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
Famous quotes containing the words mixing, left, regular and/or rules:
“Give me Catholicism every time. Father Cheeryble with his thurible; Father Chatterjee with his liturgy. What fun they have with all their charades and conundrums! If it weren’t for the Christianity they insist on mixing in with it, I’d be converted tomorrow.”
—Aldous Huxley (1894–1963)
“They seldom looked happy. They passed one another without a word in the elevator, like silent shades in hell, hell-bent on their next look from a handsome stranger. Their next rush from a popper. The next song that turned their bones to jelly and left them all on the dance floor with heads back, eyes nearly closed, in the ecstasy of saints receiving the stigmata.”
—Andrew Holleran (b. 1943)
“The solid and well-defined fir-tops, like sharp and regular spearheads, black against the sky, gave a peculiar, dark, and sombre look to the forest.”
—Henry David Thoreau (1817–1862)
“Rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.”
—Nelson Goodman (b. 1906)