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Do all standard computable problems admit an algorithm…

Do all standard computable problems admit an algorithm with joint time-space optimality?

Suppose a problem can be solved with optimal time complexity O(t(n)) and optimal space complexity O(s(n)). Ignoring pathological cases (problems with Blum speedup), is there always an algorithm that is simultaneously optimal in both time and space, i.e. runs in O(t(n)) time and O(s(n)) space?
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