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Disjunctive Interpolants for Horn-Clause Verification [chapter]

Philipp Rümmer, Hossein Hojjat, Viktor Kuncak
2013 Lecture Notes in Computer Science  
Interpolation methods remains one of the most promising techniques for such verification, and are closely related to solving Horn clause constraints.  ...  We have implemented Horn clause verification algorithms that use disjunctive interpolants and evaluate them on benchmarks expressed as Horn clauses over the theory of integer linear arithmetic.  ...  The experiments show comparable verification times and performance for tree interpolation and disjunctive interpolation runs.  ... 
doi:10.1007/978-3-642-39799-8_24 fatcat:eniwpo3b4rbzlgdyneyxkwsjpq

Disjunctive Interpolants for Horn-Clause Verification (Extended Technical Report) [article]

Philipp Rümmer , Viktor Kuncak
2013 arXiv   pre-print
Interpolation methods remain one of the most promising techniques for such verification, and are closely related to solving Horn clause constraints.  ...  We have implemented Horn clause verification algorithms that use disjunctive interpolants and evaluate them on benchmarks expressed as Horn clauses over the theory of integer linear arithmetic.  ...  The experiments show comparable verification times and performance for the Tree Interpolation and Disjunctive Interpolation runs.  ... 
arXiv:1301.4973v1 fatcat:r3z4mxo26zcd5doo32utxqrcry

On recursion-free Horn clauses and Craig interpolation

Philipp Rümmer, Hossein Hojjat, Viktor Kuncak
2014 Formal methods in system design  
Finally, we give an extensive empirical evaluation using a solver for (recursive) Horn problems, in particular comparing the performance of tree interpolation and disjunctive interpolation for constraints  ...  Interpolation methods remain among the most promising techniques for such verification.  ...  Acknowledgements We would like to thank Shaz Qadeer for discussions about the complexity of checking bounded recursive programs.  ... 
doi:10.1007/s10703-014-0219-7 fatcat:jjg3o76slre2blzihe2heomlwa

Classifying and Solving Horn Clauses for Verification [chapter]

Philipp Rümmer, Hossein Hojjat, Viktor Kuncak
2014 Lecture Notes in Computer Science  
Horn constraints are related to Craig interpolation, which is one of the main techniques used to construct and refine abstractions in verification, and to synthesise inductive loop invariants.  ...  For a logic that has the binary interpolation property, all of these problems are solvable, but have different complexity.  ...  The authors of [16] propose Horn clauses for verification of multi-threaded programs.  ... 
doi:10.1007/978-3-642-54108-7_1 fatcat:4pj36cazfjhzjnphhw3ltrlb5y

The Relationship between Craig Interpolation and Recursion-Free Horn Clauses [article]

Philipp Rümmer , Viktor Kuncak
2013 arXiv   pre-print
Horn constraints are related to Craig interpolation, which is one of the main techniques used to construct and refine abstractions in verification, and to synthesise inductive loop invariants.  ...  We also discuss techniques for solving systems of recursion-free Horn constraints.  ...  Related Work The use of Horn clauses as intermediate representation for verification was proposed in [26] . The authors is [15] use Horn clauses for verification of multi-threaded programs.  ... 
arXiv:1302.4187v1 fatcat:5uzolpkwkja2fkg2l2a526wxkq

The ELDARICA Horn Solver

Hossein Hojjat, Philipp Rummer
2018 2018 Formal Methods in Computer Aided Design (FMCAD)  
Over the last years we have been developing and maintaining ELDARICA as a state-of-the-art solver for Horn clauses over integer arithmetic.  ...  In the version 2, we have extended the solver to support also algebraic data types and bit-vectors, theories that are commonly applied in verification, but currently unsupported by most Horn solvers.  ...  ELDARICA accepts input in a range of formats: the main input format for Horn clauses is (standard-compliant) SMT-LIB v2 [6] , writing each clause as an explicitly quantified disjunction or implication  ... 
doi:10.23919/fmcad.2018.8603013 dblp:conf/fmcad/HojjatR18 fatcat:zl3zruilu5gglkr2pa5s5srnu4

Reformulating Queries: Theory and Practice

Michael Benedikt, Egor V. Kostylev, Fabio Mogavero, Efthymia Tsamoura
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
We present a classification of the complexity of the problem, then provide algorithms for solving the problems in practice and evaluate their performance.  ...  between interpolation for reformulation and verification.  ...  In the propositional setting, (full) TGDs are just Horn formulas; hence, we also refer to full disjunctive TGDs as disjunctive Horn formulas.  ... 
doi:10.24963/ijcai.2017/116 dblp:conf/ijcai/BenediktKMT17 fatcat:k7jrrwnglvfrfb2hli673ubqxm

