CE308_2_Regular_Languages.pdf - Computing Theory(CE 308 G\u00fcl BOZTOK ALGIN PhD Fall 2019 What is a Computer Real computers are quite complicated to allow

CE308_2_Regular_Languages.pdf - Computing Theory(CE 308...

This preview shows page 1 - 14 out of 107 pages.

Computing Theory ±CE ²³!´ Gül BOZTOK ALGINµ PhD Fall ¶³·"
Image of page 1
.
Image of page 2
Finite Automata Finite automata are good models for computers with an extremely limited amount of memory. An automaton is an abstract computing device. Note that a “device” need not even be a physical hardware! Such computers lie at the heart of various electromechanical devices. e.g. The controller for an automatic door, a dishwasher, an electronic thermostat, etc.
Image of page 3
Finite Automata A finite automaton is informally ± a state diagram that comprehensively captures all possible states and transitions that a machine can take while responding to a stream or sequence of input symbols. It is recognizer for “Regular Languages”. +)eterministic +inite (&utomata ±+)+(&° The machine can exist in only one state at any given time. 2Non²deterministic +inite (&utomata ±2N+(&° The machine can exist in multiple states at the same time.
Image of page 4
The Chomsky Hierarchy [¸] Hierarchy of classes of formal languages.
Image of page 5
Finite Automata 7Some (&pplications%! Software for designing and checking the behavior of digital circuits Lexical analyzer of a typical compiler Software for scanning large bodies of text (e.g., web pages) for pattern finding Software for verifying systems of all types that have a finite number of states e.g., stock market transaction, communication/network protocol
Image of page 6
Finite Automata A simple Example: The controller for an automatic door
Image of page 7
Finite Automata Finite automata Their probabilistic counterpart are Markov chains*. Are used to recognize patterns in data, ŷ in speech processing, ŷ in optical character recognition. Markov chains have been used to model and predict price changes in financial markets. * A process satisfies the Markov property if one can make predictions for the future of the process based solely on its present state; that is, conditional on the present state of the system, its future and past states are independent.
Image of page 8
Example Finite Automata On/Off Switch Recognition modeling of the word “ then
Image of page 9
A Finite Automaton M · The state diagram of a finite automaton called M 1 with three states. 7States : q 1 , q 2 , q 3 8Transitions : The arrows going from one state to another The start state : q 1 ( indicated by the arrow pointing at it from nowhere ) The accept ±final° state : q 2 ( indicated with a double circle ) ! Note that if the start state is also an accept state, M 1 accepts the empty string ε. Input , output (accept or reject for now). Which input strings will 22M ² accept%$%% Which ones will it reject%$%%
Image of page 10
Finite Automata _ Formal Definition 1 δ specifies exactly one next state for each possible combination of a state and an input symbol. 2 Zero accept states is allowable.
Image of page 11
A Finite Automaton M · M 1 = (Q, Σ, δ, q 1 , F) 1. Q = {q 1 , q 2 , q 3 } 2. Σ = {0, 1} 3. δ : 4. q 1 : start state 5. F = {q 2 }
Image of page 12
Finite Automata _ Formal Definition Let '&''A
Image of page 13
Image of page 14

You've reached the end of your free preview.

Want to read all 107 pages?

  • Spring '20
  • Formal language, Regular expression, Nondeterministic finite state machine, Automata theory

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture