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lfa:2022:lab11-cfl_3 [2022/12/18 21:41] mihai.udubasa |
lfa:2022:lab11-cfl_3 [2022/12/18 23:26] (current) mihai.udubasa add some notes to 11.4.2 |
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| Create a graph $math[G=(V,E)] where the nodes are **terminals and non-terminals**. For each rule of the form $math[X \leftarrow aY] create a directed edge $math[(X,Y)]. For each rule $math[X \leftarrow a], also generate an edge $math[(X,a)]. | Create a graph $math[G=(V,E)] where the nodes are **terminals and non-terminals**. For each rule of the form $math[X \leftarrow aY] create a directed edge $math[(X,Y)]. For each rule $math[X \leftarrow a], also generate an edge $math[(X,a)]. | ||
| - First, we need to check first if the grammar generates a language different from $math[\emptyset]. So we check if there is a path from the start symbol to some terminal. | - First, we need to check first if the grammar generates a language different from $math[\emptyset]. So we check if there is a path from the start symbol to some terminal. | ||
| - | - Second, we need to check if there are //loops//. It suffices to check if the graph is a tree. | + | - Second, we need to check if there are //loops//. It suffices to check if the graph is a tree. MU: the condition is not sufficient as a grammar could generate a finite language while also having looping rules (if the grammar comes from the dfa transformation, these would be from the sink states of the dfa; see state 3 of the second dfa from 11.3.1) |
| </hidden> | </hidden> | ||
| **11.4.3.** Prove that any DFA can be converted to a regular grammar. | **11.4.3.** Prove that any DFA can be converted to a regular grammar. | ||
| - | <hidden> See lecture</hidden> | + | <hidden> See lecture </hidden> |
| **11.4.4.** Is there a decidable algorithm to remove ambiguity from regular grammars? | **11.4.4.** Is there a decidable algorithm to remove ambiguity from regular grammars? | ||
| <hidden> | <hidden> | ||