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Paper Abstract and Keywords
Presentation 2026-03-04 10:00
On the Complexity of Transformation from Tractable Boolean Formulas to Binary Decision Diagrams
Giovanni Buzzega (PU), Kazuhiro Kurita (OU), Kazuhisa Seto (HU) COMP2025-21
Abstract (in Japanese) (See Japanese page) 
(in English) In this paper, we discuss the complexity of the problem of transforming a given Boolean formula $f$ into a binary decision diagram (BDD) that is equivalent to the Boolean function represented by $f$. A Binary Decision Diagram is a directed acyclic graph representation of a truth table, and in general, multiple BDDs may represent the equivalent Boolean function. It is known that the minimum-size BDD representing a given Boolean function is unique. Thus, we consider the problem of transforming a Boolean function $f$ into the minimum-size BDD that represents $f$. When analyzing the complexity of this problem, it is important to note that the size of the output BDD may be exponentially larger than the size of the input formula. Hence, we investigate the output-sensitive complexity of this problem. Moreover, it is known that if a Boolean formula is unsatisfiable, the size of its BDD can be bounded linearly in the input size. This implies that, unless unsatisfiability can be decided in polynomial time, no output-polynomial time algorithm for this problem exists under the assumption that $P neq NP$.
For this reason, we focus on classes of Boolean formulas for which the satisfiability problem is solvable in polynomial time,
such as 2-CNF, Horn-CNF, and XOR-CNF, and we discuss the complexity of transforming such Boolean formulas into BDDs.
Keyword (in Japanese) (See Japanese page) 
(in English) Binary Decision Diagram / NP-hardness / Output Sensitive algorithm / / / / /  
Reference Info. IEICE Tech. Rep., vol. 125, no. 390, COMP2025-21, pp. 1-4, March 2026.
Paper # COMP2025-21 
Date of Issue 2026-02-25 (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 COMP2025-21

Conference Information
Committee COMP  
Conference Date 2026-03-04 - 2026-03-04 
Place (in Japanese) (See Japanese page) 
Place (in English) Chuo University Korakuen Campus Building 6 4F Room 6402 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Theoretical Computer Science, General 
Paper Information
Registration To COMP 
Conference Code 2026-03-COMP 
Language English (Japanese title is available) 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) On the Complexity of Transformation from Tractable Boolean Formulas to Binary Decision Diagrams 
Sub Title (in English)  
Keyword(1) Binary Decision Diagram  
Keyword(2) NP-hardness  
Keyword(3) Output Sensitive algorithm  
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1st Author's Name Giovanni Buzzega  
1st Author's Affiliation Pisa University (PU)
2nd Author's Name Kazuhiro Kurita  
2nd Author's Affiliation Okayama University (OU)
3rd Author's Name Kazuhisa Seto  
3rd Author's Affiliation Hokkaido University (HU)
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Speaker Author-2 
Date Time 2026-03-04 10:00:00 
Presentation Time 30 minutes 
Registration for COMP 
Paper # COMP2025-21 
Volume (vol) vol.125 
Number (no) no.390 
Page pp.1-4 
#Pages 4 
Date of Issue 2026-02-25 (COMP) 

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