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Efficient generation of small interpolants in CNF
2015
Formal methods in system design
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The main novelty of our work is that we generate small interpolants in Conjunctive Normal Form (CNF) using a twofold procedure: First we propose an algorithm that exploits resolution refutation properties ...
In this work we present a novel technique for interpolant generation in the context of model checking. ...
The main contribution of this work is the ability to produce small interpolants in Conjunctive Normal Form (CNF) efficiently. ...
doi:10.1007/s10703-015-0224-5
fatcat:45ojahzc6be4tl557wpdz5p7k4
Efficient Generation of Small Interpolants in CNF
[chapter]
2013
Lecture Notes in Computer Science
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The main novelty of our work is that we generate small interpolants in Conjunctive Normal Form (CNF) using a twofold procedure: First we propose an algorithm that exploits resolution refutation properties ...
In this work we present a novel technique for interpolant generation in the context of model checking. ...
The main contribution of this work is the ability to produce small interpolants in Conjunctive Normal Form (CNF) efficiently. ...
doi:10.1007/978-3-642-39799-8_23
fatcat:ki7trsnbubhzvpexjbdjw2euti
Lifting Propositional Interpolants to the Word-Level
2007
Formal Methods in Computer Aided Design (FMCAD'07)
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Craig interpolants are often used to approximate inductive invariants of transition systems. ...
Arithmetic relationships between numeric variables require word-level interpolants, which are derived from word-level proofs of unsatisfiability. ...
All of these verification techniques require an efficient decision procedure that is able to generate interpolants for unsatisfiable formulas. ...
doi:10.1109/famcad.2007.13
dblp:conf/fmcad/KroeningW07
fatcat:7eyzhw3hmbc7ndieu7vwnp2m5e
Lifting Propositional Interpolants to the Word-Level
2007
Formal Methods in Computer Aided Design (FMCAD'07)
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Craig interpolants are often used to approximate inductive invariants of transition systems. ...
Arithmetic relationships between numeric variables require word-level interpolants, which are derived from word-level proofs of unsatisfiability. ...
All of these verification techniques require an efficient decision procedure that is able to generate interpolants for unsatisfiable formulas. ...
doi:10.1109/fmcad.2007.4401986
fatcat:bla6hsxmc5f3jg3fho2nszvsbq
Learning the Boundary of Inductive Invariants
[article]
2020
arXiv
pre-print
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We further harness Bshouty's seminal result in concept learning to efficiently infer invariants of a larger syntactic class of invariants beyond monotone DNF. ...
The condition requires the invariant's boundary---the states whose Hamming distance from the invariant is one---to be backwards reachable from the bad states in a small number of steps. ...
Efficient Inference of Short Monotone Invariants. The fence condition guarantees that the generated interpolants underapproximate an invariant . ...
arXiv:2008.09909v2
fatcat:ccdrf54d4jf7lmjpc7bz2q27su
SAT-Based Methods for Circuit Synthesis
[article]
2014
arXiv
pre-print
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This is an extended version of [2], with an additional appendix. ...
This includes methods based on QBF-certification, interpolation, and computational learning. ...
Here, we discuss an efficient implementation of the CNF-learning algorithm using a QBF-solver. Since QBF-solvers operate on CNFs, this algorithm is particularly suitable. ...
arXiv:1408.2333v2
fatcat:xpqs7nbk6zayfp4f7enxl5jj4q
Learning the boundary of inductive invariants
2021
Proceedings of the ACM on Programming Languages (PACMPL)
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We further harness Bshouty's seminal result in concept learning to efficiently infer invariants of a larger syntactic class of invariants beyond monotone DNF. ...
The condition requires the invariant's boundaryÐthe states whose Hamming distance from the invariant is oneÐto be backwards reachable from the bad states in a small number of steps. ...
Efficient Inference of Short Monotone Invariants. The fence condition guarantees that the generated interpolants underapproximate an invariant I . ...
doi:10.1145/3434296
fatcat:jwuskhwavrffbj7liolbg5mcoy
Computing Interpolants without Proofs
[chapter]
2013
Lecture Notes in Computer Science
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We achieve this by combining model enumeration with the ability to easily generate interpolants in the special case that one of the formulas is a cube. ...
We describe an incremental algorithm for computing interpolants for a pair ϕA, ϕB of formulas in propositional logic. ...
