Before revision:  In particular, several attempts at defining and/or quantifying complexity have  , at some point , run into intrinsic difficulties. This didactic text provides a brief review of some of the approaches that have been used to characterize complexity, and also suggests a possible definition of complexity based on the cost assigned to mapping the entity of interest, as well as on the  cost of the error implied by its respective reconstruction .
After revision:  In particular, several attempts at defining and/or quantifying complexity have , at some point , run into intrinsic limitations. Two are the main objectives of the present work: (i) to review some of the approaches that have been used to characterize complexity, and also suggests a possible definition of complexity based on the cost assigned to mapping the entity of interest, as well as on the cost of the error implied by its respective reconstruction .