in set theory or in our course? I think what bothers you (

an infinite process you are left with a meager finite automata.

As to the fairness of life (or lack thereof), talk to us after the examâ€¦

]]>We build a new DFA, based on the original DFA (the one accepting R).

For each state s of the DFA accepting R, go over all strings in E. If any of them leads (on the DFA) to an accept state of the DFA, mark s as an accept state.

What you get is a new DFA that accepts the desired language (also known as a quotient language).

You may protest and say this is an infinite process, it is not constructive, life is unfair, etc. etc. All these claims are true.

**But** note that the end result is a DFA doing what you want, so the language **is** regular.

Another observation is that E need not be recursive. Any language will work.

]]>k is a parameter. So take it to be equal to the number of nodes in G, and this becomes the question of whether G has

a Hamiltonian path, which is NPC (I believe you even saw something like that in one of the recitations).

We try to be fair and balanced and to ask only about things related to what we touched upon in class/recitation/homework.

If we think homomorphisms are within this category, we can include them.

In other words, I'm not going to say what topics exactly will be or won't be in the exam.

We did say what topics touched upon as above will **not** be in the exam (see "exam" page).

The answers say it is, but how can that be? We know prefix(R) is regular, but this isn't all the prefixes, it's supposed to screen which prefixes are allowed and which are not by something not necessarily regular.

2. Is the following problem in NPC? Input: graph and a natural number k. Question: is there a simple path in the graph that is k edges long?

I can easily see that the problem is in NP, but I'm having trouble proving it's NP-hard.

3. A lot of the multiple-choice questions have to do with homomorphisms and how they affect relations between languages, something I also recall seeing in a lot of midterms in semesters the class was given by Dershowitz. Is this something we need to be familiar with?

]]>