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...

We introduce a new class of strongly degenerate nonlinear parabolic PDEs ( p − 2 ) Δ ∞ , X N + u Y t m ⋅ ∇ ∂ = 0 ∈ R × 1 combining the classical PDE Kolmogorov and normalized -Laplace operator. characterize solutions in terms an asymptotic mean value property results are connected to analysis certain tug-of-war games with noise. The functions for introduced approximate stated when parameter tha...