Infinite time Turing machines extend the classical Turing machine concept to transfinite ordinal time, thereby providing a natural model of infinitary computability that sheds light on the power and limitations of supertask algorithms.

Frequency computation was introduced in [16]. Trakhtenbrot [17] proved the existence of a continuum of functions computable by frequency Turing machines with frequency 1 2 . In contrast, every function computable by a frequency Turing machine with frequency exceeding

The time separation results concerning classes of languages over a single-1etteK alphabet accepted by multi-tape nondeterministic Turing machines. well-known from Seiferas, Fischer and Meyer (1978), are supplemented. Moreover, via a universal machine a modified time complexity measure UTIME of Turing machines computations which is sensitive to multiplication by constants (i.e., UTIME(t) s UTIME...