Here's how I think it works
In formal language, what it means to accept a verification means does the result fall into the list of acceptable values.
Consider adding two 2-bit numbers:
- Alphabet: { 0, 1}
- Language: { x | x consists of four binary digits representing two 2-bit binary numbers where the result of adding these two numbers is a valid 2-bit binary number (i.e. falls between 00 and 11) }
- Then you have an automata that will:
- Start from the rightmost bit
- Add the corresponding bits (+ carry from any previous iterations)
- Carry over to the left if needed
- Repeat for both bits
- Check for acceptance
- Machine as a whole simply checks did the inputs produce a valid 2-bit number, so it just accepts or rejects
The machine itself simply holds this automata and language, so all it does is take input and reject/accept end state. I think you're just getting caught up in definitions
A sum of a list of numbers I think would be something like
- Alphabet: digits 0-9 and ','
- Language: a single string of digits or a single string of digits followed by a comma and another valid string
- Automata:
- Are we a single string of digits? If yes, accept
- Sum the last number into the first and remove the comma
- Repeat
- Machine: Does the some operation result in a valid string?
Machines accept a valid state or hit an error state (accept/reject). The computation happens between the input and accept/reject.
But maybe I don't understand it either. It's been a while since I poked around at this stuff.
Can't wait to see the video!