**Convert Right-Linear
Grammar to FA**

## Contents

__Definition__

__How
to Convert Right-Linear Grammar to Finite Automaton (FA)__

##
Definition

A right-linear grammar is a special
type of regular grammar, in which all productions of G must have
at most one variable in the right-hand side, and this variable must
be to the right of any terminals.

Using JFLAP, we will show how to
convert a right-linear grammar to a finite automaton.

## How
to Convert Right-Linear Grammar to Finite Automaton (FA)

We will begin by loading the grammar. You
can either enter the grammar (shown below) or load the file
regGrammarToNFA.jff.

Now click on **Convert **and then
C**onvert Right-Linear Grammar to FA**. Your window should look
like this after entering Convert to FA mode. Each variable from the
grammar is shown as a label for a state, with the start variable the
label for the start state. In addition, there is one final state not
associated with a variable.

Now, we need to add
transitions to finish the FA. When we expand the production “S->aB”,
it is similar to reading “a” in state S and moving to state B.
Thus, we should create a transition from state S to state B with the
transition “a”. After we create that transition on JFLAP, your
window should look like this :

***NOTE**
: For a tutorial on how to use the FA panel, you should first read
the tutorial pages on finite automata.

For productions that have no
variable on the right-side, a transition is created that goes to the
final state. You can check how many transitions you need to add by
clicking the **Done?** button. Finish entering the transitions.
JFLAP will notify you which productions are successfully created in
the FA. You can also let JFLAP automatically fill in the transitions
by clicking the **Show All** button. When you finish entering all
the transitions into FA, your window should look like :

***NOTE
**: We moved the states in the FA to produce a better picture.

Now,
since all the transitions are added, we have successfully transformed
right-linear grammar to finite automaton. You can export this FA.
When you export the converted FA, the new **Finite Automaton **window
will pop up with the created FA states and transitions. After
exporting the FA, your **Finite Automaton** window would look like
this :

**This concludes our brief
tutorial on Converting Right-Linear Grammar to FA. Thanks for
reading!**