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Paper Abstract and Keywords
Presentation 2019-12-13 11:15
Computational complexity of satisfiability problem with exact number of solutions
Hiromu Horiuchi, Naoyuki Morimoto, Toshiyuki Yamada, Akinori Kawachi (Mie Univ.) COMP2019-34
Abstract (in Japanese) (See Japanese page) 
(in English) Valiant and Vazirani proved the isolation lemma for SAT to show a polynomial-time randomized reduction from SAT to Unique-SAT, which is the problem in which a given formula is promised to have a unique satisfying assignment or no satisying assignment. The isolation lemma transforms satisfiable propositional formula to one which has a unique satisfying assignment (and it does not transform unsatisfiable ones to satisfiable ones). This lemma has been widely known to have many important applications for analysis of computational complexity and algorithm design.
This paper provides a new generalization of the isolation lemma.We define $t$-solution SAT, which is the problem in which a given formula is promised to have exactly $t$ satisfying assignments or no satisfying assignment.By generalizing the technique of Valiant and Vazirani, we show a polynomial-time randomized reduction from SAT to $t$-solution SAT if $t < lg n / lg lg n$, where $n$ is the number of variables in a given formula. This implies that $t$-solution SAT is as hard as SAT for polynomial-time randomized algorithms if $t < lg n /lglg n$.
Keyword (in Japanese) (See Japanese page) 
(in English) SAT / Unique-SAT / Isolation lemma / Randomized algorithms / / / /  
Reference Info. IEICE Tech. Rep., vol. 119, no. 340, COMP2019-34, pp. 39-43, Dec. 2019.
Paper # COMP2019-34 
Date of Issue 2019-12-06 (COMP) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
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. (No. 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee COMP  
Conference Date 2019-12-13 - 2019-12-13 
Place (in Japanese) (See Japanese page) 
Place (in English) Ikaho Seminar House, Gunma University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2019-12-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Computational complexity of satisfiability problem with exact number of solutions 
Sub Title (in English)  
Keyword(1) SAT  
Keyword(2) Unique-SAT  
Keyword(3) Isolation lemma  
Keyword(4) Randomized algorithms  
1st Author's Name Hiromu Horiuchi  
1st Author's Affiliation Mie University (Mie Univ.)
2nd Author's Name Naoyuki Morimoto  
2nd Author's Affiliation Mie University (Mie Univ.)
3rd Author's Name Toshiyuki Yamada  
3rd Author's Affiliation Mie University (Mie Univ.)
4th Author's Name Akinori Kawachi  
4th Author's Affiliation Mie University (Mie Univ.)
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Date Time 2019-12-13 11:15:00 
Presentation Time 25 
Registration for COMP 
Paper # IEICE-COMP2019-34 
Volume (vol) IEICE-119 
Number (no) no.340 
Page pp.39-43 
#Pages IEICE-5 
Date of Issue IEICE-COMP-2019-12-06 

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