State machines are used in fighting games to keep track of what moves can transition to other moves. The state machine in this game is composed of multiple state objects, that each keep track of what states they are connected to. The states are connected via state links, each state only knows which states it can transition to. The state links have conditions that need to be met for the transition to happen, the conditions in this case are input sequences needed from the player.
Every time the player hits a button it is added to the input stream. The state the player is in then goes through all of its links until it finds a link with an input sequence that ends with that button being pushed. The state then looks through the input stream to find the first input required in the sequence. If the state manages to find both the last and the first input requirements in the inputstream, it then compares their time stamps to see if they are within an acceptable input time window.
If the timestamps are within the required time frame, the state then defines a search area in the input stream between the found inputs, and starts looking through that for additional required inputs. Every time a required input is found, the search area shrinks, until all required inputs are found or the area shrinks to zero. At last if every required input is found within the search area, the link is accepted and the state transitions to the move connected via that link.