Politeness and Stable Infiniteness: Stronger Together

Ying Sheng, Yoni Zohar, Christophe Ringeissen, Andrew Reynolds, Clark Barrett, Cesare Tinelli

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


We make two contributions to the study of polite combination in satisfiability modulo theories. The first is a separation between politeness and strong politeness, by presenting a polite theory that is not strongly polite. This result shows that proving strong politeness (which is often harder than proving politeness) is sometimes needed in order to use polite combination. The second contribution is an optimization to the polite combination method, obtained by borrowing from the Nelson-Oppen method. The Nelson-Oppen method is based on guessing arrangements over shared variables. In contrast, polite combination requires an arrangement over all variables of the shared sorts. We show that when using polite combination, if the other theory is stably infinite with respect to a shared sort, only the shared variables of that sort need be considered in arrangements, as in the Nelson-Oppen method. The time required to reason about arrangements is exponential in the worst case, so reducing the number of variables considered has the potential to improve performance significantly. We show preliminary evidence for this by demonstrating a speed-up on a smart contract verification benchmark.

Original languageEnglish
Title of host publicationAutomated Deduction – CADE 28 - 28th International Conference on Automated Deduction, 2021, Proceedings
EditorsAndré Platzer, Geoff Sutcliffe
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages18
ISBN (Print)9783030798758
StatePublished - 2021
Externally publishedYes
Event28th International Conference on Automated Deduction, CADE 28 2021 - Virtual, Online
Duration: 12 Jul 202115 Jul 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12699 LNAI


Conference28th International Conference on Automated Deduction, CADE 28 2021
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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