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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: DD specifies non-terminating behavior to HHH --- RECURSIVE CHAIN --- Saving Democracy Date: Sat, 22 Feb 2025 14:03:47 -0600 Organization: A noiseless patient Spider Lines: 121 Message-ID: References: <855e571c6668207809e1eb67138de6af48d164fa@i2pn2.org> <8fa176d46bf5b8c36def9e32ced67a1a3f81bae1@i2pn2.org> <2e999502c40f736a3f3579d23bdb2b42dc74e897@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 22 Feb 2025 21:03:49 +0100 (CET) Injection-Info: dont-email.me; posting-host="9ac4b0f7013656f9614fe2304e793339"; logging-data="129328"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/VILVIKG55WJw9MqPOgp/T" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:YROub8mCa14pI0avnLQbsgxsSLE= X-Antivirus: Norton (VPS 250222-4, 2/22/2025), Outbound message In-Reply-To: Content-Language: en-US X-Antivirus-Status: Clean Bytes: 6263 On 2/22/2025 1:40 PM, dbush wrote: > On 2/22/2025 2:33 PM, olcott wrote: >> On 2/22/2025 1:17 PM, dbush wrote: >>> On 2/22/2025 1:54 PM, olcott wrote: >>>> On 2/22/2025 12:21 PM, dbush wrote: >>>>> On 2/22/2025 1:02 PM, olcott wrote: >> >>>>>>> >>>>>> 01 int F(int i) >>>>>> 02 { >>>>>> 03      if (i<10) { >>>>>> 04          return 0; >>>>>> 05      } else { >>>>>> 06          return F(i+1); >>>>>> 07      } >>>>>> 08 } >>>>>> 09 >>>>>> 10 int no_numbers_greater_than_10() >>>>>> 11 { >>>>>> 12      return F(0); >>>>>> 13 } >>>>>> 14 >>>>>> 15 int main() >>>>>> 16 { >>>>>> 17   no_numbers_greater_than_10(); >>>>>> 18   return 0; >>>>>> 19 } >>>>> >>>>> Actually, let's update main: >>>>> >>>>> int main() >>>>> { >>>>>     F((int)no_numbers_greater_than_10); >>>>>     return 0; >>>>> } >>>>> >>>>>>> >>>>>>> The function no_numbers_greater_than_10() checks if any natural >>>>>>> number exists that is greater than 10.  It does this by checking >>>>>>> all natural numbers one at a time.  If one such number exists it >>>>>>> halts and return 0.   If no such number exists, it will run >>>>>>> forever as no such number will satisfy the condition. >>>>>>> >>>>>> >>>>>> Your code is incomplete. I added main() with line numbers. >>>>>> >>>>>>> We can see that no_numbers_greater_than_10 correctly simulated by >>>>>>> F cannot possibly terminate normal by reaching its own "return" >>>>>>> instruction.  This means that F correctly reports that >>>>>>> no_numbers_greater_than_10 is non-halting.  It further means, >>>>>>> since no_numbers_greater_than_10  doesn't halt that there is no >>>>>>> natural number greater than 10. >>>>>>> >>>>>>> Agreed? >>>>>> >>>>>> Here the execution trace that I see: >>>>>> 15, 16, 17, 10, 11, 12, 01, 02, 03, 04, 12, 18, 19 >>>>>> >>>>> >>>>> Just as you say we're not talking about the direct execution of DD, >>>>> we're also not talking about the direct execution of >>>>> no_numbers_greater_than_10.  We're talking about >>>>> no_numbers_greater_than_10 correctly simulated by F. >>>>> >>>>> It's a verified fact that no_numbers_greater_than_10 correctly >>>>> simulated by F cannot possibly return so >>>>> F(no_numbers_greater_than_10) is correct to report non-halting, >>>>> which means that there is no natural number greater than 10. >>>>> >>>>> Agreed? >>>>> >>>> >>>> Leaving out main() made this difficult. >>>> We can assume that the address of no_numbers_greater_than_10 > 10. >>>> This will emulate no_numbers_greater_than_10 at incorrect byte offsets >>>> causing it to crash. This may or may not make F crash depending >>>> on how robust its emulator is. >>>> >>> >>> Let's make a small change so that wraparound is well defined: >>> >>> int F(uintptr_t i) >>> { >>>       if (i<10) { >>>           return 0; >>>       } else { >>>           return F(i+1); >>>       } >>> } >>> >>> This ensures that F((uintptr_t)no_numbers_greater_than_10) returns 0. >>> >>> This doesn't change the fact that no_numbers_greater_than_10 correctly >>> simulated by F cannot possibly return so F(no_numbers_greater_than_10) >>> is correct to report non-halting, which means that there is no natural >>> number greater than 10. >>> >>> Agreed? >> >> i starts out as the address of >> no_numbers_greater_than_10 >> Then causes the emulation to crash. >> > > If that address is greater than 10 then F returns 0 right away, > otherwise it makes at most 10 recursive calls before returning 0, so > there would be no crash. > You may be correct yet it does not see like that to me. Please give me the line number by line number execution trace that you are assuming. > So you agree that no_numbers_greater_than_10 correctly > simulated by F (i.e. if the body of the function F is replaced by an > unconditional simulator as you said is correct) cannot possibly return? -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer