In this paper we consider networks of evolutionary processors with splicing rules and permitting context (NEPPS) as language generating and computational devices. Such a network consists of several processors placed on the nodes of a virtual graph and are able to perform splicing (which is a biologically motivated operation) on the words present in that node, according to the splicing rules present there. Before applying the splicing operation on words, we check for the presence of certain symbols (permitting context) in the strings on which the rule is applied. Each node is associated with an input and output filter. When the filters are based on random context conditions, one gets the computational power of Turing machines with networks of size two. We also show how these networks can be used to solve NP-complete problems in linear time.