Year: 2025
Type: article
Abstract: The classic TQBF problem can be viewed as a game in which two players alternate turns assigning truth values to a CNF formula's variables in a prescribed order, and the winner is determined by whether the CNF gets satisfied. The complexity of deciding which player has a winning strategy in this game is well-understood: it is -complete for 2-CNFs and -complete for 3-CNFs. We continue the study of the unordered variant of this game, in which each turn consists of picking any remaining variable and assigning it a truth value. The complexity of deciding who can win on a given CNF is less well-understood; prior work by the authors showed it is in for 2-CNFs and -complete for 5-CNFs. We conjecture it may be efficiently solvable on 3-CNFs, and we make progress in this direction by proving the problem is in , indeed in , for 3-CNFs with a certain restriction, namely that each width-3 clause has at least one variable that appears in no other clause. Another (incomparable) restriction of this problem was previously shown to be tractable by Kutz.
Source: Computational Complexity
Authors: Md Lutfar Rahman, Thomas Watson
Institutions: Amazon (United States), University of Memphis
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: National Science Foundation
OpenAlex ID: W3114265485