Define the following terms : Concatenation of strings, Language, Problems

Define the following terms : 

• Concatenation of strings
  
• Language
  
• Problems

Concatenation of strings : Let x and y be strings. Then  xy denotes the concatenation of x and y, that is , the string formed by making a copy of x and following it by a copy of y. More precisely, if x is the string composed of i symbol ; x = a1 a2.....ai and y is the string composed of j symbols y = b1 b2..........bi, the xy is the string of length, i+j : xy = a1 a2.........ai b1 b2.........bi.

Example : let x = 01101 and y = 110

               Then, xy = 01101110

                And, yx = 11001101

Languages : A set of string all of which are chosen from some summession symbol, where  summession symbol is a particular alphabet, is called Language. If summession symbol is an alphabet, The L is a language over summession symbol. The set of palindromes over the alphabet {0, 1} is an infinite language is the set of all strings over a fixed alphabet summession symbol. We denoted this language by summession symbol.

Example : If summession symbol = {a} then summession symbol = {E, a, aa, aaa.......}

L = {0, 1}, then L = {E, 0, 1, 00, 01, 10, 11, 000.......}.

Problems : In automata theory a problem is the question of deciding whether a given string is a number of some particular languages. More precisely, if summession symbol is an alphabet, and L is a language over summession symbol, then the problem is given a string W in summession symbol, decide whether or not W is in L.