TY - GEN
T1 - On Limits of Symbolic Approach to SAT Solving
AU - Itsykson, Dmitry
AU - Ovcharov, Sergei
N1 - Publisher Copyright:
© Dmitry Itsykson and Sergei Ovcharov.
PY - 2024/8/1
Y1 - 2024/8/1
N2 - We study the symbolic approach to the propositional satisfiability problem proposed by Aguirre and Vardi in 2001 based on OBDDs and symbolic quantifier elimination. We study the theoretical limitations of the most general version of this approach where it is allowed to dynamically change variable order in OBDD. We refer to algorithms based on this approach as OBDD(∧,∃,reordering) algorithms. We prove the first exponential lower bound of OBDD(∧,∃,reordering) algorithms on unsatisfiable formulas, and give an example of formulas having short tree-like resolution proofs that are exponentially hard for OBDD(∧,∃,reordering) algorithms.
AB - We study the symbolic approach to the propositional satisfiability problem proposed by Aguirre and Vardi in 2001 based on OBDDs and symbolic quantifier elimination. We study the theoretical limitations of the most general version of this approach where it is allowed to dynamically change variable order in OBDD. We refer to algorithms based on this approach as OBDD(∧,∃,reordering) algorithms. We prove the first exponential lower bound of OBDD(∧,∃,reordering) algorithms on unsatisfiable formulas, and give an example of formulas having short tree-like resolution proofs that are exponentially hard for OBDD(∧,∃,reordering) algorithms.
KW - OBDD
KW - Symbolic quantifier elimination
KW - binary pigeonhole principle
KW - error-correcting codes
KW - lower bounds
KW - proof complexity
KW - tree-like resolution
UR - https://www.scopus.com/pages/publications/85203278123
U2 - 10.4230/LIPIcs.SAT.2024.19
DO - 10.4230/LIPIcs.SAT.2024.19
M3 - Conference contribution
AN - SCOPUS:85203278123
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 27th International Conference on Theory and Applications of Satisfiability Testing, SAT 2024
A2 - Chakraborty, Supratik
A2 - Jiang, Jie-Hong Roland
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 27th International Conference on Theory and Applications of Satisfiability Testing, SAT 2024
Y2 - 21 August 2024 through 24 August 2024
ER -