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In my taste the register machine definition you found is good to go. The only difference is that it specifies its components using the phrase "is specified by", whereas the second definition lists those components explicitly as a 7-tuple. The components of the register machine in tuple style are probably a sequence of registers, a set of labels, ...

1

The theory you seem to be looking for is called AFA or "abstract family of acceptors". You can read an early version of it on wikipedia, but its notions are hard to parse, without examples and such. For AFA theory we first define an abstract type of memory. This is very similar to abstract data type now common in data structures. Such a memory type ...

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The difference here comes from the requirement to halt. An algorithm that returns "true", must always do so in finite time, hence, it will never be able to go through all strings in $\Sigma^*$ and confirm that it is either generated not by both CFGs. However, for the complement problem, the requirement changes drastically: It is enough to show one ...

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Ask the prover to give you any node from $k$ distinct connected components. You have only to verify that the nodes are not in the same connected components (hence, they are in $k$ different components, meaning that $\langle G, k\rangle \in K_{SCC}$) Also, ask for the proof of $st-CON$ between any two of them. Notice that even though the proof is gigantic, at ...

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The reduction is sketched on Wikipedia.

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I am not aware of any different conventinos so it is probably implied that your expression is $X'.(X + Y)$ By definition in Boolean Algebra, $+$ and $.$ are distributive over one another. This means that $x.(y+z)=xy+xz$ and $x+(y.z)=(x+y).(x+z)$. Obviously what you are asking is the first case, so let's take $x.(y+z)=xy+xz$. This is not a proof, I am writing ...

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I can only react to this as seen from the perspective of a theoretical computer scientist. A finite state machine/automaton is, as you know, usually represented by a finite directed graph. The vertices of the graph repesent the states of the automaton, the edges are the instructions: in state $p$, upon reading symbol $a$, move to state $q$. Next to this ...

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