Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.1 6/24/83; site mmintl.UUCP
Path: utzoo!linus!philabs!pwa-b!mmintl!franka
From: franka@mmintl.UUCP (Frank Adams)
Newsgroups: net.philosophy,net.math
Subject: Re: Mind as Turing Machine: a proof *and* a disproof!
Message-ID: <775@mmintl.UUCP>
Date: Tue, 5-Nov-85 11:27:40 EST
Article-I.D.: mmintl.775
Posted: Tue Nov  5 11:27:40 1985
Date-Received: Fri, 8-Nov-85 08:25:15 EST
References: <509@klipper.UUCP> <1096@jhunix.UUCP> <2081@umcp-cs.UUCP>
Reply-To: franka@mmintl.UUCP (Frank Adams)
Distribution: net
Organization: Multimate International, E. Hartford, CT
Lines: 23
Xref: linus net.philosophy:2780 net.math:2121
Summary: Another fallacy


In article <2081@umcp-cs.UUCP> mangoe@umcp-cs.UUCP (Charley Wingate) writes:
>  2) Suppose we do have to return to a reference value that is an extra M
>     units away, and it takes F*(M+K) to make a comparison with an element
>     at position K (i.e., we have to make that many "passes" between the
>     two).  For the sequential search this is clearly O(N**2).  For the tree
>     version, we get something like
>
>       FM+F(M+2)+F(M+4)+ ... F(M+K/2) which is
>
>       FMlogK+FK   giving us O(N).
>
>The reason why we get these unusual results is that ordinarily the costs of
>seeking are negligible.  In this case, they are quite important.

This would be correct if you really had to return to the orignal value.
You don't; you drag it along with you.  I.e., you keep a single copy of the
search value near the Turing machine head.  When you move to the next
element, you swap the search value with the last value looked at.  This
algorithm is technically O(N*K), where K is the size of the objects being
searched for; it is customary to ignore this last factor.

Frank Adams                           ihpn4!philabs!pwa-b!mmintl!franka
Multimate International    52 Oakland Ave North    E. Hartford, CT 06108