20k views

### Maximum number of states in minimized DFA from NFA with $n$ states [duplicate]

If an NFA with $n$ states is converted to an equivalent minimized DFA then what will be the maximum number of states in the DFA? Will it be $2^n$ or $2n$?
2k views

### Size comparison of NFA and minimal DFA [duplicate]

Except for isomorphisms, the minimal DFA of a regular language is unique. However, is it possible that an equivalent NFA has less states than the minimal DFA? If so, what is the reasoning behind this? ...
43 views

### Can there exist a smaller NFA then a minimal DFA [duplicate]

So every NFA can be transformed to a DFA and every DFA can be transformed to a minimal DFA. But every NFA can also be transformed to a GNFA (generalized NFA) with 2 states. This is just the start and ...
25 views

### Worst case of subset construction (NFA to DFA) [duplicate]

I am wondering what generic example there is so that an NFA with $n$ states results into a DFA with $2^n$ states after the conversion by the subset construction. I know there is the example by ...
22 views

### NFA -> DFA powerset construction worst case [duplicate]

I am wondering what generic example there is so that an NFA with n states results into a DFA with $2^n$ states after the conversion by the subset construction. I know there is the example by Hopcroft ...
6k views

### How to prove that DFAs from NFAs can have exponential number of states?

All non-deterministic finite automata can be turned into equivalent deterministic finite automata. However, a deterministic finite automata only allows a single arrow per symbol pointing from a state. ...
13k views

### does a DFA converted from NFA always contain 2^Q states?

when converting an NFA to DFA, we create sub-sets of states in the NFA. does it mean that every DFA-converted-from-NFA contain 2^Q states? or if some sub-sets are unreachable then they are not ...
1k views

### Does NFA to DFA conversion give the minimal DFA as result?

When converting NFA to DFA, do I always get the minimal DFA or not?
88 views

### Maximal minimal DFA for some language of n-bit strings

Notation: $M$ is a DFA; $L(M)$ is the language accepted by $M$; $\min(M)$ is the minimal automaton equivalent to $M$ derived from a minimization algorithm such as the Hopcroft algorithm; and $|M|$ is ...
111 views

### Given an non-deterministic finite automaton, will its determinization always have unreachable states?

Given an NFA that accepts the regular language L, will its equivalent DFA which accepts the same language L always have unreachable states. If it does, why?
### Languages such that DFA requires $\Omega(c^k)$ states but NFA needs only $O(k)$ states?
Given an alphabet $\Sigma$, let $c=|\Sigma|$. Can a set of languages $\{L_k\}$ be created, such that any DFA for $L_k$ has $\Omega(c^k)$ states and a NFA for $L_k$ exists with $O(k)$ states? I'm ...