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Results tagged with context-free
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user 2367
Context-free languages and grammars.
7
votes
Lengths of "all-accepted" words in Context Free languages
The shortest word in $A_L$ is not bounded by a recursive function in the size of a given context-free grammar describing $L$. See here for more results in that direction:
https://doi.org/10.4230/LIPIc …
- 6,795
6
votes
Complexity of intersection of regular languages as context-free grammars
Let me second Michael's judgment, this is indeed an interesting
question. Michael's main idea can be combined with a result from the literature, thus providing a similar lower bound with a rigorous pr …
- 6,795
6
votes
Finding a minimal context free grammar that recognizes a finite set of strings of bounded le...
The following inapproximability result is known (Theorem 17 in Gruber/Holzer/Wolfsteiner, DLT 2018):
Given a context-free grammar of size $s$ generating a finite
language $L$, it is impossible to appr …
- 6,795
7
votes
Continuous mathematics and formal language theory
Lamine commented on the connection to the Chomsky-Schützenberger enumeration theorem. Recently, a few research problems in formal language theory were solved using continuous mathematics via this conn …
- 6,795
3
votes
Different definitions of grammar complexity
I think that among the most obvious measures are variable and production complexity. These are structural measures, in the sense there is for each k an infinitude of languages having measure k. And th …
- 6,795
3
votes
Accepted
Modify DCFG to enforce length limit
A partial answer: The number of productions needed by a (not necessarily deterministic) context-free grammar generating $L\cap \Sigma^{\le N}$ in the worst case is $\Theta(N^2)$, as given in Theorem 4 …
- 6,795
1
vote
Accepted
Compressing grammars by introducing ambiguity and left-recursion
Regarding your second question about succinctness, there is a nonrecursive tradeoff in grammar size when moving from general cfgs to unambiguous cfgs. See here:
Erik Meineche Schmidt, Thomas G. Szym …
- 6,795