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Bound Propagation for Arithmetic Reasoning in Vampire

Ioan Dragan, Konstantin Korovin, Laura Kovacs, Andrei Voronkov
2013 2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing  
To make the method efficient, we use various strategies for representing numbers, selecting variable orderings, choosing variable values and propagating bounds.  ...  This paper describes an implementation and experimental evaluation of a recently introduced bound propagation method for solving systems of linear inequalities over the reals and rationals.  ...  We describe how bound propagation is implemented and used in Vampire for solving systems of linear inequalities. Also we made an overview of options we have implemented.  ... 
doi:10.1109/synasc.2013.30 dblp:conf/synasc/DraganKKV13 fatcat:ddaewur2hrayfcytrvh4rkuxuu

First-Order Theorem Proving and Vampire [chapter]

Laura Kovács, Andrei Voronkov
2013 Lecture Notes in Computer Science  
Further, we also cover more recent topics and features of VAMPIRE designed for advanced applications, including satisfiability checking, theory reasoning, interpolation, consequence elimination, and program  ...  In this paper we give a short introduction in first-order theorem proving and the use of the theorem prover VAMPIRE.  ...  Our implementation is based on the bound propagation algorithm of [16] , BPA in the sequel.  ... 
doi:10.1007/978-3-642-39799-8_1 fatcat:bhabf63t35h3fdvmqb23d3w2jq

AN EMPIRICAL EVALUATION OF AUTOMATED THEOREM PROVERS IN SOFTWARE CERTIFICATION

EWEN DENNEY, BERND FISCHER, JOHANN SCHUMANN
2006 International journal on artificial intelligence tools  
We describe a system for the automated certification of safety properties of NASA software.  ...  safety obligations and ultimately to more than 25,000 proof tasks which have been used to determine the suitability of the high-performance provers DCTP, E-Setheo, E, Gandalf, Otter, Setheo, Spass, and Vampire  ...  Both variable initialization and usage as well as array bounds certification are logically simple and rely just on propositional and simple arithmetic reasoning, respectively, but can require a lot of  ... 
doi:10.1142/s0218213006002576 fatcat:ngisg2ralvdfvbwq2wb5wogs2u

Solving quantified verification conditions using satisfiability modulo theories

Yeting Ge, Clark Barrett, Cesare Tinelli
2009 Annals of Mathematics and Artificial Intelligence  
Inspired by Simplify and motivated by a desire to provide a competitive alternative to ATP systems, this paper describes a methodology for reasoning about quantifiers in SMT systems.  ...  One clue on how to get the best of both worlds can be found in the legacy system Simplify which combines built-in theory reasoning with quantifier instantiation heuristics.  ...  However, practical verification conditions often require reasoning with respect to well-established first order theories such as arithmetic.  ... 
doi:10.1007/s10472-009-9153-6 fatcat:ykgbztkinjemtc4rmjr2zdqwcq

Using Automated Theorem Provers to Certify Auto-generated Aerospace Software [chapter]

Ewen Denney, Bernd Fischer, Johann Schumann
2004 Lecture Notes in Computer Science  
We describe a system for the automated certification of safety properties of NASA software.  ...  For full automation, however, the obligations must be aggressively preprocessed and simplified.  ...  Both variable initialization and usage as well as array bounds certification are logically simple and rely just on propositional and simple arithmetic reasoning, respectively, but can require a lot of  ... 
doi:10.1007/978-3-540-25984-8_12 fatcat:ragxctc5fvexhhb5ovhhliu5ru

SCL with Theory Constraints [article]

Martin Bromberger and Alberto Fiori and Christoph Weidenbach
2020 arXiv   pre-print
In a nutshell, the SCL(T) calculus describes a new way to guide hierarchic resolution inferences by a partial model assumption instead of an a priori fixed order as done for instance in hierarchic superposition  ...  We lift the SCL calculus for first-order logic without equality to the SCL(T) calculus for first-order logic without equality modulo a background theory.  ...  One reason why model-based reasoning for LIA is currently inferior compared to classical branch and bound approaches used in SMT [NOT06, BSW15] is a missing non-redundancy guarantee for inferred inequations  ... 
arXiv:2003.04627v5 fatcat:6g3iyuz7prfrrb6leq75zya3lm

