Newsgroups: comp.lang.apl
Path: watmath!watserv2.uwaterloo.ca!torn!cs.utexas.edu!usc!zaphod.mps.ohio-state.edu!caen!uunet!s5!sethb
From: sethb@fid.morgan.com (Seth Breidbart)
Subject: Re: Numerical Analysis + APL/J
Message-ID: <1992Aug27.145141.22803@fid.morgan.com>
Organization: Morgan Stanley & Co., New York, NY
References: <1177@kepler1.rentec.com> <1992Aug17.165305.2364@fid.morgan.com> <1184@kepler1.rentec.com>
Date: Thu, 27 Aug 1992 14:51:41 GMT
Lines: 30

In article <1184@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:
>In article <1992Aug17.165305.2364@fid.morgan.com> sethb@fid.morgan.com (Seth Breidbart) writes:
>>In article <1177@kepler1.rentec.com> andrew@rentec.com (Andrew Mullhaupt) writes:
>>> [argument that because it's hard to check an object for a
>>>property, it must be at least as hard to construct an object with that
>>>property.]

>>I can generate the "group operation matrix" for the integers mod n
>>under addition in time n^2; you can't check an arbitrary nxn matrix to
>>see if it's a group that fast.
>
>Depends on what the problem is.

The problem is "Find a group multiplication table with some other
property".  I, the oracle, happen to know that addition mod n has that
property; you don't.

My claim was that it is sometimes easier to generate an object with a
given property than to prove that a specific (general) object has that
property.  A better example might be "Produce a 200-digit number that
is the product of two 100-digit primes".  It's not that hard to find
100-digit primes and multiply them, but if I only give you the
200-digit number, it's very hard (we believe) to determine whether it
is the product of two 100-digit primes.

None of this is meant to say that I think the original problem under
discussion can be done in time less than matrix multiplication, only
that lower-bound proofs are very hard to construct.

Seth		sethb@fid.morgan.com
