A theory for Log-Space and NLIN versus coNLIN

Abstract

The use of Nepomnjaščiǐ’s Theorem in the proofs of independence results for bounded arithmetic theories is investigated. Using this result and similar ideas, it is shown that at least one of S₁ or TLS does not prove the Matiyasevich-Robinson-Davis-Putnam Theorem. It is also established that TLS does not prove a statement that roughly means nondeterministic linear time is equal to co-nondeterministic linear time. Here S₁ is a conservative extension of the well-studied theory IΔ and TLS is a theory for LOGSPACE reasoning.