Context-free Grammar Question I'm working on some homework for Theory of Computation. There is this one...
Context-free Grammar Question
I'm working on some homework for Theory of Computation. There is this one problem that I can't figure out:
Define and Design a context-free grammar that generates the language L1 = { w | |w| mod 2 != 0}
I sort of understand how simple grammars work but if you could explain the process behind it I'd appreciate it.
Thanks
Homework Answers
Let's see what the language is.
|w| is length of w
|w| mod 2 != 0
means the length of the word shouldn't be evenly divisible by
2
In turn length shouldn't be even that means it should be odd
GRAMMAR
S -> aA | bA | a | b
A -> aS | bS
EXPLANATION
S is to have odd number of symbols. S -> a | b is to have the
least odd number which is 1.
A is to go back to S on any symbol
-- Please up vote or comment if you have any doubts.
Happy Learning!
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Context-free Grammar Question
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Define a context-free grammar (CFG) that generates exactly the following language. B = {1'0'ik | i+j = k or i+k=j with i, j, k > 0} Both ambiguous and unambiguous grammars are acceptable (it does not matter in this question). For grading purposes, please use as the starting variable. Alphabet E = {0,1}
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