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| Presentation | 2017-03-10 10:45 Proving Confluence of Hierarchical Conditional Term Rewriting Systems without Sufficient Completeness Takayuki Kuroda, Naoki Nishida, Hiroyuki Seki (Nagoya Univ.)  SS2016-77 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | A transformational approach to confluence proofs for conditional term rewriting systems (CTRS) has been investigated, but confluence of a CTRS defining sorting over natural numbers has not been proved yet by any existing confluence prover. Such a CTRS defines behavior of function symbols hierarchically, called a hierarchical CTRS, and is not sufficiently complete. In this article, we propose a method to prove confluence of hierarchical CTRSs that are not sufficiently complete. More precisely, we first extend rewriting induction for conditional equations to TRSs that are not sufficiently complete, and then we prove joinability of a conditional critical pair by inducing other conditions from the original conditional part. Next, we design a simplification order that takes conditional parts of rewrite rules into account, and propose a method to prove termination of hierarchical CTRSs by means of the designed simplification order. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | conditional term rewriting system / confluence / rewriting induction / sufficient completeness / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 116, no. 512, SS2016-77, pp. 103-108, March 2017. | |
| Paper # | SS2016-77 | |
| Date of Issue | 2017-03-02 (SS) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and 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) | |
| Download PDF | SS2016-77 |
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| Conference Information | |
| Committee | SS |
| Conference Date | 2017-03-09 - 2017-03-10 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | SS |
| Conference Code | 2017-03-SS |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Proving Confluence of Hierarchical Conditional Term Rewriting Systems without Sufficient Completeness |
| Sub Title (in English) | |
| Keyword(1) | conditional term rewriting system |
| Keyword(2) | confluence |
| Keyword(3) | rewriting induction |
| Keyword(4) | sufficient completeness |
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| 1st Author's Name | Takayuki Kuroda |
| 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 | Hiroyuki Seki |
| 3rd Author's Affiliation | Nagoya University (Nagoya Univ.) |
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| Speaker | Author-1 |
| Date Time | 2017-03-10 10:45:00 |
| Presentation Time | 25 minutes |
| Registration for | SS |
| Paper # | SS2016-77 |
| Volume (vol) | vol.116 |
| Number (no) | no.512 |
| Page | pp.103-108 |
| #Pages | 6 |
| Date of Issue | 2017-03-02 (SS) |
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