Semistates

Semistates are a concept used in the study of formal languages and automata theory. They represent an intermediate stage in the processing of an input string by a computational machine, such as a finite automaton. Instead of a finite automaton having a discrete set of "states" that it can be in at any given moment, a semistate can be thought of as a distribution over the possible states. This means that at any point during processing, the machine is not definitively in one state, but rather has a certain probability or degree of belonging to each of the possible states.

This probabilistic or graded notion of state is particularly relevant in fuzzy automata or other generalized models of computation. In a standard finite automaton, a transition from one state to another is deterministic or probabilistic, but the machine is always in a single, well-defined state. In contrast, with semistates, the machine can exist in a superposition of states. This allows for the modeling of systems with inherent uncertainty or imprecision, where strict state transitions are not sufficient. The concept of semistates enriches the theoretical framework for understanding computational processes beyond the classical deterministic and probabilistic models.