Linear-Time Reductions of Resolution Proofs

Bar-Ilan, Omer; Fuhrmann, Oded; Hoory, Shlomo; Shacham, Ohad; Strichman, Ofer

doi:10.1007/978-3-642-01702-5_14

Cited by 25 publications

(40 citation statements)

References 14 publications

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“…In this section, we will present our notation and one of the proof reduction algorithms presented in [3].…”

Section: Preliminariesmentioning

confidence: 99%

“…We focus on such an algorithm introduced in [3], namely Recycle-Pivots. The observation behind the algorithm is that if there is a node v ∈ V such that each path from v to v 0 contains a node v such that piv(v) = piv(v ) then the resolution at node v is redundant.…”

Section: Conjunctive Normal Form(cnf)mentioning

confidence: 99%

“…In figure 1, we present an algorithm RmRedundancies, which is a reproduction of Recycle-Pivots from [3]. RmRedundancies takes a resolution Fig.…”

Section: Conjunctive Normal Form(cnf)mentioning

confidence: 99%

“…In this case, v is treated as a flagged node(line [13][14]. Please look in [3] for more detailed description of RestoreResTree. Example 1.…”

Section: Conjunctive Normal Form(cnf)mentioning

confidence: 99%

“…In [3], two low complexity algorithms for optimizing the proofs are presented. Our work is focused on one of the two, namely Recycle-Pivots.…”

Section: Introductionmentioning

confidence: 99%

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Improved Single Pass Algorithms for Resolution Proof Reduction

Gupta

2012

Theory and Applications of Satisfiability Testing – SAT 2012

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Abstract. Unsatisfiability proofs find many applications in verification. Today, many SAT solvers are capable of producing resolution proofs of unsatisfiability. For efficiency smaller proofs are preferred over bigger ones. The solvers apply proof reduction methods to remove redundant parts of the proofs while and after generating the proofs. One method of reducing resolution proofs is redundant resolution reduction, i.e., removing repeated pivots in the paths of resolution proofs (aka Pivot recycle). The known single pass algorithm only tries to remove redundancies in the parts of the proof that are trees. In this paper, we present three modifications to improve the algorithm such that the redundancies can be found in the parts of the proofs that are DAGs. The first modified algorithm covers greater number of redundancies as compared to the known algorithm without incurring any additional cost. The second modified algorithm covers even greater number of the redundancies but it may have longer run times. Our third modified algorithm is parametrized and can trade off between run times and the coverage of the redundancies. We have implemented our algorithms in OpenSMT and applied them on unsatisfiability proofs of 198 examples from plain MUS track of SAT11 competition. The first and second algorithm additionally remove 0.89% and 10.57% of clauses respectively as compared to the original algorithm. For certain value of the parameter, the third algorithm removes almost as many clauses as the second algorithm but is significantly faster.

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“…In this section, we will present our notation and one of the proof reduction algorithms presented in [3].…”

Section: Preliminariesmentioning

confidence: 99%

Section: Conjunctive Normal Form(cnf)mentioning

confidence: 99%

“…In figure 1, we present an algorithm RmRedundancies, which is a reproduction of Recycle-Pivots from [3]. RmRedundancies takes a resolution Fig.…”

Section: Conjunctive Normal Form(cnf)mentioning

confidence: 99%

“…In this case, v is treated as a flagged node(line [13][14]. Please look in [3] for more detailed description of RestoreResTree. Example 1.…”

Section: Conjunctive Normal Form(cnf)mentioning

confidence: 99%