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<node id="809922" title="Re^3: Turing completeness and regular expressions" created="2009-11-28 12:52:31" updated="2009-11-28 12:52:31">
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blokhead</author>
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You may be right about bottom-up evaluation of SK expressions. Larger terms must be treated as first-class objects to be passed around, etc.

&lt;p&gt;

But we both missed the obvious way to just use "plain" regex substitutions to simulate Turing-completeness: [wp://Unrestricted grammar|unrestricted (type-0) grammars]. They are basically &lt;i&gt;defined&lt;/i&gt; as the repeated evaluation of plain regex substitutions, and are Turing-complete. A universal TM converted to a type-0 grammar will only have a finite number of substitution rules, and you can simulate it with a substitution + finite lookup table (or a finite # of separate s/// statements).

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blokhead
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