Pruning techniques for bottom-up SemGuS enumerators

Develop an appropriate pruning technique for bottom-up enumeration in the SemGuS framework that effectively reduces the search space for imperative semantics where standard observational equivalence does not readily apply to sub-programs.

Background

The bottom-up enumerator constructs subterms by increasing size or height and typically applies observational equivalence to prune duplicates. However, in SemGuS with imperative semantics, sub-program input states can differ from top-level inputs due to state changes during execution, making straightforward observational-equivalence pruning infeasible.

The authors explicitly state that devising a suitable pruning technique for bottom-up enumeration in SemGuS remains open and suggest potential directions such as equality saturation and lifted interpretation.