Abstract
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.
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Czyzowicz, J., Fraczak, W., Yazdani, M.: Throughput of high-performance concatenation state machines. In: AWOCA 2005. Proceedings of the sixteenth Australasian Workshop on Combinatorial Algorithms, pp. 85–94 (2005)
Dasdan, A., Gupta, R.: Faster maximum and minimum mean cycle algorithms for system-performance analysis. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 17(10), 889–899 (1998)
Esparza, J., Kiefer, S., Luttenberger, M.: On fixed point equations over commutative semirings. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 296–307. Springer, Heidelberg (2007)
Hopkins, M.W., Kozen, D.: Parikh’s theorem in commutative Kleene algebra. In: Logic in Computer Science, pp. 394–401 (1999)
Karp, R.M.: A characterization of the minimum cycle mean in a digraph. Discrete Mathematics 23, 309–311 (1978)
Parikh, R.J.: On context-free languages. J. ACM 13(4), 570–581 (1966)
Yazdani, M., Fraczak, W., Welfeld, F., Lambadaris, I.: A criterion for speed evaluation of content inspection engines. In: ICN/ICONS/MCL 2006. Fifth International Conference on Networking and the International Conference on Systems, pp. 19–24. IEEE Computer Society, Los Alamitos (2006)
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Caucal, D., Czyzowicz, J., Fraczak, W., Rytter, W. (2007). Efficient Computation of Throughput Values of Context-Free Languages. In: Holub, J., Žďárek, J. (eds) Implementation and Application of Automata. CIAA 2007. Lecture Notes in Computer Science, vol 4783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76336-9_20
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DOI: https://doi.org/10.1007/978-3-540-76336-9_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76335-2
Online ISBN: 978-3-540-76336-9
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