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Paper Abstract and Keywords
Presentation 2016-03-10 11:15
Program Verification Using Non-linear Loop Invariants Generated by Partially Applying an Extended Farkas' Lemma
Makishi Yanagisawa, Naoki Nishida, Masahiko Sakai (Nagoya Univ.) SS2015-81
Abstract (in Japanese) (See Japanese page) 
(in English) To generate loop invariants, methods that, using Farkas' lemma, convert verification formulas obtained from a given template, a pre-condition, and a post-condtion of a program have been investigated. Farkas' lemma transforms formulas consisting of inequalities over linear polynomials into equivalent formulas. This lemma has been extended to deal with polynomials including non-linear monomials that may have function calls, and some examples that the extended Farkas' lemma succeeds in generating loop invariants having non-linear polynomials have been shown. However, it has not been discussed how useful the extended lemma is in verifying programs. In this paper, we evaluate the usefulness of a loop-invariant generation based on the extended Farkas' lemma, and propose a verification method that uses the extended lemma effectively. More precisely, using the extended lemma, we transform some of verification formulas that contain unknown coefficients for a given template, into another formula, and then we verify the validity of the formula obtained from the remaining formulas by applying an assignment for the unknown coefficients to satisfy the transformed formula.
Keyword (in Japanese) (See Japanese page) 
(in English) program verification / loop invariant / Hoare logic / Farkas' lemma / / / /  
Reference Info. IEICE Tech. Rep., vol. 115, no. 508, SS2015-81, pp. 31-36, March 2016.
Paper # SS2015-81 
Date of Issue 2016-03-03 (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 2016-03-10 - 2016-03-11 
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 2016-03-SS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Program Verification Using Non-linear Loop Invariants Generated by Partially Applying an Extended Farkas' Lemma 
Sub Title (in English)  
Keyword(1) program verification  
Keyword(2) loop invariant  
Keyword(3) Hoare logic  
Keyword(4) Farkas' lemma  
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1st Author's Name Makishi Yanagisawa  
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.)
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Speaker Author-1 
Date Time 2016-03-10 11:15:00 
Presentation Time 25 minutes 
Registration for SS 
Paper # SS2015-81 
Volume (vol) vol.115 
Number (no) no.508 
Page pp.31-36 
#Pages 6 
Date of Issue 2016-03-03 (SS) 

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