Fall 2006Costas Busch - RPI1 Deterministic Finite Automaton (DFA) Input Tape “Accept” or “Reject” String Finite Automaton Output

Fall 2006Costas Busch - RPI2 Formal Definition Deterministic Finite Automaton (DFA) : set of states : input alphabet : transition function : initial state : set of accepting states

Fall 2006Costas Busch - RPI3 Language Accepted:

Fall 2006Costas Busch - RPI4 Transition Graph initial state accepting state transition

Fall 2006Costas Busch - RPI5 For every state, there is a transition for every symbol in the alphabet

Fall 2006Costas Busch - RPI6 Set of States Example

Fall 2006Costas Busch - RPI7 Input Alphabet :the input alphabet never contains Example

Fall 2006Costas Busch - RPI8 Initial State Example

Fall 2006Costas Busch - RPI9 Set of Accepting States Example

Fall 2006Costas Busch - RPI10 Transition Function Describes the result of a transition from state with symbol

Fall 2006Costas Busch - RPI11 Example:

Fall 2006Costas Busch - RPI12

Fall 2006Costas Busch - RPI13 Transition Table for states symbols

Fall 2006Costas Busch - RPI14 To accept a string: all the input string is scanned and the last state is accepting To reject a string: all the input string is scanned and the last state is non-accepting

Fall 2006Costas Busch - RPI15 Initial Configuration Input String Initial state Input Tape head

Fall 2006Costas Busch - RPI16 Scanning the Input

Fall 2006Costas Busch - RPI17

Fall 2006Costas Busch - RPI18

Fall 2006Costas Busch - RPI19 accept Input finished

Fall 2006Costas Busch - RPI20 A Rejection Case Input String

Fall 2006Costas Busch - RPI21

Fall 2006Costas Busch - RPI22

Fall 2006Costas Busch - RPI23 reject Input finished

Fall 2006Costas Busch - RPI24 Another Rejection Case Tape is empty reject Input Finished

Fall 2006Costas Busch - RPI25 Extended Transition Function Describes the resulting state after scanning string from state

Fall 2006Costas Busch - RPI26 Example:

Fall 2006Costas Busch - RPI27

Fall 2006Costas Busch - RPI28

Fall 2006Costas Busch - RPI29 Another Example Accept state Accept state Accept state

Fall 2006Costas Busch - RPI30 Empty Tape accept Input Finished

Fall 2006Costas Busch - RPI31 Another Example Accept state trap state

Fall 2006Costas Busch - RPI32 Input String

Fall 2006Costas Busch - RPI33

Fall 2006Costas Busch - RPI34

Fall 2006Costas Busch - RPI35 accept Input finished

Fall 2006Costas Busch - RPI36 A rejection case Input String

Fall 2006Costas Busch - RPI37

Fall 2006Costas Busch - RPI38

Fall 2006Costas Busch - RPI39 reject Input finished

Fall 2006Costas Busch - RPI40 Language Accepted:

Fall 2006Costas Busch - RPI41 Another Example Alphabet: Language Accepted:

Fall 2006Costas Busch - RPI42 More DFA Examples Empty languageAll strings

Fall 2006Costas Busch - RPI43 Language of the empty string

Fall 2006Costas Busch - RPI44 = { all strings with prefix }

Fall 2006Costas Busch - RPI45 = { all binary strings containing substring }

Fall 2006Costas Busch - RPI46 = { all binary strings without substring }

Fall