10.2168/LMCS-4(4:13)2008
https://lmcs.episciences.org/860
Buss, Samuel R.
Samuel R.
Buss
Hoffmann, Jan
Jan
Hoffmann
Johannsen, Jan
Jan
Johannsen
Resolution Trees with Lemmas: Resolution Refinements that Characterize
DLL Algorithms with Clause Learning
Resolution refinements called w-resolution trees with lemmas (WRTL) and with
input lemmas (WRTI) are introduced. Dag-like resolution is equivalent to both
WRTL and WRTI when there is no regularity condition. For regular proofs, an
exponential separation between regular dag-like resolution and both regular
WRTL and regular WRTI is given.
It is proved that DLL proof search algorithms that use clause learning based
on unit propagation can be polynomially simulated by regular WRTI. More
generally, non-greedy DLL algorithms with learning by unit propagation are
equivalent to regular WRTI. A general form of clause learning, called
DLL-Learn, is defined that is equivalent to regular WRTL.
A variable extension method is used to give simulations of resolution by
regular WRTI, using a simplified form of proof trace extensions. DLL-Learn and
non-greedy DLL algorithms with learning by unit propagation can use variable
extensions to simulate general resolution without doing restarts.
Finally, an exponential lower bound for WRTL where the lemmas are restricted
to short clauses is shown.
episciences.org
Computer Science - Logic in Computer Science
Computer Science - Computational Complexity
F.2.2
I.2.8
2015-06-25
2008-12-05
2008-12-05
eng
journal article
arXiv:0811.1075
10.48550/arXiv.0811.1075
1860-5974
https://lmcs.episciences.org/860/pdf
VoR
application/pdf
Logical Methods in Computer Science
Volume 4, Issue 4
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