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text: 'As the Church-Turing thesis is not a [ proper mathematical sentence] we cannot prove it. However, we can collect [-3s] to increase our confidence in its correctness.\n\n#The inductive argument\nEvery computational model we have seen so far is [ reducible] to Turing's model.\n\nIndeed, the thesis was originally formulated independently by Church and Turing in reference to two different computational models ([Turing_machines] and [Lambda_Calculus] respectively). When they were shown to be [equivilance_relation equivalent] it was massive evidence in favor of both of them.\n\nA non-exhaustive list of models which can be shown to be reducible to Turing machines are:\n\n* [Lambda_calculus]\n* [Quantum_computation]\n* [Nondeterministic_Turing_machines Non-deterministic_Turing_machines]\n* [Register_machines]\n* The set of [-recursive_functions]\n\n#Lack of counterexamples\nPerhaps the strongest argument we have for the CT thesis is that there is not a widely accepted candidate to a counterexample of the thesis. This is unlike the [-4ct], where quantum computation stands as a likely counterexample.\n\nOne may wonder whether the computational models which use a source of [ randomness] (such as quantum computation or [-probabilistic_Turing_machines]) are a proper counterexample to the thesis: after all, Turing machines are fully [-deterministic], so they cannot simulate randomness.\n\nTo properly explain this issue we have to recall what it means for a quantum computer or a probabilistic Turing machine to compute something: we say that such a device computes a function $f$ if for every input $x$ the probability of the device outputting $f(x)$ is greater or equal to some arbitrary constant greater than $1/2$. Thus we can compute $f$ in a classical machine, for there exists always the possibility of simulating every possible outcome of the randomness to deterministically compute the probability distribution of the output, and output as a result the possible outcome with greater probability.\n\nThus, randomness is reducible to Turing machines, and the CT thesis holds.',
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