Generating Models of a Matched Formula With a Polynomial Delay (Extended Abstract)

0480888 - ÚI 2018 DE eng C - Conference Paper (international conference)
Savický, Petr - Kučera, P.
Generating Models of a Matched Formula With a Polynomial Delay (Extended Abstract).
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence. Freiburg: IJCAI, 2017 - (Sierra, C.), s. 5055-5059. ISBN 978-0-9992411-0-3.
[IJCAI 2017. International Joint Conference on Artificial Intelligence /26./. Melbourne (AU), 19.08.2017-25.08.2017]
R&D Projects: GA ČR GBP202/12/G061
Grant - others:GA ČR GA15-15511S
Institutional support: RVO:67985807
Keywords : conjunctive normal form * matched formula * pure literal satisfiable formula
Subject RIV: BA - General Mathematics
https://www.ijcai.org/proceedings/2017/0721.pdf

A matched formula is a CNF formula whose incidence graph admits a matching which matches a distinct variable to every clause. Such a formula is always satisfiable. Matched formulas are used, for example, in the area of parameterized complexity. We prove that the problem of counting the number of the models (satisfying assignments) of a matched formula is # P-complete. On the other hand, we define a class of formulas generalizing the matched formulas and prove that for a formula in this class one can choose in polynomial time a variable suitable for splitting the tree for the search of the models of the formula. As a consequence, the models of a formula from this class, in particular of any matched formula, can be generated sequentially with a delay polynomial in the size of the input. On the other hand, we prove that this task cannot be performed efficiently for linearly satisfiable formulas, which is a generalization of matched formulas containing the class considered above.
Permanent Link: http://hdl.handle.net/11104/0276554