Generating Models of a Matched Formula with a Polynomial Delay

0450591 - ÚI 2017 RIV US eng J - Journal Article
Savický, Petr - Kučera, P.
Generating Models of a Matched Formula with a Polynomial Delay.
Journal of Artificial Intelligence Research. Roč. 56, č. 6 (2016), s. 379-402. ISSN 1076-9757. E-ISSN 1943-5037
R&D Projects: GA ČR GBP202/12/G061
Grant - others:GA ČR(CZ) GA15-15511S
Institutional support: RVO:67985807
Keywords : conjunctive normal form * matched formula * pure literal satisfiable formula
Subject RIV: BA - General Mathematics
Impact factor: 2.284, year: 2016

A matched formula is a CNF formula, such that the system of the sets of the variables, which appear in individual clauses, has a system of distinct representatives. Such a formula is always satisfiable. Matched formulas are used, for example, in the area of parametrized 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 the linearly satisfiable formulas, which is a generalization of matched formulas containing the class considered above.
Permanent Link: http://hdl.handle.net/11104/0251864