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computable sets and functions, Turing degrees, c.e. degrees, models of computability, primitive recursion, oracle computation, models of computability, decision problems, undecidability, Turing jump, halting problem, notions of computable randomness, computable model theory, computable equivalence relation theory, arithmetic and hyperarithmetic hierarchy, infinitary computability, $\alpha$-recursion, complexity theory.
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Constructing hard inputs for the complement of bounded halting
No, such $\langle N', x'\rangle$ is not constructible at all given only a description of $M$, even if you remove the requirement of polynomial time.
Suppose that $CONSTRUCT$ is such a deterministic t …