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Paper Abstract and Keywords
Presentation 2026-05-21 13:20
A Deterministic $O^*(2^{n/2})$-time Algorithm for 2-CNF Satisfiability in a Subspace
Atsuki Nagao (Ochanomizu Univ.), Kazuhisa Seto (Hokkaido Univ.), Junichi Teruyama (Univ. of Hyogo) COMP2026-5
Abstract (in Japanese) (See Japanese page) 
(in English) The problem of $k$-CNF satisfiability in a subspace asks whether there exists an assignment that satisfies both a $k$-CNF formula and a system of $mathbb{F}_2$-linear equations.
Even for $k=2$, known as $2$-SUB-SAT, this problem is NP-complete.
Arvind and Guruswami presented a randomized algorithm for $2$-SUB-SAT that runs in $O^*(1.432^n)$-time.
In this report, we improve the running time to a deterministic $O^*(2^{n/2})$ by providing a new branch-and-bound algorithm.
Keyword (in Japanese) (See Japanese page) 
(in English) $2$-SAT in a subspace / deterministic algorithm / polynomial-space algorithm / / / / /  
Reference Info. IEICE Tech. Rep., vol. 126, no. 28, COMP2026-5, pp. 23-25, May 2026.
Paper # COMP2026-5 
Date of Issue 2026-05-13 (COMP) 
ISSN 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 COMP2026-5

Conference Information
Committee COMP IPSJ-AL  
Conference Date 2026-05-20 - 2026-05-21 
Place (in Japanese) (See Japanese page) 
Place (in English) Osaka Univ. (Toyonaka) 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Theoretical Computer Science, General 
Paper Information
Registration To COMP 
Conference Code 2026-05-COMP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A Deterministic $O^*(2^{n/2})$-time Algorithm for 2-CNF Satisfiability in a Subspace 
Sub Title (in English)  
Keyword(1) $2$-SAT in a subspace  
Keyword(2) deterministic algorithm  
Keyword(3) polynomial-space algorithm  
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1st Author's Name Atsuki Nagao  
1st Author's Affiliation Ochanomizu University (Ochanomizu Univ.)
2nd Author's Name Kazuhisa Seto  
2nd Author's Affiliation Hokkaido University (Hokkaido Univ.)
3rd Author's Name Junichi Teruyama  
3rd Author's Affiliation University of Hyogo (Univ. of Hyogo)
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Speaker Author-2 
Date Time 2026-05-21 13:20:00 
Presentation Time 30 minutes 
Registration for COMP 
Paper # COMP2026-5 
Volume (vol) vol.126 
Number (no) no.28 
Page pp.23-25 
#Pages 3 
Date of Issue 2026-05-13 (COMP) 

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