One instance of this algorithm is the original Davis Putnam algorithm that was later refined into the DPLL algorithm that removed the need for explicit representation of the resolvents.
42.
Graph representations can be as compact in the number of clauses as list representations and they also store structural information regarding which clauses were resolved to derive each resolvent.
43.
The second rule of unit propagation can be seen as a restricted form of resolution, in which one of the two resolvents must always be a unit clause.
44.
A complex number ? is said to be in the "'resolvent set "', that is, the complement of the spectrum of a linear operator
45.
Among other uses, the resolvent may be used to solve the inhomogeneous Fredholm integral equations; a commonly used approach is a series solution, the Liouville-Neumann series.
46.
Let l denote a literal and p \ oplus _ x n denote the resolvent of clauses p and n where x \ in p and \ neg x \ in n.
47.
Conversely, given a subgroup of, an invariant of is a "'resolvent invariant "'for if it is not an invariant of any bigger subgroup of.
48.
For example, for degree five polynomials there is never need for a resolvent of D _ 5 : resolvents for A _ 5 and M _ { 20 } give desired information.
49.
For example, for degree five polynomials there is never need for a resolvent of D _ 5 : resolvents for A _ 5 and M _ { 20 } give desired information.
50.
But it can be shown that the resolvent function " R " is Liouville's theorem, this function is constant, thus everywhere zero as it is zero at infinity.
