How can I simplify boolean Algebra Expressions without using outside Java addons? -

i trying take boolean algebra expression generated part of project , simplify before output it. boolean expression include or statements due nature of rest of program.

an example starting expression ac + bc + bc + ab + ac + ac + ab , ending + c. lower case letters indicate not e.g. means not a.

i have struggled hours trying figure out, every time solve 1 case ruin another. imagine there recursive function problem struggled find elsewhere.

edit: clear, understand how simplify expression on paper, unable simplify using java.

thanks in advance.

public static void mutate (arraylist<string> final, arraylist<string> factored, string a){  int multiples = 0;  string holder = "";  (int = 0; < final.size(); i++){  if (final.get(i).contains(a)){      multiples++;      if (multiples == 1)         holder = final.get(i);      if (multiples >=2)          factored.add(final.get(i));  }  } if (multiples > 1)  factored.add(holder);  } public static void simplify (arraylist<string> factored, char a, arraylist<string> main){ string temp = ""; int size = factored.size(); int cnt = 0; int cnt2 = 0; int holder = 0; system.out.println(factored); int menial = 0;  if (factored.size() == 0) menial = 1; else{     (int = 0; < size; i++){             //gets rid of leading letters     if(factored.get(i).charat(0) == a){         temp = factored.get(i).substring(1);         factored.add(temp);     } } (int = 0; < size; i++){             //gets rid of leading letters     if(factored.get(i).charat(1) == a){         temp = factored.get(i).substring(1);         factored.add(temp);     } }     (int j = 0; j < size; j++){                      factored.remove(j - cnt);         cnt++;     }    (int = 0; < factored.size(); i++){              //gets rid of duplicates if exist         (int j = + 1; j < factored.size();j++)         if (factored.get(i).equals(factored.get(j))){             cnt2++;             if (cnt2 == 1)                 holder = i;         }  }     if (cnt2 >= 1)             factored.remove(holder);          string temp1 = "";     int size1 = factored.size();     (int = 0; < size1; i++){      //makes uppercase         temp1 = factored.get(i).touppercase();         factored.add(temp1);     }     int cnt3 = 0;     (int = 0; <size1; i++){         factored.remove(i-cnt3);         cnt3++;     }     int sizeover2 = factored.size()/2;     int holder1 = 0; int holder2 = 0;     (int q = 0; q < sizeover2; q++){         int cnt4 = 0;     (int = 0; < factored.size(); i++){              //gets rid of duplicates if exist there caps         (int j = + 1; j < factored.size();j++)         if (factored.get(i).equals(factored.get(j))){             cnt4++;             if (cnt4 == 1)                 holder1 = i;                 holder2 = j;         }          if (cnt4 >= 1){             factored.remove(holder1);             factored.remove(holder2 - 1);         }      }     }     if (factored.size() == 0)         main.add(character.tostring(a));     else if (factored.size() > 1)             menial = 5;     else         (int = 0; < factored.size(); i++)             main.add(factored.get(i)); }}  } 

edit2: have added code above. apologize slopiness in advance, got pretty messy towards end. factored arraylist has of elements of boolean expression separated e.g. first element ac, , second bc, etc. plan find duplicates , try factor them out, after coding of realized egregious logic error. has more complicated , @ point i'm lost in own code.