Alternating weighted automata Conference Paper


Author(s): Chatterjee, Krishnendu; Doyen, Laurent; Henzinger, Thomas A
Title: Alternating weighted automata
Title Series: LNCS
Affiliation IST Austria
Abstract: Weighted automata are finite automata with numerical weights on transitions. Nondeterministic weighted automata define quantitative languages L that assign to each word w a real number L(w) computed as the maximal value of all runs over w, and the value of a run r is a function of the sequence of weights that appear along r. There are several natural functions to consider such as Sup, LimSup, LimInf, limit average, and discounted sum of transition weights. We introduce alternating weighted automata in which the transitions of the runs are chosen by two players in a turn-based fashion. Each word is assigned the maximal value of a run that the first player can enforce regardless of the choices made by the second player. We survey the results about closure properties, expressiveness, and decision problems for nondeterministic weighted automata, and we extend these results to alternating weighted automata. For quantitative languages L 1 and L 2, we consider the pointwise operations max(L 1,L 2), min(L 1,L 2), 1 − L 1, and the sum L 1 + L 2. We establish the closure properties of all classes of alternating weighted automata with respect to these four operations. We next compare the expressive power of the various classes of alternating and nondeterministic weighted automata over infinite words. In particular, for limit average and discounted sum, we show that alternation brings more expressive power than nondeterminism. Finally, we present decidability results and open questions for the quantitative extension of the classical decision problems in automata theory: emptiness, universality, language inclusion, and language equivalence.
Conference Title: FCT: Fundamentals of Computation Theory
Volume: 5699
Conference Dates: September 2-4, 2009
Conference Location: Wroclaw, Poland
Publisher: Springer  
Location: Berlin, Heidelberg
Date Published: 2009-09-10
Start Page: 3
End Page: 13
URL:
DOI: 10.1007/978-3-642-03409-1_2
Notes: This research was supported in part by the Swiss National Science Foundation under the Indo-Swiss Joint Research Programme, by the European Network of Excellence on Embedded Systems Design (ArtistDesign), by the European Combest, Quasimodo, and Gasics projects, by the PAI program Moves funded by the Belgian Federal Government, and by the CFV (Federated Center in Verification) funded by the F.R.S.-FNRS.
Open access: yes (repository)
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
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