Generic computability and coarse computability both capture the idea of computing a function on "almost all" inputs, where "almost all" is defined in terms of asymptotic density. The difference between the two notions is that generic computability permits errors of omission (i.e., divergent computations), while coarse computability permits errors of commission (i.e., incorrect answers). We study these and two other notions of asymptotic computability, in which both forms of error may be present, including one briefly studied in the 1970's but apparently since forgotten, which requires that our computations emit a signal whenever an error may be possible. In particular, we study reducibilities and degree structures arising from these notions.

This is joint work with Eric P. Astor and Carl G. Jockusch, Jr.