Quantitative generalizations of classical languages, which assign to each word a real number instead of a boolean value, have applications in modeling resource-constrained computation. We use weighted automata (finite automata with transition weights) to define several natural classes of quantitative languages over finite and infinite words; in particular, the real value of an infinite run is computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We define the classical decision problems of automata theory (emptiness, universality, language inclusion, and language equivalence) in the quantitative setting and study their computational complexity. As the decidability of language inclusion remains open for some classes of weighted automata, we introduce a notion of quantitative simulation that is decidable and implies language inclusion. We also give a complete characterization of the expressive power of the various classes of weighted automata. In particular, we show that most classes of weighted automata cannot be determinized.
Research supported in part by the NSF grants CCR-0132780, CNS-0720884, and CCR-0225610, by the Swiss National Science Foundation, and by the European COMBEST project.
385 - 400
CSL: Computer Science Logic
Chatterjee K, Doyen L, Henzinger TA. Quantitative languages. In: Vol 5213. Springer; 2008:385-400. doi:10.1007/978-3-540-87531-4_28
Chatterjee, K., Doyen, L., & Henzinger, T. A. (2008). Quantitative languages (Vol. 5213, pp. 385–400). Presented at the CSL: Computer Science Logic, Springer. https://doi.org/10.1007/978-3-540-87531-4_28
Chatterjee, Krishnendu, Laurent Doyen, and Thomas A Henzinger. “Quantitative Languages,” 5213:385–400. Springer, 2008. https://doi.org/10.1007/978-3-540-87531-4_28.
K. Chatterjee, L. Doyen, and T. A. Henzinger, “Quantitative languages,” presented at the CSL: Computer Science Logic, 2008, vol. 5213, pp. 385–400.
Chatterjee K, Doyen L, Henzinger TA. 2008. Quantitative languages. CSL: Computer Science Logic, LNCS, vol. 5213. 385–400.
Chatterjee, Krishnendu, et al. Quantitative Languages. Vol. 5213, Springer, 2008, pp. 385–400, doi:10.1007/978-3-540-87531-4_28.