https://machinelearning.subwiki.org/w/index.php?action=history&feed=atom&title=User%3AIssaRice%2FComputability_and_logic%2FLeast_search_operator 2026-06-18T03:15:08Z Revision history for this page on the wiki MediaWiki 1.41.2 https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Computability_and_logic/Least_search_operator&diff=1143&oldid=prev 2018-12-21T05:07:37Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 05:07, 21 December 2018</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The &#039;&#039;&#039;least search operator&#039;&#039;&#039;, &#039;&#039;&#039;minimzation operator&#039;&#039;&#039;, or &#039;&#039;&#039;μ-operator&#039;&#039;&#039; is used in computability theory to define new functions.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The &#039;&#039;&#039;least search operator&#039;&#039;&#039;, &#039;&#039;&#039;minimzation operator&#039;&#039;&#039;, or &#039;&#039;&#039;μ-operator&#039;&#039;&#039; is used in computability theory to define new functions.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The least search operator allows us to move from primitive recursive functions to general recursive functions.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The least search operator allows us to move from primitive recursive functions to general recursive <ins style="font-weight: bold; text-decoration: none;">(total or partial) </ins>functions.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition==</div></td></tr> </table>

IssaRice https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Computability_and_logic/Least_search_operator&diff=1142&oldid=prev 2018-12-21T05:07:19Z

<p><span dir="auto"><span class="autocomment">Definition</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 05:07, 21 December 2018</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l4">Line 4:</td> <td colspan="2" class="diff-lineno">Line 4:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition==</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* note: the least search operator may run into an "infinite loop". This means that partial recursive functions are not in general total.</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Notation==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Notation==</div></td></tr> </table>

IssaRice https://machinelearning.subwiki.org/w/index.php?title=User:IssaRice/Computability_and_logic/Least_search_operator&diff=1141&oldid=prev 2018-12-21T05:04:47Z

<p>Created page with &quot;The &#039;&#039;&#039;least search operator&#039;&#039;&#039;, &#039;&#039;&#039;minimzation operator&#039;&#039;&#039;, or &#039;&#039;&#039;μ-operator&#039;&#039;&#039; is used in computability theory to define new functions. The least search operator allows us...&quot;</p> <p><b>New page</b></p><div>The &#039;&#039;&#039;least search operator&#039;&#039;&#039;, &#039;&#039;&#039;minimzation operator&#039;&#039;&#039;, or &#039;&#039;&#039;μ-operator&#039;&#039;&#039; is used in computability theory to define new functions.<br /> <br /> The least search operator allows us to move from primitive recursive functions to general recursive functions.<br /> <br /> ==Definition==<br /> <br /> ==Notation==<br /> <br /> Most texts seem to write the least search operator was &lt;math&gt;\mu&lt;/math&gt; as in &lt;math&gt;\mu y[f(y) = 0]&lt;/math&gt; or maybe &lt;math&gt;\mu y.f(y) = 0&lt;/math&gt; (like the &lt;math&gt;\lambda&lt;/math&gt; operator for defining anonymous functions).<br /> <br /> Boolos/Burgess/Jeffrey use &lt;math&gt;\mathrm{Mn}&lt;/math&gt; (for &quot;minimization&quot;).<br /> <br /> ==Intuition==<br /> <br /> bounded search vs unbounded search; bounded for-loop vs while-loop.</div>

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