The complexity issues are addressed in another paper . It is sufficient for the verifier to know that the answer is close to correct. The model used is based on interactive proof systems, probabilistically checkable proofs, program checkers, and CS proofs. Complexity Theory Boolean branching programs are simple, yet powerful models of computation. A fundamental issue in complexity theory is the understanding of determinism vs. non-determinism.
Lattices play an important role in many algebraic and combinatorial algorithms.
A long standing open problem has been to understand the complexity of computing the shortest non-zero vector in a lattice. Descriptive complexity is the complexity of describing problems in some logical formalism. There is often a close connection between the descriptive complexity of a problem and its computational complexity.