The permanent is believed to be more difficult to compute than the determinant. While the determinant can be computed in polynomial time by Gaussian elimination , Gaussian elimination cannot be used to compute the permanent. Moreover, computing the permanent of a (0,1)-matrix is #P-complete . Thus, if the permanent can be computed in polynomial time by any method, then FP = #P , which is an even stronger statement than P = NP . When the entries of A are nonnegative, however, the permanent can be computed approximately in probabilistic polynomial time, up to an error of ε M , where M is the value of the permanent and ε > 0 is arbitrary. 
The regress problem provides a powerful argument for foundationalism. The regress argument, though, does not resolve particular questions about foundationalism. The regress provides little guidance about the nature of basic beliefs or the correct theory of inferential support. As we just observed with the discussion of holistic coherentism, considerations from the regress argument show, minimally, that the data used for coherence reasoning must have some initial presumption in its favor. This form of foundationalism may be far from the initial hope of a rational reconstruction of common sense. Such a reconstruction would amount to setting out in clear order the arguments for various commonsense claims (for example, I have hands , there is a material world , I have existed for more than five minutes , etc) that exhibits the ultimate basis for our view of things. We shall consider the issues relating to varieties of foundationalists views below.