TESTING FOR FORBIDDEN POSETS IN ORDERED ROOTED FORESTS

We initiate the study of testing for general forbidden posets in a colored ordered rooted forest whose structure is fixed. First, we consider the case where the forbidden set consists of (ancestral) chains, and second, we consider the case in which it consists of one general ordered rooted forest. For both cases, we provide 1-sided error, non-adaptive tests, whose query complexity is polynomial in ∊-1 and is independent of the input size and the number of colors. Both tests do not require additional time complexity beyond the complexity of making the queries, except an O(n) time preprocessing stage in the test for a set of chains.