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Max and Sum Semantics for Alternating Weighted Automata

  • Conference paper
Automated Technology for Verification and Analysis (ATVA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6996))

Abstract

In the traditional Boolean setting of formal verification, alternating automata are the key to many algorithms and tools. In this setting, the correspondence between disjunctions/conjunctions in the specification and nondeterministic/universal transitions in the automaton for the specification is straightforward. A recent exciting research direction aims at adding a quality measure to the satisfaction of specifications of reactive systems. The corresponding automata-theoretic framework is based on weighted automata, which map input words to numerical values. In the weighted setting, nondeterminism has a minimum semantics – the weight that an automaton assigns to a word is the cost of the cheapest run on it. For universal branches, researchers have studied a (dual) maximum semantics. We argue that a summation semantics is of interest too, as it captures the intuition that one has to pay for the cost of all conjuncts.

We introduce and study alternating weighted automata on finite words in both the max and sum semantics. We study the duality between the min and max semantics, closure under max and sum, the added power of universality and alternation, and arithmetic operations on automata. In particular, we show that universal weighted automata in the sum semantics can represent all polynomials.

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Author information

Authors and Affiliations

  1. School of Engineering and Computer Science, Hebrew University, Jerusalem, Israel

    Shaull Almagor & Orna Kupferman

Authors
  1. Shaull Almagor
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  2. Orna Kupferman
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Editor information

Editors and Affiliations

  1. University of California, Santa Barbara, CA, USA

    Tevfik Bultan

  2. Department of Computer Science and Information Engineering, National Chung Cheng University, 168 University Road, Min-Hsiung, 62102, Chiayi, Taiwan, ROC

    Pao-Ann Hsiung

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Almagor, S., Kupferman, O. (2011). Max and Sum Semantics for Alternating Weighted Automata. In: Bultan, T., Hsiung, PA. (eds) Automated Technology for Verification and Analysis. ATVA 2011. Lecture Notes in Computer Science, vol 6996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24372-1_2

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  • DOI: https://doi.org/10.1007/978-3-642-24372-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24371-4

  • Online ISBN: 978-3-642-24372-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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