State Diagram

A state diagram is a labeled directed graph together with state information that can be used to indicate that certain paths on in a system may be traversed only in a certain way. State diagrams are also known as problem space models (Atallah 1998, p. 36-2). For example, in the left figure above (due to R. Abbott), a car must traverse a town while obeying all traffic laws, and making no U-turns. Initially, the car is at position 4, travelling east, and has a choice of moving to position 1, travelling east, or position 5, travelling east. The State diagram corresponding to the maze is illustrated in the above right figure.

Another example created by R. Abbott is illustrated above. While the maze is very similar to the first one, the state diagram is not. This maze therefore illustrates that a minor change to the rules of a system can have a large impact on its state diagram.

Other puzzles, problems, and programs use state diagrams as an analysis tool. For example, the 15 puzzle can be represented as a state diagram with  nodes.

REFERENCES

Abbott, R. "The Farmer Goes to Market." Sci. Amer. Oct. 1962.

Abbott, R. Mad Mazes: Intriguing Mind Twisters for Puzzle Buffs, Game Nuts and Other Smart People. Bob Adams Publishers, p. 8, 1990.

Abbott, R. "Logic Mazes." http://www.logicmazes.com/.Atallah, M. J. (Ed.). Algorithms and Theory of Computation Handbook. Boca Raton, FL: CRC Press, 1998.

Gilbert, A. "Click Mazes: Interactive Puzzles and Mazes." http://www.clickmazes.com/.Pegg, E. Jr. "Math Games: Multi-State Mazes." Nov. 14, 2003. http://www.maa.org/editorial/mathgames/mathgames_11_24_03.html.