Analysis of algorithms for the recognition of rational and context-free trace languages

We present an algorithm for the recognition of rational trace languages that has a time complexity at most proportional to the number of prefixes of the input trace. In the worst case it requires O(nα) time and O(nα-1) space, where α is the size of the maximum clique in the independence alphabet; in the average case, it works in O (nk) time, where k is the number of connected components of the dependence alphabet. This algorithm is based on a dynamic programming technique that can also be applied for the recognition of context-free trace languages. Here we present an extension of the classical CYK algorithm that requires O (n3α) time and O (n2α) space in the worst case, and O (n3k) time and O (n2k) space in the average case.