Making weighted containment feasible: A heuristic based on simulation and abstraction

Guy Avni*, Orna Kupferman

*Corresponding author for this work

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

10 Scopus citations


Weighted automata map input words to real numbers and are useful in reasoning about quantitative systems and specifications. The containment problem for weighted automata asks, given two weighted automata A and B, whether for all words w, the value that A assigns to w is less than or equal to the value B assigns to w. The problem is of great practical interest, yet is known to be undecidable. Efforts to approximate weighted containment by weighted variants of the simulation pre-order still have to cope with large state spaces. One of the leading approaches for coping with large state spaces is abstraction. We introduce an abstraction-refinement paradigm for weighted automata and show that it nicely combines with weighted simulation, giving rise to a feasible approach for the containment problem. The weighted-simulation pre-order we define is based on a quantitative two-player game, and the technical challenge in the setting origins from the fact the values that the automata assign to words are unbounded. The abstraction-refinement paradigm is based on under- and over-approximation of the automata, where approximation, and hence also the refinement steps, refer not only to the languages of the automata but also to the values they assign to words.

Original languageAmerican English
Title of host publicationConcurrency Theory - 23rd International Conference, CONCUR 2012, Proceedings
Number of pages16
StatePublished - 2012
Event23rd International Conference on Concurrency Theory, CONCUR 2012 - Newcastle upon Tyne, United Kingdom
Duration: 4 Sep 20127 Sep 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7454 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Conference on Concurrency Theory, CONCUR 2012
Country/TerritoryUnited Kingdom
CityNewcastle upon Tyne


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