Tree Evaluation in Logspace

Determine whether the Tree Evaluation problem is solvable in deterministic logarithmic space (L), i.e., ascertain if evaluating a rooted function tree with constant-arity operations and succinct node descriptions can be performed using O(log n) workspace on a deterministic Turing machine.

Background

Tree Evaluation (TE) is a foundational problem in small-space complexity: given a rooted tree whose internal nodes compute fixed functions of their children and whose leaves are inputs, the task is to evaluate the root value. The complexity of TE has long been studied in connection with logspace computation and branching programs.

In the context of this paper, the authors achieve space-efficient evaluation for a specific class of succinct computation trees arising from block-respecting simulations, but they note that the broader, classical question about TE’s placement in L is unresolved and has implications for circuit evaluation lower bounds and the limits of logspace algorithms.