Analysis of a Class of Algorithms for Problems on Trace Languages

The time complexity of a class of algorithms for problems on trace languages is studied both in the worst and in the average case. Membership problem for regular trace languages and the problem of counting the cardinality of a trace can be solved by algorithms belonging to such a class. These algorithms are described by a recursive procedure scheme whose input is a trace represented by a corresponding string. Under reasonable assumptions the worst case time complexity on traces of length n is ϑ(nα), where α is the cardinality of the largest clique in the concurrent alphabet .