Merge pull request #58 from codingnirvana/patch-1

Typo: enrolling instead of unrolling

chapters/circuit-compilers-moonmath.tex

@@ -1923,7 +1923,7 @@ \subsubsection{Loops} In many programming languages, various loop control struct
   }
 \end{lstlisting}
 
-In contrast to this, algebraic circuits and Rank-1 Constraint Systems are not general enough to express arbitrary computation, but bounded computation only. As a consequence,  it is not possible to implement unbounded loops, or loops with bounds that are unknown at compile time in those models. This can be easily seen since circuits are acyclic by definition, and implementing an unbounded loop as an acyclic graph requires a circuits of unbounded size.  However, circuits are general enough to express bounded loops, where the upper bound on its execution is known at compile time. Those loop can be implemented in circuits by enrolling the loop. 
+In contrast to this, algebraic circuits and Rank-1 Constraint Systems are not general enough to express arbitrary computation, but bounded computation only. As a consequence,  it is not possible to implement unbounded loops, or loops with bounds that are unknown at compile time in those models. This can be easily seen since circuits are acyclic by definition, and implementing an unbounded loop as an acyclic graph requires a circuits of unbounded size.  However, circuits are general enough to express bounded loops, where the upper bound on its execution is known at compile time. Those loop can be implemented in circuits by unrolling the loop. 
 
 As a consequence, any programing language that compiles to algebraic circuits can only provide loop structures where the bound is a constant known at compile time. This implies that loops cannot depend on execution inputs, but on compile time parameters only.  
 \begin{example} To give an intuition of how a real-world circuit compiler might transform any high-level description of a bounded \texttt{for} loop into a circuit, consider the following \lgname{PAPER} code: