Left Linear Grammar to Right Linear Grammar | Summary and Q&A

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April 7, 2022
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Left Linear Grammar to Right Linear Grammar

TL;DR

The content explains the procedure to convert a left linear grammar to a right linear grammar using the same steps as the conversion from right linear grammar to finite automata.

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Key Insights

  • 🗯️ Left linear grammar can be easily converted to right linear grammar using the same steps as the conversion from right linear grammar to finite automata.
  • ❓ The conversion involves swapping the first and last steps of the conversion process.
  • 👷 The crucial steps in the conversion include constructing equivalent finite automata, interchanging initial and final states, reversing edge directions, and constructing RLG from the modified FA.

Questions & Answers

Q: What is the difference between converting LLG to RLG and RLG to FA?

The difference lies in the construction process, where the variables are replaced either to the rightmost or leftmost of the arrow in RLG construction, while in RLG to FA conversion, no such replacement occurs.

Q: Can you explain the steps involved in converting LLG to RLG?

The steps include converting LLG to equivalent FA, interchanging initial and final states, reversing edge directions, and constructing RLG from the FA by replacing variables to the rightmost or leftmost of the arrows.

Q: What should be done if there are non-generating states in the FA?

Non-generating states, such as "D" in the example, should have their corresponding productions removed in the final RLG solution.

Q: Is converting LLG to RLG a complex topic in automata theory?

According to the content, converting LLG to RLG is considered one of the simplest topics in automata theory.

Summary & Key Takeaways

  • Left linear grammar (LLG) can be converted to right linear grammar (RLG) using the same procedure as RLG to finite automata conversion but with the first and last steps swapped.

  • The procedure involves converting LLG to equivalent finite automata (FA), interchanging the initial and final states, reversing the direction of all edges, and constructing RLG from the FA.

  • An example is provided to demonstrate the conversion process step by step.

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