  We study the problem of answering conjunctive queries with free access
patterns (CQAP) under updates. A free access pattern is a partition of the free
variables of the query into input and output. The query returns tuples over the
output variables given a tuple of values over the input variables.
  We introduce a fully dynamic evaluation approach for CQAP queries. We also
give a syntactic characterisation of those CQAP queries that admit constant
time per single-tuple update and whose output tuples can be enumerated with
constant delay given a tuple of values over the input variables. Finally, we
chart the complexity trade-off between the preprocessing time, update time and
enumeration delay for CQAP queries. For a class of CQAP queries, our approach
achieves optimal, albeit non-constant, update time and delay. Their optimality
is predicated on the Online Matrix-Vector Multiplication conjecture. Our
results recover prior work on the dynamic evaluation of conjunctive queries
without access patterns. We also illustrate an application of our dynamic
evaluation approach to tractable CQAP queries over probabilistic databases.
