Lecture 7 - DFA

Question 1

What does a deterministic finite state automata consist of?

Answer 1

• finite input alphabet Σ
• a finite set of states Q
• initial state q in Q
• set of accepting states F in Q
• control program / transition relation

Question 2

Why do we look at a determinisic FA?

Answer 2

As then each relation has only one place to go (no choice has to be made at all)

Question 3

How are accepting states denoted?

Answer 3

double circles

Question 4

How is a starting state denoted?

Answer 4

arrow from nothing to state

Question 5

What does a DFA define?

Answer 5

A language

Question 6

What does a DFA do?

Answer 6

Check whether language on tape belongs to language of DFA (whether a decision problem can be solved by the DFA)

Question 7

Are nondeterministic FAs possible?

Answer 7

YES

Question 8

What is a recognition for NFA?

Answer 8

only requires there exists a single execution ending in the accepting state

Question 9

Can NFA be converted to DFA ?

Answer 9

yes

Question 10

Are NFAs more powerful than DFAs ?

Answer 10

NO, as it doesn’t expand the language

Question 11

How to convert NFA to DFA?

Answer 11

states of NFA are converted to set of states in DFA if reuiqred

Question 12

Danger of reducing NFA to DFA?

Answer 12

blow up N, states can go up to 2^n

Question 13

Name of language recognisable by DFA?

Answer 13

regular language

Question 14

How can a regular language be expressed?

Answer 14

a regular expression

Question 15

What is ε?

Answer 15

empty string

• always think about in dfa

Question 16

What is σ?

Answer 16

The regular expression

Question 17

What is RS?

Answer 17

concatenation

Question 18

What is R|S?

Answer 18

choice

Question 19

What is R*

Answer 19

0 or more copies of R

• aka closure

Question 20

What is (R)?

Answer 20

used for precedence

Question 21

Order of precedence in regular expressions?

Answer 21

brackets
closure
concat
choice

Question 22

What is ?

Answer 22

or on all characters

• any char

Question 23

What is !x

Answer 23

equivalent to or of all characters in alphabet except x

Question 24

What can a DFA not recognise?

Answer 24

when we need to count a certain number of characters e.g. a^nb^m

Question 25

Why cannot DFA recognise this?

Answer 25

As there are inifintely many values for n and m and hence there would need to be an infinite amount of states , but it is a ‘finite’ machine

Question 26

What is not a regular language?

Answer 26

a^nb^m

Question 27

What can recognise a^mb^n?

Answer 27

pushdown automata or tm

Question 28

How to recognise this a^mb^n

Answer 28

push a onto stack then pop when you read bs