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In computability theory, a decider is a Turing machine that halts for every input. A decider is also called a total Turing machine as it represents a total function.
Because it always halts, such a machine is able to decide whether a given string is a member of a formal language. The class of languages which can be decided by such machines is the set of recursive languages.
Given an arbitrary Turing machine, determining whether it is a decider is an undecidable problem. This is a variant of the halting problem, which asks for whether a Turing machine halts on a specific input.