Update README.md

Author: mynttt

README.md

@@ -1,2 +1,74 @@
-# CYK-algorithm
-Java implementation of the CYK algorithm
+# CYK Algorithm
+
+## A Java implementation of the CYK-Algorithm.
+
+The CYK-Algorithm can be used to check if a word can be derived from a CFG (context-sensitive grammar).
+
+You only need you grammar to be in the CNF (Chomsky normal form) format. This Java application will parse an external grammar file and then output the result visualized in a table.
+
+## Grammar File
+
+A grammar file will have the following structure.
+
+```
+S                             -> Starting Symbol
+a b                           -> Terminals
+S A B E C X Y Z               -> Non-Terminals
+S YB XA *                     -> 4th and all following lines are production rules
+E YB XA                       -> You can add multiple to one terminal if you seperate them by a space
+A a YE XC                     -> This reads as A -> a | YE | XC
+B b XE YZ
+C AA
+X b
+Y a
+Z BB
+```
+
+After you compiled the .java file you can simply run it via
+
+```
+java CYK <GrammarFile> <Word>
+```
+
+Sample output for the supplied grammar above:
+
+```
+$ java CYK grammar.txt abbbabaa
+Word: abbbabaa
+
+G = ({a, b}, {S, A, B, E, C, X, Y, Z}, P, S)
+
+With Productions P as:
+A -> a | YE | XC
+B -> b | XE | YZ
+C -> AA
+E -> YB | XA
+S -> YB | XA | *
+X -> b
+Y -> a
+Z -> BB
+
+Applying CYK-Algorithm:
+
++-------+-------+-------+-------+-------+-------+-------+-------+
+| a     | b     | b     | b     | a     | b     | a     | a     |
++-------+-------+-------+-------+-------+-------+-------+-------+
+| A,Y   | B,X   | B,X   | B,X   | A,Y   | B,X   | A,Y   | A,Y   |
++-------+-------+-------+-------+-------+-------+-------+-------+
+| E,S   | Z     | Z     | E,S   | E,S   | E,S   | C     |
++-------+-------+-------+-------+-------+-------+-------+
+| B     | -     | B     | B     | A     | A     |
++-------+-------+-------+-------+-------+-------+
+| Z     | Z     | Z     | E,S   | C     |
++-------+-------+-------+-------+-------+
+| B     | -     | B     | A     |
++-------+-------+-------+-------+
+| Z     | Z     | E,S   |
++-------+-------+-------+
+| B     | B     |
++-------+-------+
+| E,S   |
++-------+
+
+The word abbbabaa is an element of the CFG G and can be derived from it.
+```