A nondeterministic discounted-sum automaton (NDA) values a run by the discounted sum of
the visited transition weights. That is, the weight in the i-th position of a run of a λ-NDA is …

Classical automata provide acceptance mechanisms for words. The starting point of
weighted automata is to determine the number of ways a word can be accepted or the …

In automata theory, a fundamental result of Büchi and Elgot states that the recognizable
languages are precisely the ones definable by sentences of monadic second order logic …

In this paper we prove Kleene's result for formal tree series over a commutative semiring A
(which is not necessarily complete or continuous or idempotent), ie, the class of formal tree …

This is a book on weighted tree automata. We present the basic definitions and some of the
important results in a coherent form with full proofs. The concept of weighted tree automata …

Nondeterministic weighted automata are finite automata with numerical weights on
transitions. They define quantitative languages L that assign to each word wa real number L …

A discounted-sum automaton (NDA) is a nondeterministic finite automaton with edge
weights, valuing a run by the discounted sum of visited edge weights. More precisely, the …

Quantitative aspects of systems like consumption of resources, output of goods, or reliability
can be modeled by weighted automata. Recently, objectives like the average cost or the …

We introduce weighted automata over infinite words with Muller acceptance condition and
we show that their behaviors coincide with the semantics of weighted restricted MSO …

This chapter is about the verification of Markov decision processes (MDPs) which
incorporate one of the fundamental models for reasoning about probabilistic and …