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Lexikon


computability theory


The area of theoretical computer science concerning what problems can be solved by any computer. A function is computable if an ref="module.php?name=Lexikon&file=search&eid=1&query=algorithm">algorithm can be implemented which will give the correct output for any valid input. Since computer programs are ref="module.php?name=Lexikon&file=search&eid=1&query=countable">countable but ref="module.php?name=Lexikon&file=search&eid=1&query=real numbers">real numbers are not, it follows that there must exist real numbers that cannot be calculated by any program. Unfortunately, by definition, there isn' t an easy way of describing any of them! In fact, there are many tasks (not just calculating real numbers) that computers cannot perform. The most well-known is the ref="module.php?name=Lexikon&file=search&eid=1&query=halting problem">halting problem, the ref="module.php?name=Lexikon&file=search&eid=1&query=busy beaver">busy beaver problem is less famous but just as fascinating. ["Computability", N.J. Cutland. (A well written undergraduate-level introduction to the subject)]. ["The Turing Omnibus", A.K. Dewdeney]. (1995-01-13)

In addition suitable contents:
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ref="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ ref="module.php?name=Lexikon&op=content&tid=7107">li ] [ ref="module.php?name=Lexikon&op=content&tid=7410">lt ] [ ref="module.php?name=Lexikon&op=content&tid=7437">lv ] [ ref="module.php?name=Lexikon&op=content&tid=7441">ly ] [ ref="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ref="module.php?name=Lexikon&op=content&tid=7582">man ] [ ref="module.php?name=Lexikon&op=content&tid=8029">mn ] [ ref="module.php?name=Lexikon&op=content&tid=8032">mo ] [ ref="module.php?name=Lexikon&op=content&tid=8040">mod ] [ ref="module.php?name=Lexikon&op=content&tid=8079">module ] [ ref="module.php?name=Lexikon&op=content&tid=8167">mp ] [ ref="module.php?name=Lexikon&op=content&tid=8228">ms ] [ ref="module.php?name=Lexikon&op=content&tid=8258">mu ] [ ref="module.php?name=Lexikon&op=content&tid=8384">N ] [ ref="module.php?name=Lexikon&op=content&tid=8386">na ] [ ref="module.php?name=Lexikon&op=content&tid=8460">nc ] [ 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