> Do LPEG's also you some form or memoization? 

No.

> If not, then how do they achieve linear time (simply the conversion to a 
>"program" for a VM > doesn't seem to necessarily do this).


There is no linear time guarantee.
A discussion about the performance of the
parsing machine is presented in section 5 of
http://www.inf.puc-rio.br/%7Eroberto/docs/peg.pdf

Actually, it seems that PEG libraries that implement
the Packrat algorithm (that guarantees linear parsing
time) turn it off by default, because the memorization
is expensive.

Sérgio

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