Stratification, target set reachability and incremental enlargement principle

This paper presents a brief exposition of a version of the concept of stratification, call it CST for short. In our approach to stratification, CST is a computational system in which the objects of computation are strata of data. Usually, the strata are nested or stacked with nested strata centering on a target set, T. CST has a potential for significant applications in planning, robotics, optimal control, pursuit, multiobjective optimization, exploration, search and other fields. Very simple, familiar examples of stratification are dictionaries, directories and catalogues. A multi-layer perceptron may be viewed as a system with a stratified structure. In spirit, CST has similarity to dynamic programing (DP), but it is much easier to understand and much easier to implement. An interesting question which relates to neuroscience is: Does the human brain employ stratification to store information? It would be natural to represent a concept such as chair, as a collection of strata with one or more strata representing a type of chair.Underlining our approach is a model, call it FSM. FSM is a discrete-time, discrete-state dynamical system which has a finite number of states. The importance of FSM as a model derives from the fact that through the use of granulation and/or quantization almost any kind of system can be approximated to by a finite state system. A concept which plays an important role in our approach is that of target set reachability. Reachability involves moving (transitioning) FSM from a state w to a state in target state, T, in a minimum number of steps. To this end, the state space, W, is stratified through the use of what is refer as the incremental enlargement principle. It should also be noted that the concept reachability is related to the concept of accessibility in modal logic.