The composition of these two processes would be as given in Figure 2 The composition is somehow the "product" of these processes, and is a complete representation of this concurrent system. Its nodes represent the possible states that the system can be in, e.g., (1, 1) represents that I already drank my coffee, while I have thought about what to say, but have not said it yet. The edges give the possible transitions between these (composite) states, and so each path from the initial state (0, 0) to the final state (1,2) represents a possible trace of this system, e.g., think→ drink coffee → talk. start (0,0) think (0, 1) talk drink coffee drink coffee drink coffee (0, 2) (1,2) talk (1, 1) think (1,0) Figure 2: The composition of the two concurrent processes of Figure 1

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Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.