Write a program in java:

simplification of context-free grammars

1. removing ε-rules
2. remove unit- rules
3. remove useless rules

in this project, accept a cfg from keyboard, simplify it by removing ε-rules and useless rules, and print out the simplified equivalent cfg.

for example, given the following cfg as the input (0 denotes empty string and "—" denotes arrow head "→"):

s—aa|abb a—aaa|0 b—bb|bbc c—b

after processing, your program should print out the following simplified equivalent cfg: s—aa|a

a—aaa|aa