Tinted, Detached, and Lazy CNF-XOR Solving and Its Applications to Counting and Sampling

Mate Soos, Stephan Gocht, Kuldeep S. Meel

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

10 Citations (SciVal)


Given a Boolean formula, the problem of counting seeks to estimate the number of solutions of F while the problem of uniform sampling seeks to sample solutions uniformly at random. Counting and uniform sampling are fundamental problems in computer science with a wide range of applications ranging from constrained random simulation, probabilistic inference to network reliability and beyond. The past few years have witnessed the rise of hashing-based approaches that use XOR-based hashing and employ SAT solvers to solve the resulting CNF formulas conjuncted with XOR constraints. Since over 99% of the runtime of hashing-based techniques is spent inside the SAT queries, improving CNF-XOR solvers has emerged as a key challenge. In this paper, we identify the key performance bottlenecks in the recently proposed architecture, and we focus on overcoming these bottlenecks by accelerating the XOR handling within the SAT solver and on improving the solver integration through a smarter use of (partial) solutions. We integrate the resulting system, called, with the state of the art approximate model counter, and the state of the art almost-uniform model sampler. Through an extensive evaluation over a large benchmark set of over 1896 instances, we observe that leads to consistent speed up for both counting and sampling, and in particular, we solve 77 and 51 more instances for counting and sampling respectively.

Original languageEnglish
Title of host publicationComputer Aided Verification - 32nd International Conference, CAV 2020, Proceedings
EditorsShuvendu K. Lahiri, Chao Wang
PublisherSpringer Gabler
Number of pages22
ISBN (Print)9783030532871
Publication statusPublished - 2020
Event32nd International Conference on Computer Aided Verification, CAV 2020 - Los Angeles, United States
Duration: 2020 Jul 212020 Jul 24

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12224 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference32nd International Conference on Computer Aided Verification, CAV 2020
Country/TerritoryUnited States
CityLos Angeles

Subject classification (UKÄ)

  • Software Engineering


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