User:C. lorenz/Template:Infobox Complexity Class
Usage
{{User:C. lorenz/Template:Infobox Complexity Class
|class=
|image=
|long-name=
|description=
|external-urls=
|wheredefined=
|dtime=
|complete-class=
|complement-class=
|proper-supersets=
|improper-supersets=
|equals=
|related=
|notequals=
|improper-subsets=
|proper-subsets=
|properties=
|low-with=
|low-for=
|closed-reductions=
|closed-operations=
|canonical-problems=
|models=
}}
 | |
| External pages | Complexity Zoo |
|---|---|
| Complete class | PSPACE-complete |
| Complement class | self |
| Equalities | AP[1], BPPSPACE[2], IP[3], NPSPACE[4], PPSPACE[5], SAPTIME[5] |
| DTIME | , |
| Related | PTIME |
| Proper supersets | EXPSPACE[6] |
| Improper supersets | AlmostPSPACE[7], EXPTIME, RG, QPSPACE[8] |
| Inequalities | P-close, P/log |
| Improper subsets | CH[9], P^PP[10], P^#P[10], QSZK, RG[1] |
| Proper subsets | NL[6] |
| Canonical problems | QSAT |
| Properties | Syntactic |
| Low with | self |
| Low for | self |
| Closed reductions | Poly-time |
| Models | Alternating Turing machine, Turing machine |
Parameter Explanation
Regarding the meaning of "minimal" and "maximal", see the paragraph of Inclusion Guidelines.
class: The (short) name of the class. Example: "NP" but not "Polynomial Time". Default: "[[{{PAGENAME}}]]".
image: Code for image, if any. Example: "[[File:Complexity_subsets_pspace.svg|200px]]" but not "File:Complexity_subsets_pspace.svg".
long-name: Paraphrased/full name or short description of the class. Example: "Non-deterministic polynomial time" but not "the set of all decision problems for which ...".
description: Longer description of the class. Not used.
wheredefined: First definitions of the class. If not available, any suitable place. Secondly, internet sources preferred. Leave this field out rather than linking to the wikipedia page of the class. Example: "<ref>Christos H. Papadimitriou, Games against nature, FOCS 1983</ref>" (definition of SAPTIME) or "<ref>Scott Aaronsson, [https://www.blogger.com/comment.g?blogID=17392898&postID=114560148725169634&pli=1 Shetl-Optimized, What is the name of this post?], 2006</ref>" (definition of YP - Yaroslav-Percival).
external-urls: Links to the class' entry at an external site that harbors entries for many classes. Example: "[http://qwiki.stanford.edu/wiki/Complexity_Zoo:N#np|Complexity Zoo]" but not links to for instance articles.
dtime: Functions f such that the class is in DTIME[f(n)], if applicable. Example: "" (PTIME) or "" (NP).
complete-class: The complete class under a suitable reduction or none.
complement-class: The complement class.
proper-supersets: (Minimal) classes containing our class and are known not to equal our class. Example: (for NP) "[[NEXP]], [[NP_(complexity)|NP]]/one" but not "[[PSPACE]]".
improper-supersets: (Minimal) classes containing our class but not known not to equal our class. Example: (for NP) "[[NE]], [[PSPACE]], [[MA]]".
equals: Classes equaling our class. Example: (for NP) "[[Probabilistically_checkable_proof_(complexity)|PCP]](<math>O(log n)</math>, 3), Existential [[Second-order logic]]".
related: Interesting related classes that does not fall in one of the other categories. Example: (for NP) "[[coNP]], [[FNP_(complexity)|FNP]]".
notequals: Classes that are known to not to equal our class but not known to be either supersets or subsets. Example: (for NP) "[[PTIME|P]]/log".
improper-subsets: (Maximal) classes contained by our class but not known to be different. Example: (for NP) "[[PTIME|P]]".
proper-subsets: (Maximal) classes contained by our class and known to be different. Example: (for PSPACE) "[[NL_(complexity)|NL]]".
properties: Interesting properties of the class. Example: (for NP) "syntactic".
low-with: Classes that are low to the class, i.e. A such that C^A = C.
low-to: Classes the class is low to, i.e. A such that A^C = A.
closed-reductions: (Maximal) reductions under which the class is closed. Example: (for NP) "[[Polynomial-time reduction|Poly-time]]" but not "Log-space" since NP is closed under polynomial-time reductions and log-space reductions are also polynomial-time reductions.
closed-operations: Notable operations under which the class is closed. Not used.
canonical-problems: A few select canonical problems. These should typically be complete problems whenever applicable.
models: Most noteworthy models of computation for which the class can be naturally defined. Example: (for NP) "[[Non-Deterministic Turing machine]], [[Descriptive complexity]]". As a guide, list only the three most important models for the class in the info box but any number in the article. For example, the descriptive complexity characterization of PH (PH = languages expressible with second-order logic) is much more natural than that of NP (second-order logic with only first-order universal quantification) and PSPACE (second-order logic with a transitive closure operator). It should therefore take less to omit "descriptive complexity" as a natural model of computation for NP than for PH.
Inclusion Guidelines
These guidelines are still in the making. WP:BB
If all inclusions were listed in the relevant field, then most classes would have boxes with hundreds of names. The following suggestions are made to deal with this issue.
- Cite sources, even if taken from e.g. the Complexity Zoo.
- Inference based on basic set theory is considered "routine calculation" and is acceptable (see WP:NOR). In other words, if prof. X has published A ⊆ B and prof. Y has published B ⊆ C, then we may correctly infer that A ⊆ C by referring to the two sources. Any inference that is not considered "routine" should be justified with a credible source explicating the inference.
- Do not include relations that can be reasonably inferred by following relations on the relevant pages, or relations that are of little interest and involves a class not defined on Wikipedia. For instance, if the page for class B does not exist but the page of class A contains the relation A ⊆ B and the page of class C contains B ⊆ C, then it would still be reasonable to add A ⊆ C to the pages of both A and C. This would not be the case if B also listed the two relations. If B was defined but did not list these relations, then the page of B should be extended, not A or C. Even if the page of B does not exists, the relation involving B may be of interest. If there is another class D which has a relation to C that implies B ⊆ C, then one may reasonably replace the relation involving B with the relation involving D.
- Classes especially important for the class may certainly violate the above guideline. For instance, one may very well include the relations of the complement, non-deterministic, or quantum equivalences even if the status of these classes are implied by other classes. This does not mean that P or NP should be included on every page.
Example References
- ^ Chandra, A.K. and Kozen, D.C. and Stockmeyer, L.J., 'Alternation', Journal of the ACM, Volume 28, Issue 1, pp. 114-133, 1981.
- ^ Complexity Zoo, [1], accessed Mars 25, 2009
- ^ Adi Shamir. IP = PSPACE. Journal of the ACM, volume 39, issue 4, p.869–877. October 1992.
- ^ Savitch's theorem
- ^ a b Christos Papadimitriou (1985). ""Games against Nature"". "Journal of Computer and System Sciences". 31.
- ^ a b Space hierarchy theorem
- ^ Definition of Almost-PSPACE. PSPACE ⊆ PSPACE^A for every A.
- ^ Greg Kuperberg, Complexity Zoology: Active Inclusion Diagram, 2006, http://www.math.ucdavis.edu/~greg/zoology/diagram.xml
- ^ K. W. Wagner (1986). "The complexity of combinatorial problems with succinct representation". Informatica. 23: 325–356.
- ^ a b S. Toda (1989). "On the computational power of PP and ⊕P". FOCS 1989: 514–519.
See also