As we discussed in class, the proof that there is an pebbling time of $O_d(m/\log m)$ for any dag $G$ with in-degree $\le d$ has a bug (the construction of $V_a, V_b$ does not work). Give a fix for this proof so that we can apply it to for showing $DTIME(t)\ib ATIME(t/\log t)$. Try to prove as general a result as you can. More precisely: inn our application, $G$ comes from creating ``$B$-size blocks'' in the computation graph. So one way to fix the proof is to make further assumptions about the graph $G$. But we would prefer to avoid making such restrictions.
  • NO: this is actually trivial once you unroll the computation tree ... Formalize the proof of Gill (Chapter 8, section 3) that every recursively enumerable language is accepted in constant average time. [We made some intuitively plausible claims in the text, but these need to be formalized.]