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Efficient generation of small interpolants in CNF

Yakir Vizel, Alexander Nadel, Vadim Ryvchin
2015 Formal methods in system design  
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]

Yakir Vizel, Vadim Ryvchin, Alexander Nadel
2013 Lecture Notes in Computer Science  
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

Daniel Kroening, Georg Weissenbacher
2007 Formal Methods in Computer Aided Design (FMCAD'07)  
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

Daniel Kroening, Georg Weissenbacher
2007 Formal Methods in Computer Aided Design (FMCAD'07)  
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]

Yotam M. Y. Feldman and Mooly Sagiv and Sharon Shoham and James R. Wilcox
2020 arXiv   pre-print
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]

Roderick Bloem and Uwe Egly and Patrick Klampfl and Robert Koenighofer and Florian Lonsing
2014 arXiv   pre-print
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

Yotam M. Y. Feldman, Mooly Sagiv, Sharon Shoham, James R. Wilcox
2021 Proceedings of the ACM on Programming Languages (PACMPL)  
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]

Hana Chockler, Alexander Ivrii, Arie Matsliah
2013 Lecture Notes in Computer Science  
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]

Zurab Khasidashvili, Alexander Nadel
2012 Lecture Notes in Computer Science  
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]

Yotam M. Y. Feldman, Neil Immerman, Mooly Sagiv, Sharon Shoham
2020 arXiv   pre-print
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

John D. Backes, Marc D. Riedel
2010 2010 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)  
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]

Albert Atserias, María Luisa Bonet
2002 Lecture Notes in Computer Science  
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

Albert Atserias, Marı́a Luisa Bonet
2004 Information and Computation  
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

Ana Petkovska, David Novo, Alan Mishchenko, Paolo Ienne
2014 2014 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)  
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]

Friedrich Slivovsky
2020 Lecture Notes in Computer Science  
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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