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