Abstract Abductive reasoning (or Abduction, for short) is among the most fundamental AI reasoning methods, with a broad range of applications, including fault diagnosis, belief revision, and automated planning. Unfortunately, Abduction is of high computational complexity; even propositional Abduction is ?P2 -complete and thus harder than NP and co-NP. This complexity barrier rules out the existence of a polynomial transformation to propositional satisfiability (S AT). In this work we use structural properties of the Abduction instance to break this complexity barrier. We utilize the problem structure in terms of small backdoor sets. We present fixedparameter tractable transformations from Abduction to S AT, which make the power of today’s S AT solvers available to Abduction.