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Monoidal adjunction - Revision history
2026-05-13T19:38:09Z
Revision history for this page on the wiki
MediaWiki 1.43.0-wmf.28
https://en.formulasearchengine.com/index.php?title=Monoidal_adjunction&diff=13409&oldid=prev
en>Spectral sequence: disambiguate: Adjoint functors
2013-06-07T18:26:46Z
<p>disambiguate: <a href="/wiki/Adjoint_functors" title="Adjoint functors">Adjoint functors</a></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:26, 7 June 2013</td>
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<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><del style="font-weight: bold; text-decoration: none;">Hi there, I am Andrew Berryhill. I am truly fond of to go to karaoke but I</del>'<del style="font-weight: bold; text-decoration: none;">ve been using on new issues lately. Alaska </del>[<del style="font-weight: bold; text-decoration: none;">http://165</del>.<del style="font-weight: bold; text-decoration: none;">132</del>.<del style="font-weight: bold; text-decoration: none;">39</del>.<del style="font-weight: bold; text-decoration: none;">93</del>/<del style="font-weight: bold; text-decoration: none;">xe/visitors/372912 psychics online] is </del>the <del style="font-weight: bold; text-decoration: none;">only place I</del>'<del style="font-weight: bold; text-decoration: none;">ve been residing in but now I</del>'<del style="font-weight: bold; text-decoration: none;">m considering other options. Invoicing is what I do for </del>a <del style="font-weight: bold; text-decoration: none;">living but I've always needed my personal company</del>.<<del style="font-weight: bold; text-decoration: none;">br</del>><<del style="font-weight: bold; text-decoration: none;">br</del>><del style="font-weight: bold; text-decoration: none;">Feel free </del>to <del style="font-weight: bold; text-decoration: none;">surf to my blog ... [http://breenq.com/index.php?do</del>=<del style="font-weight: bold; text-decoration: none;">/profile</del>-<del style="font-weight: bold; text-decoration: none;">1144</del>/<del style="font-weight: bold; text-decoration: none;">info/ authentic psychic readings</del>] <del style="font-weight: bold; text-decoration: none;">solutions by lynne </del>([<del style="font-weight: bold; text-decoration: none;">http://www.zavodpm.ru/blogs/glennmusserrvji/14565</del>-<del style="font-weight: bold; text-decoration: none;">great</del>-<del style="font-weight: bold; text-decoration: none;">hobby</del>-<del style="font-weight: bold; text-decoration: none;">advice</del>-<del style="font-weight: bold; text-decoration: none;">assist-allow-you-get-going http</del>://<del style="font-weight: bold; text-decoration: none;">www.zavodpm.ru</del>/<del style="font-weight: bold; text-decoration: none;">blogs</del>/<del style="font-weight: bold; text-decoration: none;">glennmusserrvji</del>/<del style="font-weight: bold; text-decoration: none;">14565</del>-<del style="font-weight: bold; text-decoration: none;">great</del>-<del style="font-weight: bold; text-decoration: none;">hobby</del>-<del style="font-weight: bold; text-decoration: none;">advice-assist-allow-you-get-going</del>]<del style="font-weight: bold; text-decoration: none;">)</del></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><ins style="font-weight: bold; text-decoration: none;">A '''Multi-tape Turing machine''</ins>' <ins style="font-weight: bold; text-decoration: none;">is like an ordinary [</ins>[<ins style="font-weight: bold; text-decoration: none;">Turing machine]] with several tapes</ins>. <ins style="font-weight: bold; text-decoration: none;">Each tape has its own head for reading and writing</ins>. <ins style="font-weight: bold; text-decoration: none;">Initially the input appears on tape 1,and the others start out blank</ins>.<ins style="font-weight: bold; text-decoration: none;"><ref>{{cite book |title=Introduction to the Theory of Computation |last1=Sipser |first1=Michael |year=2005|page=148|publisher=Thomson Course Technology|isbn=0-534-95097-3}}<</ins>/<ins style="font-weight: bold; text-decoration: none;">ref></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> </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;">This model intuitively seems much more powerful than the single-tape model, but any multi-tape machine, no matter how large </ins>the ''<ins style="font-weight: bold; text-decoration: none;">k'', can be simulated by </ins>a <ins style="font-weight: bold; text-decoration: none;">single-tape machine using only quadratically more computation time</ins>.