Efficient Computation of Throughput Values of Context-Free Languages

We give the first deterministic polynomial time algorithm that computes the throughput value of a given context-free language L. The language is given by a grammar G of size n, together with a weight function assigning a positive weight to each symbol. The weight of a word w∈ L is defined as the sum of weights of its symbols (with multiplicities), and the mean weight is the weight of w divided by length of w. The throughput of L, denoted by throughput (L), is the smallest real number t, such that the mean value of each word of L is not smaller than t. Our approach, to compute throughput (L), consists of two phases. In the first one we convert the input grammar G to a grammar G', generating a finite language L′, such that throughput (L) = throughput (L′). In the next phase we find a word of the smallest mean weight in a finite language L′. The size of G′ is polynomially related to the size of G. The problem is of practical importance in system-performance analysis, especially in the domain of network packet processing, where one of the important parameters is the "guaranteed throughput" of a system for on-line network packet processing.