We argue that Martin-LL of tests provide useful techniques in proofs involving Kolmogorov complexity. Our examples cover more areas: (1) logical deenability; we prove an analogue of the 0-1 Law for various logics in terms of structures with high Kolmogorov complexity, (2) probabilistic computation: we display a relation between the Kolmogorov complexity of the random strings on which a probabil...

In this paper we study the Kolmogorov complexity for non-effective computations, that is, either halting or non-halting computations on Turing machines. This complexity function is defined as the length of the shortest inputs that produce a desired output via a possibly non-halting computation. Clearly this function gives a lower bound of the classical Kolmogorov complexity. In particular, if t...

P-printable sets were defined by Hartmanis and Yesha and have been investigated by several researchers. The analogous notion of Lprintable sets was defined by Fortnow et al; both P-printability and L-printability were shown to be related to notions of resource-bounded Kolmogorov complexity. NL-printability was defined by Jenner and Kirsig, but some basic questions regarding this notion were lef...