10.1007/978-3-540-87531-4_28
Krishnendu Chatterjee
Krishnendu
Chatterjee0000-0002-4561-241X
Doyen, Laurent
Laurent
Doyen
Thomas Henzinger
Thomas A
Henzinger0000−0002−2985−7724
Quantitative languages
LNCS
Springer
2008
2018-12-11T12:05:40Z
2019-08-02T12:38:20Z
conference
https://research-explorer.app.ist.ac.at/record/3879
https://research-explorer.app.ist.ac.at/record/3879.json
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.