title: Is this BNF grammar LL(1)?
body: <p>Can someone please confirm for me if the following BNF grammar is LL(1):</p>
  
  <pre><code>S ::= A B B A
  A ::= a
  A ::=
  B ::= b
  B ::=
  </code></pre>
  
  <p>where S is the start symbol and non terminals A and B can derive to epsilon. I know if there are 2 or more productions in a single cell in the parse table, then the grammar isn't LL(1). But if a cell already contains epsilon, can we safely replace it with the new production when constructing the parse table?</p>