Can a regular grammar be ambiguous? An ambiguous grammar is a context-free grammar for which there exists a string that has more than one leftmost derivation, while an unambiguous grammar is a context-free grammar for which every valid string has a unique leftmost derivation.  
A regular grammar is a mathematical object, $G$, with four components, $G = (N, \Sigma, P, S)$, where 


*

*$N$ is a nonempty, finite set of nonterminal symbols, 

*$\Sigma$ is a finite set of terminal symbols, or alphabet, symbols, 

*$P$ is a set of grammar rules, each of one having one of the forms:  


*

*$A \rightarrow aB$

*$A \rightarrow a$

*$A \rightarrow \varepsilon$
for $A, B \in N$, $a \in Σ$, and $\varepsilon$ the empty string, and


*$S ∈ N$ is the start symbol.


Now the question is: Can a regular grammar also be ambiguous?

There do indeed exist ambiguous regular grammars. Take for example
$S\rightarrow A~|~B$
$A\rightarrow a$
$B\rightarrow a$
