考虑以下所示的NFAM。
令M接受的语言为L。令L1为NFA M1接受的语言,这是通过将M的接受状态更改为不接受状态并将M的不接受状态更改为接受状态而获得的。下列哪项为真 ?
(A) L1 = {0,1} * – L
(B) L1 = {0,1} *
(C) L1⊆L
(D) L1 = L答案: (B)
解释:
In case of a Deterministic Finite Automata (DFA) when we change
the accepting states into non-accepting states and non-accepting
states into accepting states, the new DFA obtained accepts the complement
of the language accepted by the initial DFA. It is because we have one
single movement for a particular input alphabet from one state so the strings
accepted by the transformed DFA will be all those which are not accepted by
the actual DFA.
But it is not the case with the NFA’s (Non-Deterministic Finite
Automata). In case of NFA we need to have a check on the language accepted by the
NFA. The NFA obtained by changing the accepting states to non-accepting states and
non-accepting states to accepting states is as follows:-
Here we can see that as
i. The initial state is an accepting state hence null string is always accepted by
the NFA.
ii. There is a movement from state 1 to state 2 on both {0, 1} input alphabets and
further any number of 1’s and 0’s or even none in the string lets the string be
at an accepting state(state 2).
Hence the language accepted by the NFA can be any string with any combination of 0’s
and 1’s including a null string i.e. {null, 0, 1, 00, 01, 10, 11,……………..} so L1= {0, 1}*.
本说明由Yashika Arora贡献。这个问题的测验