Geodesic
A~lower bound for the coding cost and the asymptotically optimal coding of stochastic context-free languages
Diskretnyj analiz i issledovanie operacij, Tome 8 (2001) no. 3, pp. 26-45

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We consider a language generated by a stochastic context-free grammar with unique derivation for which the matrix of first moments is indecomposable, nonperiodic, and its Perron root is strictly less than one. For such a language we obtain an unimprovable lower bound for the binary coding cost. We also construct an algorithm for asymptotically optimal coding. 
@article{DA_2001_8_3_a2,
     author = {L. P. Zhil'tsova},
     title = {A~lower bound for the coding cost and the asymptotically optimal coding of stochastic context-free languages},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {26--45},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2001_8_3_a2/}
}
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L. P. Zhil'tsova. A~lower bound for the coding cost and the asymptotically optimal coding of stochastic context-free languages. Diskretnyj analiz i issledovanie operacij, Tome 8 (2001) no. 3, pp. 26-45. http://geodesic.mathdoc.fr/item/DA_2001_8_3_a2/