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Every Turing-recognizable language is Turing-decidable. Every context-free language is Turing-decidable. Every context-free language is regular. A decider D can be in an infinite loop as

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Every Turing-recognizable language is Turing-decidable. Every context-free language is Turing-decidable. Every context-free language is regular. A decider D can be in an infinite loop as long as the input string is not a member of L(D). For every (deterministic) decider there is a non-deterministic decider that recognizes the same language

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