Basics of Computation Theory

What is "abstraction"? Abstraction unifies multiple and different objects into one concept  describes the common properties of those objects common properties that are exclusive to those objects. Examples:  Vehicle is an abstraction of car, truck, motorcycle  Bird is an abstraction of duck, chicken, dove, eagle etc.  Emotion is an abstraction of anger, love, fear, sadness etc. Abstraction is an essential process in science  It helps identify commonalities and differences  It helps focus on important properties  a model is an abstraction.

Finite State Machines (automata) A Finite State Machine is an abstraction of a computing system that consists of  States of the system  Events (or triggers) that happen to the system  Actions performed by the system  Transitions between states A FSM is usually depicted by its state transition diagram.  Also, by the state transition table. State (another) state S1: Sitting S2: Standing S3: Walking E1: hear "go" Stand and walk, S3 walk, S3S3 E2: hear "stop" (no action), S1 sit, S1 Stop walking, S2

Finite State Machines: Examples A traffic light A soda dispenser A gum ball machine An elevator An ATM

Abstraction of a computing machine Finite State Machines cannot abstract all computers or all that they can do There is another model of a computer that can solve any problem that any other computer can  Alan Turing's Universal Computing Machine Known as "Universal Turing Machine" or "Turing machine"

Universal Turing Machine UTM consists of  A tape of discrete positions The tape is readable and writable Each position contains one symbol from a set of symbols  A head that reads and writes on the tape  A control unit that controls the tape and the head, and consists of A finite state machine, where:  Every event is about reading a certain symbol  Every action is about writing a symbol and moving forward or backward along the tape

UTM and the basic model of computing Computer: Universal Turing Machine Input: The tape before processing Program: The control unit's FSM specification Output: The tape after processing Computer Input Program Output