考虑如下所示的 NFA M。
设 M 接受的语言为 L。设 L1 为 NFA M1 接受的语言，通过将 M 的接受状态变为非接受状态并将 M 的非接受状态变为接受状态而获得。下面哪个描述是正确的 ?
(A) L1 = {0, 1}* – L
(B) L1 = {0, 1}*
(C) L1 ⊆ L
(D) L1 = L答案：(乙)
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 提供。这个问题的测验