This document outlines a state machine and how to implement breadth-first search (BFS) using a state machine. It discusses: 1. What a state machine is and how it works as a computation machine based on current and previous inputs. 2. How to construct a state transition diagram showing states, inputs, and outputs. 3. How to create an abstract state machine class in Python that defines attributes like start state and current state, and methods like getting next values, stepping, and transducing output. 4. How to implement BFS to find the shortest path from a start to goal state by exploring neighboring vertices first before going deeper, using a StateSpaceSearch state machine and additional classes