This way the final interpolant is in CNF, but in most applications the precise form of the interpolant is not important (in case it is, see [BKK11] for an efficient method to convert between the two ...
doi:10.1007/978-3-642-39611-3_12
fatcat:3c45mwkt6rexrglxd2lewx2sv4
Implicative Simultaneous Satisfiability and Applications
[chapter]
2012
Lecture Notes in Computer Science
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This paper proposes an efficient algorithm for the systematic learning of implications. This is done as part of a new search and restart strategy in the SAT solver. ...
In addition, we experimentally demonstrate the superiority of an application of our new algorithm to BMC. ...
Baruch Sterin contributed to the ideas and the implementation of some of the reported algorithms. ...
doi:10.1007/978-3-642-34188-5_9
fatcat:gnpshg27pfex5ci4hblowep5xi
Complexity and Information in Invariant Inference
[article]
2020
arXiv
pre-print
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of Hoare queries can lead to an efficient invariant inference procedure in this class. ...
We show that in general an algorithm in the Hoare-query model requires an exponential number of queries. ...
When efficient interpolation is supported in the logic and solver, the SAT solver can produce an interpolant C: a formula representing a set of states that (i) overapproximates the set of states reachable ...
arXiv:1910.12256v3
fatcat:wgemiyalr5fdrh7p4aprukynlq
Reduction of interpolants for logic synthesis
2010
2010 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)
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In most applications to date, interpolants have been generated directly from the proofs of unsatisfiability that are provided by SAT solvers. ...
In this work, we propose efficient methods based on incremental SAT solving for modifying resolution proofs in order to obtain more compact interpolants. ...
Even with small problem sizes, poorly structured resolution proofs can result in overly complex interpolants. ...
doi:10.1109/iccad.2010.5654209
dblp:conf/iccad/BackesR10
fatcat:qjseqqakzrhcdop2uhb76jeuha
On the Automatizability of Resolution and Related Propositional Proof Systems
[chapter]
2002
Lecture Notes in Computer Science
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Our techniques also give us a way to obtain a large class of examples that have small Resolution refutations but require relatively large width. ...
This gives a better lower bound for the monotone interpolation of Res(2) and a separation from Resolution as a byproduct. ...
We are grateful to Pavel Pudlák for stimulating discussions on the idea of Theorem 11. ...
doi:10.1007/3-540-45793-3_38
fatcat:vxg4gu2sw5aglizzinrjp6mj74
On the automatizability of resolution and related propositional proof systems
2004
Information and Computation
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Our techniques also give us a way to obtain a large class of examples that have small Resolution refutations but require relatively large width. ...
This gives a better lower bound for the monotone interpolation of Res(2) and a separation from Resolution as a byproduct. ...
We are grateful to Pavel Pudlák for stimulating discussions on the idea of Theorem 11. ...
doi:10.1016/j.ic.2003.10.004
fatcat:sbfnlio72zdonmh2leevz7gveu
Constrained interpolation for guided logic synthesis
2014
2014 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)
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The proposed methods can be efficiently employed for rewriting circuits in some synthesis-based algorithms. ...
In each iteration, we force a base function by generating a new dependency function used as a target function for the next iteration. ...
One such application is the generation of Craig interpolants that was integrated in variety of logic synthesis algorithms [1] [2] [3] [4] . ...
doi:10.1109/iccad.2014.7001392
dblp:conf/iccad/PetkovskaNMI14
fatcat:oc6aquelurdqndvbwvr2cbvjhi
Interpolation-Based Semantic Gate Extraction and Its Applications to QBF Preprocessing
[chapter]
2020
Lecture Notes in Computer Science
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Experiments with a prototype implementation demonstrate that functions can be efficiently extracted from formulas in standard benchmark sets, and that many of these definitions remain undetected by syntactic ...
Compared to syntactic gate detection, we see a significant increase in the number of solved QBF instances, as well as a modest increase for DQBF instances. ...
As a back end SAT solver we use ItpMiniSat, a modified version of MiniSat [11] bundled with the ExtAvy model checker that efficiently generates interpolants in memory and supports both assumptions and ...
doi:10.1007/978-3-030-53288-8_24
fatcat:6isbsnhnnrhqxpwgzrq5zdmod4
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