Mixing Left and Right Regular Rules
If mixing of left-regular and right-regular rules is allowed, we still have a linear grammar, but not necessarily a regular one. What is more, such a grammar need not generate a regular language: all linear grammars can be easily brought into this form, and hence, such grammars can generate exactly all linear languages, including nonregular ones.
For instance, the grammar G with N = {S, A}, Σ = {a, b}, P with start symbol S and rules
- S → aA
- A → Sb
- S → ε
generates, the paradigmatic non-regular linear language.
Read more about this topic: Regular Grammar
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