Let L CT b e any language, not necessarily regular. We associate with 1 the foll

Question

Let L CT b e any language, not necessarily regular. We associate with 1 the following boolean infinite matrix, its rows and columns are indexed by words froin 1 where Tdw.r) = 1 if the concat enation wr e L and T. (w, ?)-0 otherwise. e rows of the matrix Ti(sometimes called factors or derivatives) can also be viewed as languages Let R1, = : { Ri . R.. ..) be the sot of all distinct rows of T. The ith class is the set of rows all equal to R, eheren: A language L is regular iffthe set RD, is finite. We denote as Row(Ti.) the row of Ti indexed by the wordw: Rottw(7.) {T.(w.uh) : w, ? ?. }. 2 Problems 1. Prove that any finite set of words is regular. How many states is suffi- í

Explanation / Answer

1:If you want an automation that accept only w1.....................Wm ?you will need m+1 states as you have asked how many states sufficient if you can show you can only ascept w1...................wm using m+1 states than that is fime that what is question asked.note that reusing a state on a path to an accept state causes the autonuation to have loop in that path which will cause it to accept infinity many words.So if you want to asccept the language consisting of onlu that word then you will need m+1 states

2-

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