closed A-tree languages with membership conditional rewriting mechanism

RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications

Symbolic reachability analysis using narrowing and its application to verification of cryptographic protocols

Higher-Order and Symbolic Computation
Narrowing and Rewriting Logic: from Foundations to Applications

Electronic Notes in Theoretical Computer Science (ENTCS)
Closure of Hedge-Automata Languages by Hedge Rewriting

RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Tree Automata for Non-linear Arithmetic

RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Symbolic Reachability Analysis Using Narrowing and its Application to Verification of Cryptographic Protocols

Electronic Notes in Theoretical Computer Science (ENTCS)
Recognizing boolean closed A-tree languages with membership conditional rewriting mechanism

RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Symbolic model checking of infinite-state systems using narrowing

RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Rewrite-based verification of XML updates

Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Monotone AC-Tree automata

LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A sufficient completeness reasoning tool for partial specifications

RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper provides an algorithm to compute the complement of tree languages recognizable with A-TA (tree automata with associativity axioms [16]). Due to this closure property together with the previously obtained results, we know that the class is boolean closed, while keeping recognizability of A-closures of regular tree languages. In the proof of the main result, a new framework of tree automata, called sequence-tree automata, is introduced as a generalization of Lugiez and Dal Zilio's multi-tree automata [14] of an associativity case. It is also shown that recognizable A-tree languages are closed under a one-step rewrite relation in case of ground A-term rewriting. This result allows us to compute an under-approximation of A-rewrite descendants of recognizable A-tree languages with arbitrary accuracy.