Max and sum semantics for alternating weighted automata

Shaull Almagor*, Orna Kupferman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations


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.

Original languageAmerican English
Title of host publicationAutomated Technology for Verification and Analysis - 9th International Symposium, ATVA 2011, Proceedings
Number of pages15
StatePublished - 2011
Event9th International Symposium on Automated Technology for Verification and Analysis, ATVA 2011 - Taipei, Taiwan, Province of China
Duration: 11 Oct 201114 Oct 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6996 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Symposium on Automated Technology for Verification and Analysis, ATVA 2011
Country/TerritoryTaiwan, Province of China


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