Induction details for proof of closure of regular languages under unions

I was reading M. Sipser, Introduction to the theory of computation 3ed. where he presents a proof by construction that the class of regular languages is closed under unions (Theorem 1.25). However, he omits the induction details for a formal proof of correctness. I tried filling in the details myself but it was a mess; how is this usually done?

Can a character rest while under the Etherealness spell?

Etherealness lasts for 8 hours and doesn’t require concentration:

You step into the border regions of the Ethereal Plane, in the area where it overlaps with your current plane. You remain in the Border Ethereal for the Duration or until you use your action to dismiss the spell…

A Short Rest is:

… a period of downtime, at least 1 hour long, during which a character does nothing more strenuous than eating, drinking, reading, and tending to wounds.

Meanwhile a Long Rest is:

…a period of extended downtime, at least 8 hours long, during which a character sleeps for at least 6 hours and performs no more than 2 hours of light activity, such as reading, talking, eating, or standing watch.

If I did nothing for an hour while on the Ethereal Plane, could that count as a short rest? Likewise, if I did nothing for the full 8 hours, would that count as a long rest?

Prove that regular languages are closed under kleen

Given $ L$ is a regular language, how can i prove that $ L^*$ is a regular language too? I’ve constructed a NFA which contains a new start state that has an $ \epsilon$ -transition to the original starting state, and also connected all the final states to the original starting state with an $ \epsilon$ -transition.

How can i formally prove that this is correct?

apache server under attack

Hi all,
I run a small community . Iam using apache web server with smf forums on a vps with centos 7. I have all good firewalls going (csf) . Iam trying to solve an issue with a user crashing my7 forums. The memory on the vps and cpu will spike to 100% and create a "cannot connect to mysql database" error. on the apache error logs I get a mpm_prefork error showing AH00159 error out of memory. can anyone tell me how to prevent this attack. thanks.

understanding an integer overflow under windows 10

I did this test case that checks for the lens of contents, and based on what I was researching on the internet it says from -128 to 127 the length range, but the code was compiled under visual studio 2019 with the following: /GS , /dynamicbase , however, the proof of concepts is below. once I got executed the POC of concept in order to overwrite EIP / seh chains. I got __report_gsfailure which is where it detects the overflow. i am trying to overwrite the seh chains in order to get code execution. I also tried to overwrite seh chains eb 0 pointing to a non safeseh , but it doesnt work either

exp poc

junk = "A" * 1000  nseh = struct.pack('<I', 0x42424242) #struct.pack('<I',0x90906eb) #struct.pack('<I', 0x42424242)  seh = struct.pack("<I", 0x43434343) # 320 nseh # 316 seh  payload = junk #+ nseh + seh  

stack trace

0:000> g WARNING: Continuing a non-continuable exception (1534.1d3c): Security check failure or stack buffer overrun - code c0000409 (!!! second chance !!!) eax=00000001 ebx=006d9000 ecx=00000002 edx=000001e3 esi=00d347b8 edi=00d38718 eip=00a71b04 esp=008ff7d0 ebp=008ffaf4 iopl=0         nv up ei pl nz na po nc cs=0023  ss=002b  ds=002b  es=002b  fs=0053  gs=002b             efl=00000202 demo!__report_gsfailure+0x17: 00a71b04 cd29            int     29h  0:000> k  # ChildEBP RetAddr   00 008ffaf4 00a71258 demo!__report_gsfailure+0x17 [d:\agent\_work\s\src\vctools\crt\vcstartup\src\gs\gs_report.c @ 220]  01 008ffc2c 41414141 demo!main+0x258 [C:\Users\user\Source\Repos\demo\demo\Source.cpp @ 38]  WARNING: Frame IP not in any known module. Following frames may be wrong. 02 008ffce0 777a7b44 0x41414141 03 008ffcf0 00000000 ntdll!_RtlUserThreadStart+0x1b  0:000> !exchain 008ffc64: 41414141 Invalid exception stack at 41414141 

program output 1k “A”

size: -113 length: 399 

source code

#define MAX_DATA_SIZE 255   char buffer[MAX_DATA_SIZE];    memcpy(buffer,contents,strlen(contents));  if(size < MAX_DATA_SIZE)  {   memset(buffer, '', MAX_DATA_SIZE);   memcpy(buffer,contents,strlen(contents));   printf("[+] overflow");  }  else  {   printf("Error!! Max Size:300\n");   exit(1);  } 

What happens when a creature under an effect gains immunity to that effect?

For my first example, let’s say that a creature has contracted Filth Fever, and subsequently gains immunity to disease. The source could be anything, a Periapt of Health, or perhaps they gained their third level of Paladin, granting them the Divine Health ability.

What happens to the disease?

  • Is the disease removed completely and instantly? (this seems highly abuseable)

  • Do they retain the disease, but its effects are suspended until they no longer benefit from the immunity, ie taking off the Periapt, or falling and losing their Paladin class features?

  • Do they continue to make saves against the disease, but without suffering the negatives of failed saves, until eventually they save against the disease and shake it off? (This one makes the most sense to me)

  • Do they continue to make saves against the disease and suffer its negative effects until they are cured?

Second example: Fear effects.

Lets say a Paladin and Antipaladin are in a throw-down. The Antipaladin uses intimidate to demoralize the Paladin, which, due to his Aura of Cowardice ability, allows him to succeed and makes the Paladin shaken for 4 rounds. The Paladin backs up to outside the aura, regaining his immunity, then walks back in. Is he still shaken, or is he fine now?

How does a TPM inform me that someone has tampered with the BIOS under Linux / Ubuntu?

I read guides on how to set up a TPM but none of them tells me how a TPM actually works in practice (under Linux/Ubuntu which I use).

My understanding is that a TPM can inform me whether any of the components which load before the main operating system (Bios, bootloader, firmware) have changed in any way since the TPM was activated.

But how exactly would I know whether something has actually changed? If someone (an attacker) has tampered with with the BIOS or some firmware component, will the next boot process simply not complete? If that is correct, will the system boot successfully again, if I manage to put the BIOS back into the state that is known to the TPM?

Does the Scent ability function under water in conjunction with the Aegis’ Underwater Breathing Astral suit option?

Does the Scent ability function under water in conjunction with the Aegis’ Underwater Breathing Astral suit option?

PC in party is an Aegis 4, Druid 7 and managed to get the scent ability, wonders if he can track by scent under water using the that suit option.

Underwater Breath: The aegis can safely breathe underwater as long as he is wearing his astral suit.

https://www.d20pfsrd.com/alternative-rule-systems/psionics-unleashed/classes/aegis/astral-suits