Lecture 6+7

Question 1

What is a deterministic finite state automata?

Answer 1

A machine that consists of a finite set of states, a finite alphabet of actions, a total function which describes what state to go to based depending on the given action. A subset of the states called the accepting states and a distinguished state called the starting state.

Question 2

What is a non deterministic finite automata?

Answer 2

The same as a DFA, except that the total function can be a partial function, if a non specified input is given it will typically be an error. The total function can also have multiple states for each action, if any of these paths reaches an accepting state it will be accepted.
Empty string transitions are also accepted, these do not consume input.

Question 3

How can we encapsulate NFAs so that there are no incoming transitions to the initial state and there is one unique final state with no outgoing transitions?

Answer 3

Create a new state linking to original start state via empty string transition, any accepting state leads to finishing state via empty string transition.

Question 4

Can NFAs accept all regular languages?

Answer 4

yes, This is obvious since it’s clear that there are NFAs which accept the “basic” regular
languages ∅, λ, and x for x ∈ Σ. And NFAs can encapsulate other regular languages using empty string transitions.

Question 5

How can we transform an NFA into a DFA

Answer 5

To remove lambda transitions we ask the question what could we get to with just a single character that isn’t lambda assuming the character is surrounded by lambdas, we then draw out this NFA, it will now have more outgoing arrows. To remove multiple outgoing transitions we create a new state which is a concatenation of all the states a single letter can reach. We then do the same for the remaining letters. This could take up to 2N states.

Question 6

Are NFAs and DFAs equivalent?

Answer 6

yes, a DFA can be made from an NFA and vice versa.