The proof of NTM-DTM decidability equivalence relies on simulation arguments that collapse non-deterministic branching into deterministic search, preserving halting but not computational meaning.
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When a computer program finishes running and stops, as opposed to running forever in an infinite loop.
NTM (Non-Deterministic Turing Machine)(as used in computability theory)
A theoretical computer that can explore multiple possible paths at once, like a person who can try all routes through a maze simultaneously instead of one at a time.
Non-deterministic branching(as used in computability theory)
The ability to split into multiple possible paths or choices at the same time, exploring many options in parallel.
Simulation argument(a modern thought experiment about the nature of reality)
A philosophical idea suggesting that if civilizations can create detailed computer simulations of universes, we might ourselves be living inside such a simulation.
decidability(Key property for automated theorem proving; equivalent to the satisfiability problem since ⊨ φ iff ¬φ is not satisfiable)
A logic is decidable when there exists an algorithm that answers YES or NO in finite time to the question of whether a given formula φ is valid