Let sigma = {a, b, c, d, e} and S = {a, b, dec} How many words arc there of leng

Question

Let sigma = {a, b, c, d, e} and S = {a, b, dec} How many words arc there of length six in S'? Construct an FA that accepts abb^ +b^ baa^. What is the shortest word in the language? a) Is the English language a regular language as defined in this course? Explain with examples b) What purpose does the empty string serve? Give examples Prove that l^2 - 2^2 + 3^2 - 4^2- + (-l)^n - 1 n^2 = (-l)^n - 1 (n + l)/ 2, whenever n is a positive integer. Find the union of the two automata below: Construct the regular expression that is accepted by the FA below: Find the equivalence classes of the FA below and find the reduced FA, if

Explanation / Answer

1) Length is 6.

There are two cases:

i)dec is included: Out of 6 places, dec can be placed at 4 places. For the other 3 spots, there are two possibilities for each sport.

So in total there are: 2x2x2x4 = 32

ii) dec is no included: So there are 6 spots. There are two possibilities for each sport.

So in total there are: 2^6 = 64

Total is 32+64 = 96

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