Journal of the ACM (JACM)
Parikh's Theorem in Commutative Kleene Algebra
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A Criterion for Speed Evaluation of Content Inspection Engines
ICNICONSMCL '06 Proceedings of the International Conference on Networking, International Conference on Systems and International Conference on Mobile Communications and Learning Technologies
On fixed point equations over commutative semirings
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Faster maximum and minimum mean cycle algorithms for system-performance analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Derivation Tree Analysis for Accelerated Fixed-Point Computation
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Solving fixed-point equations by derivation tree analysis
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Path algorithms on regular graphs
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
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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.