| 41. | There are two distinct senses of the word " undecidable " in mathematics and computer science.
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| 42. | Many problems in mathematics have been shown to be undecidable after these initial examples were established.
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| 43. | Many of the examples of undecidable first-order theories given above are of this form.
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| 44. | Without this restriction, the automaton has undecidable emptiness and expressive power beyond regular tree languages.
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| 45. | It has been shown that some code optimization problems are NP-complete, or even undecidable.
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| 46. | Gregory Chaitin produced undecidable statements in algorithmic information theory and proved another incompleteness theorem in that setting.
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| 47. | The halting problem is therefore called non-computable or "'undecidable " '.
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| 48. | Badiou's ultimate ethical maxim is therefore one of :'decide upon the undecidable '.
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| 49. | Likewise, a reduction computing a noncomputable function can reduce an undecidable problem to a decidable one.
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| 50. | Deciding on extensional equality is undecidable in general and even for functions with finite domains often intractable.
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