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Chapter 8: Q30P (page 360)

Show that EDFAis NL-complete.

Short Answer

Expert verified

If there is a path to an accept state, it must include at least n stages. M does not accept any string if there is no path to an accept state within n steps, therefore M鈭� M鈭�EDFA.The string is not accepting path then l(m)鈮�蠒And 尘尉贰DFA.

Step by step solution

01

Step-1: NL complete

NL-complete is a complexity class in computational complexity theory that includes all languages that are complete for NL, a class of decision problems that can be handled by a nondeterministic Turing machine with a logarithmic amount of memory space.

02

Step-2: EDFA  is NL complete

The complexity of the task is referred to as a function of the input size. DFA is NL-complete because it recognises the language of finite states.

EDFAis context-free since it is regular.EDFAis in NL. Because a DFA with n states can start at the beginning state and nondeterministically go throughMstates for at most n steps, saving just the current state, it can start at the initial state and nondeterministically traverse through M states for at most n steps.

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