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