# Algebra Seminar talk

2019-01-18 (10:15-11:15)

Manfred **Droste***Weighted automata and quantitative logics*

Abstract:

Quantitative models and quantitative analysis in Computer Science are
receiving increased attention. The goal of this talk is to investigate
quantitative automata and quantitative logics. Weighted automata on finite
words have already been investigated in seminal work of Schützenberger (1961).
They consist of classical finite automata in which the transitions carry
weights. These weights may model, e.g., the cost, the consumption of
resources, or the reliability or probability of the successful execution of
the transitions. This concept soon developed a flourishing theory. We
investigate weighted automata and their relationship to weighted logics. For
this, we present syntax and semantics of a quantitative logic; the semantics
counts ‘how often’ a formula is true in a given word. Our main result,
extending the classical result of Büchi, shows that if the weights are taken
from an arbitrary semiring, then weighted automata and a syntactically defined
fragment of our weighted logic are expressively equivalent. A corresponding
result holds for infinite words. Moreover, this extends to quantitative
automata investigated by Henzinger et al. with (non-semiring) average-type
behaviors, or with discounting or limit average objectives for infinite words.