If space reuse across computation branches is permitted in the deterministic simulation, the correctness of the simulation depends on confluence properties that are not guaranteed by f(n)-time bounds alone.

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computation branches(as used in computer science): Different paths or sequences of steps that a calculation can follow, like choosing between multiple routes to reach the same destination.
confluence properties(as used in logic and computer science): A guarantee that different paths through a calculation will always lead to the same final answer, no matter which route you take.
deterministic simulation(as used in logic and computer science): A computer model where the same input always produces the exact same output every time, with no randomness or unpredictability.
f(n)-time bounds(as used in computer science and complexity theory): Mathematical limits on how long a calculation should take, where 'f(n)' represents a formula describing the maximum time needed based on the size of the input.

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