On the computational complexity of infinite words

This paper contains answers to several problems in the theory of the computational complexity of infinite words. We show that the problem whether all infinite words generated by iterating deterministic generalized sequential machines have logarithmic space complexity is equivalent to the open problem asking whether the unary classes of languages in P and in DLOG are equivalent. Similarly, the problem to find a concrete infinite word which cannot be generated in logarithmic space is equivalent to the problem to find a concrete language which does not belong to DSPACE(n). Finally, we separate classes of infinite words generated by double and triple DOL TAG systems. (C) 2002 Elsevier Science B.V. All rights reserved.