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The Study of the Mathematical Properties of Such Robots is the Theory of the Robot

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In the science of the theoretical computation, the automata theory is the study of mathematical objects called abstract machines or the computer robots and problems that can be solved using them. Robot comes from the Greek word a?t?µata that means “autoactuante”.

The automata theory also closely is related to the formal language theory. A robot is a finite representation of a formal language that can be an infinite set. The robots often classify themselves by the class of formal languages that can recognize.


What follows is an introductory definition of a type of robot, who tries to help us to catch the implied essential concepts in the automata theory.

Informal description

One assumes that a robot must execute himself in a certain sequence of entrances in discreet passages of time. In each passage of time, a robot obtains an entrance that picks up of a letter or symbol set, that is called an alphabet. At any time, the symbols until now fed the robot as entered form a finite sequence of symbols, that is called a word. A robot contains a finite set of states. In each instance in the time of some execution, the robot is in one of his states. In each passage of time when the robot reads a symbol, jumps or journeys to a following state that is decided by a function that at the moment takes the present state and the symbol read like parameters.

This function is called transition function. The robot reads the symbols of the word of entrance one after another one and journeys of state to state in agreement with the transition function, until the word is read completely. Once the entrance word has been read, it says that the robot has paused and the state in which the robot paused is called final state. Following the final state, he says themselves that the robot accepts or he rejects an entrance word. There is a subgroup of states of the robot, who defines himself as the set of acceptance states. If the final state is an acceptance state, then the robot accepts the word. Otherwise, the word is rejected. The set of all the words accepted by a robot denominates language recognized by the robot. In summary, a robot is a mathematical object that takes a word as entered and decides to accept it or to reject it. Since all the computer problems are reducible in the acceptance question/rejection of the words (all the instances of problems can imagine in a finite length of symbols), the automata theory plays a crucial role in the computer theory.

Formal definition

A robot is represented formally by one 5-tupla (Q, S, d, q0, F), where:

  • Q is a finite set of states.
  • S is a finite set of symbols, call alphabet of the robot.
  • d is the function of transition, that is to say, d: Q × S ? Q.
  • q0 is the state of beginning, that is to say, the state of the robot before processing any entrance, where q0 ? Q.
  • F is a set of states of Q (that is to say, F ? Q) calls acceptance states.

Word of entrance

A robot reads a finite chain of symbols a1, a2,…., an, where ai ? S, that is called an entrance word. The set of all the words is denoted by S *. to run A sequence of states q0, q1, q2,…., qn, where qi ? Q like q0 is the state of beginning and qi = d (qi-1, ai) for 0

Recognizable languages

The recognizable languages are the set of languages that a robot recognizes. For the previous definition of robots, the recognizable languages are the regular languages. For different definitions from robot, the recognizable languages are different.

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