From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-1.9 required=5.0 tests=BAYES_00 autolearn=ham autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 103376,c42dbf68f5320193 X-Google-Attributes: gid103376,public X-Google-ArrivalTime: 2002-05-07 19:27:26 PST Path: archiver1.google.com!postnews1.google.com!not-for-mail From: dewar@gnat.com (Robert Dewar) Newsgroups: comp.lang.ada Subject: Re: Generation of permutations Date: 7 May 2002 19:27:25 -0700 Organization: http://groups.google.com/ Message-ID: <5ee5b646.0205071827.643501ee@posting.google.com> References: <3CD71F4D.C29A60FC@san.rr.com> <5ee5b646.0205070239.77c6bac2@posting.google.com> NNTP-Posting-Host: 205.232.38.14 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1020824846 29252 127.0.0.1 (8 May 2002 02:27:26 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: 8 May 2002 02:27:26 GMT Xref: archiver1.google.com comp.lang.ada:23688 Date: 2002-05-08T02:27:26+00:00 List-Id: > Actually I am interested where you picked up the phrase > "recursively undecidable". A better phrase would be "not > recursive" since we are referring to recursive languages. It's a very standard phrase in my vocabulary. And I did not invent it. To pick up one quick reference from many, the following is the statement of Richardson's Theorem from Eric Weisstein's world of mathematics: Let R be the class of expressions generated by 1. The rational numbers and the two real numbers pi and ln 2, 2. The variable x, 3. The operations of addition, multiplication, and composition, and 4. The sine, exponential, and absolute value functions. Then if E in R, the predicate "E = 0" is recursively undecidable. (I must say this thread has gone splendidly off topic, even for CLA :-)