Recover PRNG description from consecutive outputs

Question

Given the outputs of the pseudorandom numbers generator how can one determine the type (e.g. Linear Feedback Shift Register), Multiply-With-Carry, Linear Congruential Generator etc.) and recover the function and the seed?

The given array of numbers is for sure generated by PRNG (not Cryptographically Secure) - this is known in advance. The outputs are clean, the PRNG is a black box returning consecutive numbers (no modified, no skipped values. Now the task is to find the function and seed from the values.

The simple idea is try all schemes until match is found, but I am interested in more algorithmic approach.