Alternation with restrictions on looping

Alternating Turing machines with restrictions preventing them from returning to a previous configuration model games with rules enforcing such a restriction, for instance, the Chinese version of Go. Such restrictions do not affect the time complexity of problems for alternating Turing machines but space S on a machine with the restriction is equivalent either to time or to space exponential in S on a normal alternating machine, depending on the precise nature of the restriction.