Verification of Programs by Combining Iterated Specialization with Interpolation

Emanuele De Angelis, Fabio Fioravanti, Jorge A. Navas, Maurizio Proietti
2014 Electronic Proceedings in Theoretical Computer Science  
We present a verification technique for program safety that combines Iterated Specialization and Interpolating Horn Clause Solving.  ...  Then the output set of specialized verification conditions is analyzed by an Interpolating Horn Clause solver, hence adding the effect of interpolation to the effect of widening.  ...  Acknowledgments We would like to thank the anonymous referees for their helpful and constructive comments.  ... 
doi:10.4204/eptcs.169.3 fatcat:quhoibxm6rdxflppfc4jpfkpua

Solving Existentially Quantified Horn Clauses [chapter]

Tewodros A. Beyene, Corneliu Popeea, Andrey Rybalchenko
2013 Lecture Notes in Computer Science  
For example, a deductive approach to CTL verification reduces to solving such clauses.  ...  for equations in form of universally quantified Horn clauses extended with well-foundedness conditions.  ...  Acknowledgements We thank Byron Cook and Eric Koskinen for valuable discussion and for generously making their benchmarks available.  ... 
doi:10.1007/978-3-642-39799-8_61 fatcat:yqg7uaglwvd4hg6rehedl53nyq

Convex polyhedral abstractions, specialisation and property-based predicate splitting in Horn clause verification

Bishoksan Kafle, John P. Gallagher
2014 Electronic Proceedings in Theoretical Computer Science  
The purpose of the work is to investigate how analysis and transformation tools developed for constraint logic programs (CLP) can be applied to the Horn clause verification problem.  ...  We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using  ...  Conclusion and Future works We described an iterative procedure for Horn clause verification which interleaves abstract interpretation with specialisation.  ... 
doi:10.4204/eptcs.169.7 fatcat:bxshq32yjndlfetstc2ykwuckm

Lazy Annotation Revisited [chapter]

Kenneth L. McMillan
2014 Lecture Notes in Computer Science  
Lazy Annotation is a method of software model checking that performs a backtracking search for a symbolic counterexample.  ...  In this sense, the method is closely analogous to conflict-driven clause learning in SAT solvers. In this paper, we develop several improvements to the basic Lazy Annotation approach.  ...  The author would like to thank Akash Lal for assistance in using SDV and corral.  ... 
doi:10.1007/978-3-319-08867-9_16 fatcat:ma7r5ihrjzcdhpbgfwnueyz33u

Reduction for compositional verification of multi-threaded programs

Corneliu Popeea, Andrey Rybalchenko, Andreas Wilhelm
2014 2014 Formal Methods in Computer-Aided Design (FMCAD)  
The verification conditions of our method are Horn clauses, thus facilitating automation by using off-the-shelf Horn clause solvers.  ...  In this paper we explore the applicability of the theory of reduction for pruning of equivalent interleavings for the automated verification of multi-threaded programs with infinite-state spaces.  ...  ACKNOWLEDGMENTS We thank Klaus von Gleissenthall for comments and suggestions. This research was supported in part by the ERC project 308125.  ... 
doi:10.1109/fmcad.2014.6987612 dblp:conf/fmcad/PopeeaRW14 fatcat:at23zescevh7xfkhy4q22zimo4

Uniform Interpolants in EUF: Algorithms using DAG-representations [article]

Silvio Ghilardi and Alessandro Gianola and Deepak Kapur
2022 arXiv   pre-print
interpolant as a conjunction of Horn clauses.  ...  The first algorithm is non-deterministic and generates a uniform interpolant expressed as a disjunction of conjunctions of literals, whereas the second algorithm gives a compact representation of a uniform  ...  Horn clauses.  ... 
arXiv:2002.09784v5 fatcat:yh7emh2n6jfvfn3oycsqqfkxbm

Symbolic Polytopes for Quantitative Interpolation and Verification [chapter]

Klaus von Gleissenthall, Boris Köpf, Andrey Rybalchenko
2015 Lecture Notes in Computer Science  
We cast our algorithm in terms of a cardinality-constrained interpolation procedure, which we put to work in a solver for recursive Horn clauses with cardinality constraints based on abstraction refinement  ...  Existing approaches for dealing with such verification conditions operate by checking cardinality bounds for given formulas.  ...  We choose Horn clauses as a basis for representing our verification conditions as they provide a uniform way to encode a variety of verification tasks [5, 6, 8, 17] .  ... 
doi:10.1007/978-3-319-21690-4_11 fatcat:rxmyywpcqjgh7liwjih424onwa

Synthesizing software verifiers from proof rules

Sergey Grebenshchikov, Nuno P. Lopes, Corneliu Popeea, Andrey Rybalchenko
2012 SIGPLAN notices  
In this paper, we present a method for the automatic synthesis of software verification tools.  ...  Our experimental comparison of the resulting verifiers with existing state-of-the-art verification tools confirms the practicality of the approach.  ...  Acknowledgments We thank Jasmin Blanchette for comments and suggestions.  ... 
doi:10.1145/2345156.2254112 fatcat:ro45kc2kb5gzbfh4z62vptiitm
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