User:C. lorenz/Template:Infobox Complexity Class/doc

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: " ".

image: Code for image, if any. Example: " " 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: " " (definition of SAPTIME) or " " (definition of YP - Yaroslav-Percival).

external-urls: Links to the class' entry at an external site that harbors entries for many classes. Example: " |Complexity Zoo " but not links to for instance articles.

dtime: Functions f such that the class is in DTIME[f(n)], if applicable. Example: "$$n^{\Theta(1)}$$" (PTIME) or "$$n^{\Omega(1)}, 2^{n^{O(1)}}$$" (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/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) " PCP($$O(log n)$$, 3), Existential Second-order logic ".

related: Interesting related classes that does not fall in one of the other categories. Example: (for NP) " coNP, FNP ".

notequals: Classes that are known to not to equal our class but not known to be either supersets or subsets. Example: (for NP) " P/log ".

improper-subsets: (Maximal) classes contained by our class but not known to be different. Example: (for NP) " P ".

proper-subsets: (Maximal) classes contained by our class and known to be different. Example: (for PSPACE) " 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) " 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.