Complexity of Langtonʹs ant Original Research Article

The virtual ant introduced by Langton [Physica D 22 (1986) 120] has an interesting behavior, which has been studied in several contexts. Here we give a construction to calculate any boolean circuit with the trajectory of a single ant. This proves the P-hardness of the system and implies, through the simulation of one-dimensional cellular automata and Turing machines, the universality of the ant and the undecidability of some problems associated to it.