Optimal 6-state algorithms for the behavior of several moving creatures

Abstract

The goal of our investigation is to find automatically the absolutely best rule for a moving creature in a cellular field. The task of the creature is to visit all empty cells with a minimum number of steps. We call this problem creature's exploration problem. The behaviour was modelled using a variable state machine represented by a state table. Input to the state table is the current state and the neighbour's state in front of the creature's moving direction. The problem is that the search space for the possible rules grows exponentially with the number of states, inputs and outputs. We could solve the problem for six states, two inputs and two outputs with the aid of a parallel hardware platform (FPGA technology). The set of all possible n-state algorithms was first reduced by discarding equivalent, reducible and not strongly connected ones. The algorithms which showed a certain performance for five initial configurations during simulation were extracted by the hardware and send to the host PC. Additional tests for robustness and the behaviour of several creatures was carried out in software. One creature with the best algorithm can visit 99.92 % of the empty cells of 26 test configurations. Several creatures up to 16 can perform the task more efficiently for the tested initial configuration. © Springer-Verlag Berlin Heidelberg 2006.