Name
Abstract | ||
|---|---|---|
In this paper we study relationships between CNF representations of a given Boolean function f and certain sets of implicates of f. We introduce two definitions of sets of implicates which are both based on the properties of resolution. The first type of sets, called exclusive sets of implicates, is shown to have a functional property useful for decompositions. The second type of sets, called essential sets of implicates, is proved to possess an orthogonality property, which implies that every CNF representation and every essential set must intersect. The latter property then leads to an interesting question, to which we give an affirmative answer for some special subclasses of Horn Boolean functions. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.dam.2009.08.012 | Discrete Applied Mathematics |
Keywords | Field | DocType |
boolean function,horn functions,exclusive sets,orthogonality property,essential sets,boolean minimization,exclusive set,cnf representation,affirmative answer,certain set,functional property,horn boolean function,essential set,latter property | Boolean function,Discrete mathematics,Combinatorics,Orthogonality,Decomposition method (constraint satisfaction),Horn function,Minification,Minimisation (psychology),Circuit minimization for Boolean functions,Mathematics,The Intersect | Journal |
Volume | Issue | ISSN |
158 | 2 | Discrete Applied Mathematics |
Citations | PageRank | References |
11 | 0.69 | 12 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Endre Boros | 1 | 1779 | 155.63 |
| Ondřej Epek | 2 | 29 | 2.53 |
| A. Kogan | 3 | 142 | 12.92 |
| Petr Kučera | 4 | 40 | 6.47 |