Nested weighted limit-average automata of bounded width Conference Paper

Author(s): Chatterjee, Krishnendu; Henzinger, Thomas A; Otop, Jan
Title: Nested weighted limit-average automata of bounded width
Title Series: LIPIcs
Affiliation IST Austria
Abstract: While weighted automata provide a natural framework to express quantitative properties, many basic properties like average response time cannot be expressed with weighted automata. Nested weighted automata extend weighted automata and consist of a master automaton and a set of slave automata that are invoked by the master automaton. Nested weighted automata are strictly more expressive than weighted automata (e.g., average response time can be expressed with nested weighted automata), but the basic decision questions have higher complexity (e.g., for deterministic automata, the emptiness question for nested weighted automata is PSPACE-hard, whereas the corresponding complexity for weighted automata is PTIME). We consider a natural subclass of nested weighted automata where at any point at most a bounded number k of slave automata can be active. We focus on automata whose master value function is the limit average. We show that these nested weighted automata with bounded width are strictly more expressive than weighted automata (e.g., average response time with no overlapping requests can be expressed with bound k=1, but not with non-nested weighted automata). We show that the complexity of the basic decision problems (i.e., emptiness and universality) for the subclass with k constant matches the complexity for weighted automata. Moreover, when k is part of the input given in unary we establish PSPACE-completeness.
Keywords: complexity; Weighted automata; nested weighted automata; mean-payoff
Conference Title: MFCS: Mathematical Foundations of Computer Science (SG)
Volume: 58
Conference Dates: August 22-26, 2016
Conference Location: Kraków, Poland
Publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik  
Date Published: 2016-01-01
Start Page: 24:1
End Page: 24:14
Copyright Statement: CC BY
DOI: 10.4230/LIPIcs.MFCS.2016.24
Notes: This research was supported in part by the Austrian Science Fund (FWF) under grants S11402-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award), ERC Start grant (279307: Graph Games), Vienna Science and Technology Fund (WWTF) through project ICT15-003 and by the National Science Centre (NCN), Poland under grant 2014/15/D/ST6/04543.
Open access: yes (OA journal)
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
  2. Jan Otop
    16 Otop
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