If the number of bits is constant, then any polynomial time based on it is constant.
Big-O statements (like an algorithm taking constant or O(1) time) are statements about asymptotic behavior, i.e, how the function behaves in the limit (usually, as input size tends to infinity). If you don't look at them in the limit, then big-O-ish language (like constant time) is meaningless.
How meaningless? Even undecidable languages have a constant time "algorithm" if you consider the input size to be held to a constant. So without viewing things in the limit, all problems become computationally equivalent in the asymptotic language.
Update: added citation from parent node
-
Are you posting in the right place? Check out Where do I post X? to know for sure.
-
Posts may use any of the Perl Monks Approved HTML tags. Currently these include the following:
<code> <a> <b> <big>
<blockquote> <br /> <dd>
<dl> <dt> <em> <font>
<h1> <h2> <h3> <h4>
<h5> <h6> <hr /> <i>
<li> <nbsp> <ol> <p>
<small> <strike> <strong>
<sub> <sup> <table>
<td> <th> <tr> <tt>
<u> <ul>
-
Snippets of code should be wrapped in
<code> tags not
<pre> tags. In fact, <pre>
tags should generally be avoided. If they must
be used, extreme care should be
taken to ensure that their contents do not
have long lines (<70 chars), in order to prevent
horizontal scrolling (and possible janitor
intervention).
-
Want more info? How to link
or How to display code and escape characters
are good places to start.
|