An Efficient and Flexible Approach to Resolution Proof Reduction

Rollini, Simone Fulvio; Bruttomesso, Roberto; Sharygina, Natasha

doi:10.1007/978-3-642-19583-9_17

Cited by 16 publications

(19 citation statements)

References 12 publications

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“…These algorithms can be further harnessed by placing them in the iterative algorithm of [18]. We leave that for future work.…”

Section: Resultsmentioning

confidence: 99%

“…We leave that for future work. We specially note that the addi- tional rules (other than A1 and A2) for restructuring a resolution proof presented in [18] become redundant if applied in combination with our algorithms.…”

Section: Resultsmentioning

confidence: 99%

“…RestoreResTree traverses the proof DAG in the order of parents first. RestoreResTree takes a node v as input and returns a node v that has a valid sub-proof (line [15][16] and replaces v in the resolution proof (line [17][18][19][20]. If v is a flagged node then v is the node that also replaces the remaining parent of v (line 4-6).…”

Section: Conjunctive Normal Form(cnf)mentioning

confidence: 99%

“…In [1], a method is presented that minimizes a resolution proof by heuristically reordering resolution steps using 'linking graph' between literals. In [18], the resolution proof rewriting rules [7] are iteratively applied to reorder resolution steps locally ( [1] does it in a global context) and it is expected to expose some redundancies, which are removed by applying Recycle-Pivots after each iteration. This paper only aims to find algorithms that significantly minimize the proofs within low cost.…”

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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“…These algorithms can be further harnessed by placing them in the iterative algorithm of [18]. We leave that for future work.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Conjunctive Normal Form(cnf)mentioning

confidence: 99%

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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“…Additionally, proof manipulation procedures, as in [15], can be applied to alter the size and the strength of interpolants in the various model checking applications.…”

Section: Contributionmentioning

confidence: 99%

Leveraging Interpolant Strength in Model Checking

Rollini¹,

Šerý

Sharygina³

2012

Computer Aided Verification

Self Cite

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Craig interpolation is a well known method of abstraction successfully used in both hardware and software model checking. The logical strength of interpolants can affect the quality of approximations and consequently the performance of the model checkers. Recently, it was observed that for the same resolution proof a complete lattice of interpolants ordered by strength can be derived. Most state-of-the-art model checking techniques based on interpolation subject the interpolants to constraints that ensure efficient verification as, for example, in transition relation approximation for bounded model checking, counterexample-guided abstraction refinement and function summarization for software update checking. However, in general, these verification-specific constraints are not satisfied by all possible interpolants. The paper analyzes the restrictions within the lattice of interpolants under which the required constraints are satisfied. This enables investigation of the effect of the strength of interpolants on the particular techniques, while preserving their soundness. As an additional benefit, combination of this result with proof manipulation procedures allows the use of optimized solvers to generate interpolants of different strengths for various model checking techniques.

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Incremental Search for Conflict and Unit Instances of Quantified Formulas with E-Matching

Hoenicke

Schindler

2021

Lecture Notes in Computer Science

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We present a generic tree-interpolation algorithm in the SMT context with quantifiers. The algorithm takes a proof of unsatisfiability using resolution and quantifier instantiation and computes interpolants (which may contain quantifiers). Arbitrary SMT theories are supported, as long as each theory itself supports tree interpolation for its lemmas. In particular, we show this for the theory combination of equality with uninterpreted functions and linear arithmetic. The interpolants can be tweaked by virtually assigning each literal in the proof to interpolation partitions (colouring the literals) in arbitrary ways. The algorithm is implemented in SMTInterpol.

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An Efficient and Flexible Approach to Resolution Proof Reduction

Cited by 16 publications

References 12 publications

Improved Single Pass Algorithms for Resolution Proof Reduction

Improved Single Pass Algorithms for Resolution Proof Reduction

Leveraging Interpolant Strength in Model Checking

Incremental Search for Conflict and Unit Instances of Quantified Formulas with E-Matching

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