After two days of trying to read a string in ARDUINO environment that has already passed from Processing to ARDUINO my code(based on founded code) works, so I feel posting it to help future similar questions. Maybe it is not the best piece of code but it works and it lights an LED on/off when a certain string passes from Processing to ARDUINO through serial. I send two different strings by pressing and realising the mouse.Here I post seperately the code for ARDUINO and the code for Processing:

ARDUINO code:

char inData[20]; // Allocate some space for the string
char inChar=-1; // Where to store the character read
byte index = 0; // Index into array; where to store the character
int ledPin = 13; // Set the pin to digital I/O 4

void setup(){
 pinMode(ledPin, OUTPUT);
 Serial.begin(9600);
 Serial.write("Power On");
}





char Comp(char* This){

 while(Serial.available() > 0) // Don't read unless
   // there you know there is data
 {
   if(index < 19) // One less than the size of the array
   {
     inChar = Serial.read(); // Read a character
     inData[index] = inChar; // Store it
     index++; // Increment where to write next
     inData[index] = '\0'; // Null terminate the string
   }
 }

 if(strcmp(inData,This)  == 0){
   for(int i=0;i<19;i++){
     inData[i]=0;
   }
   index=0;
   return(0);

 }
 else{
   return(1);


 }
}


void loop()
{
 if(Comp("light on")==0){
       digitalWrite(ledPin, HIGH); // turn the LED on
 }
 if(Comp("light off")==0){
       digitalWrite(ledPin, LOW); // turn the LED off
 }
delay(100); // Wait 100 milliseconds for next reading
}



Processing Code:

import processing.serial.*;
Serial port;
void setup() {
   port = new Serial(this,Serial.list()[1], 9600);
}
void draw() {}
void mousePressed() {
 port.write("light on");
}
void mouseReleased() {
 port.write("light off");
}