Transducers Based on Networks of Evolutionary Processors
Sandra Gómez-Canaval, Víctor Mitrana, Santiago Alonso Villaverde · Hispana · 2014
We consider a new type of transducer that does not scan sequentially the input word. Instead, it consists of a directed graph whose nodes are processors which work in parallel and are specialized in just one type of a very simple evolutionary operation: inserting, deleting or substituting a symbol by another one. The computation on an input word starts with this word placed in a designated node, the input node, of the network and alternates between evolutionary and communication steps. The computation halts as soon as another designated node, the output node, is nonempty. The translation of the input word is the set of words existing in the output node when the computation halts. We prove that these transducers can simulate the work of generalized sequential machines on every input. Furthermore, all words obtained by a given generalized sequential machine by the shortest computations on a given word can also be computed by the new transducers. Unlike the case of generalized sequential machines, every recursively enumerable language can be the transduction defined by the new transducer of a very simple regular language. The same idea may be used for proving that these transducers can simulate the shortest computations of an arbitrary Turing machine, used as a transducer, on every input word. Finally, we consider a restricted variant of NEP transducer, namely pure NEP transducers and prove that there are still regular languages whose pure NEP transductions are not semilinear.