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Paper Abstract and Keywords
Presentation 2007-08-02 13:30
Recognizable Approximation of Descendant Sets for Left-Linear Oriented Conditional Term Rewriting Systems
Toshiki Murata, Naoki Nishida, Masahiko Sakai, Toshiki Sakabe, Keiichirou Kusakari (Nagoya Univ.) SS2007-16
Abstract (in Japanese) (See Japanese page) 
(in English) The reachability problem for term rewriting systems (TRSs) is to decide whether one of two given terms is reachable to the other with respect to rewriting by a given TRS. Unfortunately, this problem is undecidable in general. Hence, several methods have been widely studied in order to construct a tree automaton that accepts all terms reachable from terms in a given recognizable set. In conditional rewriting, such methods have been proposed only for left-linear join conditional TRSs. However, the techniques of approximation functions used in automatically constructing tree automata have not been formalized. In this paper, we focus on oriented conditional TRSs since every join conditional TRS can be simulated completely by an oriented one. We first propose a method that, given a left-linear oriented conditional TRS and a recognizable set of terms, constructs a tree automaton recognizing an over-approximated set of reachable terms. Then, we formalize approximation functions for join conditional TRSs and oriented ones, respectively, and compare the constructions for join and oriented systems.
Keyword (in Japanese) (See Japanese page) 
(in English) reachability / tree automaton / reduction automaton / join CTRS / / / /  
Reference Info. IEICE Tech. Rep., vol. 107, no. 176, SS2007-16, pp. 1-6, Aug. 2007.
Paper # SS2007-16 
Date of Issue 2007-07-26 (SS) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
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reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee SS  
Conference Date 2007-08-02 - 2007-08-03 
Place (in Japanese) (See Japanese page) 
Place (in English) Hokkaido Univ. 
Topics (in Japanese) (See Japanese page) 
Topics (in English) general 
Paper Information
Registration To SS 
Conference Code 2007-08-SS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Recognizable Approximation of Descendant Sets for Left-Linear Oriented Conditional Term Rewriting Systems 
Sub Title (in English)  
Keyword(1) reachability  
Keyword(2) tree automaton  
Keyword(3) reduction automaton  
Keyword(4) join CTRS  
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1st Author's Name Toshiki Murata  
1st Author's Affiliation Nagoya University (Nagoya Univ.)
2nd Author's Name Naoki Nishida  
2nd Author's Affiliation Nagoya University (Nagoya Univ.)
3rd Author's Name Masahiko Sakai  
3rd Author's Affiliation Nagoya University (Nagoya Univ.)
4th Author's Name Toshiki Sakabe  
4th Author's Affiliation Nagoya University (Nagoya Univ.)
5th Author's Name Keiichirou Kusakari  
5th Author's Affiliation Nagoya University (Nagoya Univ.)
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Speaker Author-1 
Date Time 2007-08-02 13:30:00 
Presentation Time 30 minutes 
Registration for SS 
Paper # SS2007-16 
Volume (vol) vol.107 
Number (no) no.176 
Page pp.1-6 
#Pages 6 
Date of Issue 2007-07-26 (SS) 

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