Conformant planning as a case study of incremental QBF solving

  • Uwe Egly
  • Martin Kronegger
  • Florian Lonsing
  • Andreas Pfandler
Open Access

DOI: 10.1007/s10472-016-9501-2

Cite this article as:
Egly, U., Kronegger, M., Lonsing, F. et al. Ann Math Artif Intell (2017) 80: 21. doi:10.1007/s10472-016-9501-2


We consider planning with uncertainty in the initial state as a case study of incremental quantified Boolean formula (QBF) solving. We report on experiments with a workflow to incrementally encode a planning instance into a sequence of QBFs. To solve this sequence of successively constructed QBFs, we use our general-purpose incremental QBF solver DepQBF. Since the generated QBFs have many clauses and variables in common, our approach avoids redundancy both in the encoding phase as well as in the solving phase. We also present experiments with incremental preprocessing techniques that are based on blocked clause elimination (QBCE). QBCE allows to eliminate certain clauses from a QBF in a satisfiability preserving way. We implemented the QBCE-based techniques in DepQBF in three variants: as preprocessing, as inprocessing (which extends preprocessing by taking into account variable assignments that were fixed by the QBF solver), and as a novel dynamic approach where QBCE is tightly integrated in the solving process. For DepQBF, experimental results show that incremental QBF solving with incremental QBCE outperforms incremental QBF solving without QBCE, which in turn outperforms nonincremental QBF solving. For the first time we report on incremental QBF solving with incremental QBCE as inprocessing. Our results are the first empirical study of incremental QBF solving in the context of planning and motivate its use in other application domains.


Quantified Boolean formulas (QBFs) Conformant planning Incremental solving Preprocessing Blocked clause elimination 

Mathematics Subject Classifications (2010)

68T15 68T20 68T27 

Funding information

Funder NameGrant NumberFunding Note
Austrian Science Fund (AT)
  • S11409-N23
  • P25518-N23
Deutsche Forschungsgemeinschaft (DE)
  • ER 738/2-1

Copyright information

© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Uwe Egly
    • 1
  • Martin Kronegger
    • 1
  • Florian Lonsing
    • 1
  • Andreas Pfandler
    • 1
    • 2
  1. 1.Institute of Information SystemsTU WienViennaAustria
  2. 2.School of Economic DisciplinesUniversity of SiegenSiegenGermany

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