Weighted Automata and Logics on Infinite Graphs

  title={Weighted Automata and Logics on Infinite Graphs},
  author={Stefan D{\"u}ck},
  • Stefan Dück
  • Published in DLT 25 July 2016
  • Computer Science, Mathematics
We show a Buchi-like connection between graph automata and logics for infinite graphs. Using valuation monoids, a very general weight structure able to model computations like average or discounting, we extend this result to the quantitative setting. This gives us the first general results connecting automata and logics over infinite graphs in the qualitative and the quantitative setting. 

Weighted automata

This work presents selected classical and recent results concentrating on the expressive power of weighted automata, a field of classical finite automata in which the transitions carry weights.



On Logics, Tilings, and Automata

  • W. Thomas
  • Computer Science, Mathematics
  • 1991
A notion of “graph acceptor” is introduced which can specify monadic second-order properties and allows to treat known types of finite automata in a common framework.

Weighted automata and weighted logics on infinite words

It is shown that their behaviors coincide with the semantics of weighted restricted MSO-sentences and an equivalence property of weighted Muller and weighted Büchi automata over certain semirings is established.

Weighted Automata and Logics on Graphs

A general model of weighted automata acting on graphs is introduced, which form a quantitative version of Thomas’ unweighted model of graph acceptors and it is derived that a suitable weighted MSO logic is expressively equivalent to weighted graph automata.

Weighted Muller Tree Automata and Weighted Logics

We introduce weighted Muller tree automata, over totally commutative complete semirings, acting on infinite trees. We show that their behaviours coincide with the semantics of weighted restricted

Elements of an automata theory over partial orders

  • W. Thomas
  • Computer Science
    Partial Order Methods in Verification
  • 1996
A model of nondeterministic nite automaton over ((nite) partial orders is introduced. It captures existential monadic second-order logic in expressive power and generalizes classical word automata

Weighted Tree Automata over Valuation Monoids and Their Characterization by Weighted Logics

This work establishes a characterization of the behaviors of these weighted finite tree automata by fragments of weighted monadic second-order logic, and shows that weighted tree Automata capture the expressive power of several semantics of full weighted MSO logic.

Weighted Distributed Systems and Their Logics

It is shown that any distributed system can be described by a weighted existential MSO formula and, vice versa, any formula gives rise to a weighted asynchronous cellular automaton.

Weighted tree automata and weighted logics

Weighted automata and weighted logics

Weighted versus Probabilistic Logics

This paper identifies weighted versions of MSO and CTL that generalize the classical logics and even other quantitative extensions such as probabilistic CTL and establishes expressiveness results on the authors' logics giving translations from weighted and probabilistically CTL into weighted MSO.