The position of index sets of identifiable sets in the arithmetical hierarchy
Information and Control
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Algorithmic information theory
Algorithmic information theory
On the Length of Programs for Computing Finite Binary Sequences
Journal of the ACM (JACM)
On the Simplicity and Speed of Programs for Computing Infinite Sets of Natural Numbers
Journal of the ACM (JACM)
The unknowable
How we know what technology can do
Communications of the ACM
Algorithmic complexity of recursive and inductive algorithms
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
A note on blum static complexity measures
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
Randomness behaviour in blum universal static complexity spaces
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
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There is a dependency between computability of algorithmic complexity and decidability of different algorithmic problems. It is known that computability of the algorithmic complexity C(x) is equivalent to decidability of the halting problem for Turing machines. Here we extend this result to the realm of superrecursive algorithms, considering algorithmic complexity for inductive Turing machines. We study two types of algorithmic complexity: recursive (classical) and inductive algorithmic complexities. Relations between these types of algorithmic complexity and decidability of algorithmic problems for Turing machines and inductive Turing machines are considered. In particular, it is demonsrated that computability of algorithmic complexity is equivalent not only to decidability of the halting problem, but also to decidability by inductive Turing machines of the first order of many other problems for Turing machines, such as: if a Turing machine computes a recursive (total) function; if a Turing machine gives no result only for n inputs; if a Turing machine gives results only for n inputs.