One of the most elemental result of relationship between boolean circuit size and polynomial uniform computation is Pippenger and Fishers simulation: $DTIME[T(n)]\subseteq SIZE[T(n)\log  T(n)]$.I want to consider the small branching program family simulating low space  computation.   Question1: What is the best simulation bound $S_{1}(n)$ which is known at this moment such that $DSPACE [S(n)]\subseteq BP-SIZE[S_{1}(n)]$ Question2:What is the best time complexity bound as far as we know, for the function that $1^{n}\rightarrow $a branching program in the Question 1.
Low space computation and branching program
cc.complexity theory;reference request;circuit complexity;space bounded;space complexity