<<ins style="font-weight: bold; text-decoration: none;">ref</ins>><ins style="font-weight: bold; text-decoration: none;">{{cite book |title=Computational Complexity |last1=Papadimitriou |first1=Christos |year=1994|page=53|publisher=Addison-Wesley|isbn=0-201-53082-1}}</ref> Thus, multi-tape machines cannot calculate any more functions than single-tape machines,</ins><<ins style="font-weight: bold; text-decoration: none;">ref</ins>><ins style="font-weight: bold; text-decoration: none;">{{cite book |title=Introduction </ins>to <ins style="font-weight: bold; text-decoration: none;">Languages and the Theory of Computation |last1=Martin |first1=John |year=2010 |pages=243–246 |publisher=McGraw Hill |isbn</ins>= <ins style="font-weight: bold; text-decoration: none;">978</ins>-<ins style="font-weight: bold; text-decoration: none;">0071289429}}<</ins>/<ins style="font-weight: bold; text-decoration: none;">ref> and none of the robust [[Computational complexity theory|complexity]</ins>] <ins style="font-weight: bold; text-decoration: none;">classes </ins>(<ins style="font-weight: bold; text-decoration: none;">such as [</ins>[<ins style="font-weight: bold; text-decoration: none;">P (complexity)|polynomial time]]) are affected by a change between single</ins>-<ins style="font-weight: bold; text-decoration: none;">tape and multi</ins>-<ins style="font-weight: bold; text-decoration: none;">tape machines.</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> </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;">== Formal definition ==</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;">A k</ins>-<ins style="font-weight: bold; text-decoration: none;">tape Turing machine can be described as a 6</ins>-<ins style="font-weight: bold; text-decoration: none;">tuple <math>M=\langle Q, \Gamma, s, b, F, \delta \rangle</math> where</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> </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;">*<math>Q<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> is a finite set of states</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;">*<math>\Gamma</math> is a finite set of the tape alphabet</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;">*<math>s \in Q<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> is the initial state</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;">*<math>b \in \Gamma<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> is the blank symbol</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;">*<math>F \subseteq Q<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> is the set of final or accepting states</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;">*<math>\delta: Q \times \Gamma^k \rightarrow Q \times (\Gamma \times \{L,R,S\})^k<</ins>/<ins style="font-weight: bold; text-decoration: none;">math> is a partial function called the transition function, where k is the number of tapes, L is left shift, R is right shift and S is no shift.</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> </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;">== Two</ins>-<ins style="font-weight: bold; text-decoration: none;">stack Turing machine ==</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;">Two</ins>-<ins style="font-weight: bold; text-decoration: none;">stack Turing machines have a read</ins>-<ins style="font-weight: bold; text-decoration: none;">only input and two storage tapes. If a head moves left on either tape a blank is printed on that tape, but one symbol from a “library” can be printed.</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> </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;">== See also ==</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;">* [[Turing machine]]</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;">* [[Universal Turing machine]]</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;">* [[Alternating Turing machine]]</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;">* [[Probabilistic Turing machine]]</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;">* [[Turing machine equivalents]]</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> </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;">== References ==</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;"><references/></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> </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;">[[Category:Turing machine]</ins>]</div></td></tr>
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en>Spectral sequence
https://en.formulasearchengine.com/index.php?title=Monoidal_adjunction&diff=247768&oldid=prev
en>SmackBot: Date maintenance tags and general fixes
2009-03-02T16:12:32Z
<p>Date maintenance tags and general fixes</p>
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en>SmackBot