Comments for Chad Salinas Computer Science Scratch Pad http://chadsalinas.wordpress.com Cool Computer Science and Math Puzzles Sat, 07 Jun 2008 15:29:46 +0000 http://wordpress.com/ hourly 1 Comment on Pumping Lemma by Mike Godfrey http://chadsalinas.wordpress.com/2008/04/25/pumping-lemma/#comment-5 Mike Godfrey Sat, 07 Jun 2008 15:29:46 +0000 http://chadsalinas.wordpress.com/?p=21#comment-5 The Pumping Lemma is useful for disproving the <a href="http://en.wikipedia.org/wiki/Pumping_lemma_for_regular_languages" title="wikipedia ref" rel="nofollow">regularity</a> of a language. It states that for strings beyond a certain length in your infinite-sized regular language, you are bound to find repeating strings in the form xy^i z, where xyz is in your language already. It's useful, because if the pumping lemma applies to a language, you know that it's regular. If the pumping lemma does not apply to an infinite language, you only know that the pumping lemma does not apply to that language. The Pumping Lemma is useful for disproving the regularity of a language. It states that for strings beyond a certain length in your infinite-sized regular language, you are bound to find repeating strings in the form xy^i z, where xyz is in your language already.

It’s useful, because if the pumping lemma applies to a language, you know that it’s regular. If the pumping lemma does not apply to an infinite language, you only know that the pumping lemma does not apply to that language.

]]> Comment on Worst Case & Asymptotic Analysis by John Williams http://chadsalinas.wordpress.com/2007/07/05/worst-case-asymptotic-analysis/#comment-3 John Williams Wed, 11 Jul 2007 19:17:57 +0000 http://chadsalinas.wordpress.com/2007/07/05/worst-case-asymptotic-analysis/#comment-3 You can put text in the middle of a LaTex equation that is not italicized using the \text{insert this regular text here} command. There are also specific commands to insert space in an equation, because spaces are ignored in the equation environment. $latex \Leftrightarrow \exists \, n_0 > 0 \text{ and }c >0\text{ s.t. }$ You could write $latex f(n) \in O(g(n)) \text{ if and only if }(\exists c>0)(\exists n_0 > 0)(\forall n>n_0)(0 \leq f(n) \leq c \cdot g(n))$ for example. You can put text in the middle of a LaTex equation that is not italicized using the \text{insert this regular text here} command. There are also specific commands to insert space in an equation, because spaces are ignored in the equation environment.

\Leftrightarrow \exists \, n_0 > 0 \text{ and }c >0\text{ s.t. }

You could write

f(n) \in O(g(n)) \text{ if and only if }(\exists c>0)(\exists n_0 > 0)(\forall n>n_0)(0 \leq f(n) \leq c \cdot g(n))

for example.

]]> Comment on Equivalent Regular Expressions by John Williams http://chadsalinas.wordpress.com/2007/06/27/equivalent-regular-expressions/#comment-2 John Williams Wed, 27 Jun 2007 22:13:18 +0000 http://chadsalinas.wordpress.com/2007/06/27/equivalent-regular-expressions/#comment-2 Ferret out?? I've wondered about the origins of this idiom. Do ferrets search? Bloodhounds do. Do ferrets retrieve? Perhaps we could invent a new database model and call the UI Ferret? Ferret out?? I’ve wondered about the origins of this idiom. Do ferrets search? Bloodhounds do. Do ferrets retrieve? Perhaps we could invent a new database model and call the UI Ferret?

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