Strings derivable from a grammar

Ed King asks about generating strings described by a grammar.
Our grammar tool, ydb, does this, using approximately the following
method:


For each rule and symbol in the grammar, keep track length of the
shortest derivable string. It is 1 for terminals; then you can do all rules
with only terminals on the right hand side; and so on. Just keep going
through the grammar until each one is labeled with a length. (If there
are unlabeled items and you can't get any more, they don't derive
terminal strings).


Then for any nonterminal it's a simple matter to get some derived strings.
For any rule defining the nonterminal, for each nonterminal on the
right hand side of the rule, you can pick a rule which you know will
lead to a terminal string eventually. This method leads to shortest
derivable strings.


If you want to generate lots of strings for a symbol, a search algorithm
using a stack of partial derivations would be appropriate.


We've found this idea to be very useful for debugging grammars; when
you have a grammar with problems it's handy to check if the rules
really describe what you think they do.


Peter Garst
pg@bsg.com
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