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Finite Automata question
If I am supposed to define a finite state machine for an expression described as:
w is in (0,1)* and |w|[0] mod 3 = 1 what languages does that machine accept? My main question is, what does the |w|[0] mean? The []'s mean subscript... Thanks |
Hmm. Don't know for certain about the notation in this specific context, but the |w| would mean the absolute value of w in the only context I've come across it before. That is to say take your value of w and get rid of any minus sign if there is one.
if w=x; |w|=x if w=-x; |w|=x easy |
| also means OR
W[0] is the initial case... So you have to accept: any number in the 0-1 range, or a number divisible by 3 but only if its the initial number... so: Init: Nmod3 -> Acceptor .......0<N<1 -> Acceptor ......else -> fail and no other states Transitions: 0<N<1 -> Acceptor N<0|N>1 -> Fail and no other state Something like that? |
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