I am interested in all know classes of Computatinal problems. The Wikipedia article on computational problems types is incomplete. Some of the known classes are:
1- Decision problem such as 3SAT
2- Search problem such Factoring search problem
3- Function problem such as finding a second Hamiltonian cycle on a cubic graph (given some Hamiltonian cycle) which in TFNP
4- Optimization problem such as maximum independent set problem
5- Uniqueness problem such as Unique SAT problem
6- Another solution problem such as finding a second Hamiltonian cycle on a general graph (given some Hamiltonian cycle) which is in NP
7- Counting problem such as counting perfect matchings in bipartite graphs
8- Promise problem such as finding solution of SAT under the promise that it has a unique solution
9- Inverse problem such as Inverse 3SAT
10- Extendibility problem such as edge precoloring extension problem on bipartite graphs
11- Parity problem such as Parity-SAT
What other types of computational problems should be added to the above list?
P.S. Some of the above can be cast as decision problem such as optimization problems.