On theorem proving for program checking

Maria Paola Bonacina
2010 Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '10  
This article is a survey of recent results, related works and new challenges in automated theorem proving for program checking.  ...  theory reasoning in the built-in theory T .  ...  In forward propagation, a precondition is propagated forward by computing strongest postconditions. In backward propagation, a postcondition is propagated backward by computing weakest preconditions.  ... 
doi:10.1145/1836089.1836090 dblp:conf/ppdp/Bonacina10 fatcat:mh3666vskfcxvgnisxp7hnwvi4

Proofs by Deduction [chapter]

2017 Logic and Language Models for Computer Science  
Many use models as certificates for satisfiability to extract feasible program executions; others use proof objects as certificates for unsatisfiability in the context of highintegrity systems development  ...  Models and proofs even play an integral role within deductive tools as major methods for efficient proof search rely on refining a simultaneous search for a model or a proof.  ...  An upcoming next generation of reasoning procedures employ (partial) models/proofs for proof search. They range from SAT to first-order to arithmetic reasoning and combinations thereof.  ... 
doi:10.1142/9789813229211_0003 fatcat:cqpgqtobz5gx3db5bq54gxrd4m

The TPTP Typed First-Order Form with Arithmetic [chapter]

Geoff Sutcliffe, Stephan Schulz, Koen Claessen, Peter Baumgartner
2012 Lecture Notes in Computer Science  
Recently, the TPTP World has been extended to include a typed first-order logic, which in turn has enabled the integration of arithmetic. This paper describes these developments. 8  ...  Acknowledgments: Alexandre Riazanov did the analysis of TPTP CNF problems for implicit type information. Michael Schick and Peter Watson produced many of the TFF and arithmetic problems.  ...  Mark Stickel provided a lot of useful feedback on the arithmetic syntax, and the selection of defined arithmetic functions and predicates. Uwe Waldmann provided valuable feedback on precise  ... 
doi:10.1007/978-3-642-28717-6_32 fatcat:ktx5dc5odbd43pgp7jgwt5666m

A Why3 proof of GMP algorithms

Raphael Rieu-Helft
2019 Journal of Formalized Reasoning  
Large-integer arithmetic algorithms are used in contexts where both their performance and their correctness are critical, such as cryptographic software.  ...  We have formally verified a comprehensive arbitrary-precision integer arithmetic library that implements many state-of-the-art algorithms from the GMP library.  ...  Acknowledgements We gratefully thank Guillaume Melquiond and the anonymous reviewers for their extensive feedback on earlier versions of this article.  ... 
doi:10.6092/issn.1972-5787/9730 dblp:journals/jfrea/Rieu-Helft19 fatcat:j3m5dlyimfbgvoscbbj3hejjke

Zap: Automated Theorem Proving for Software Analysis [chapter]

Thomas Ball, Shuvendu K. Lahiri, Madanlal Musuvathi
2005 Lecture Notes in Computer Science  
We describe our desiderata for such an interface to an ATP, the logics (theories) that an ATP for program analysis should support, and present how we have incorporated many of these ideas in Zap, an ATP  ...  An ATP that allows reasoning about these bounded integers, either by treating them as bit-vectors or by performing modular arithmetic, can enable analysis tools that detect overflow errors.  ...  However, these provers do not effectively support arithmetic reasoning, an important requirement for Zap.  ... 
doi:10.1007/11591191_2 fatcat:uczhvijn6vew3bmwpaqhaxrkzy

Symbolic Computation and Satisfiability Checking : Report of Dagstuhl Seminar 15471

Erika Ábrahám, Pascal Fontaine, Thomas Sturm, Dongming Wang, Dongming Wang, Erika Ábrahám, Pascal Fontaine, Thomas Sturm
2016 Dagstuhl Reports  
The seminar focused on satisfiability checking for combinations of first-order logic and subclasses thereof with arithmetic theories in a very liberal sense, also covering quantifiers and parameters.  ...  We are confident that the seminar will initiate cross-fertilization of both fields and bring improvements for both satisfiability checking and symbolic computation, and for their applications.  ...  The SMT-LIB language version 2.5 is not extendable but version 3.0 should be more flexible, and could accommodate some of the needs for a language suitable in a larger context.  ... 
doi:10.18154/rwth-2017-01217 fatcat:5aaxyhouqrdcfhhvek76vkdwjm

From Search to Computation: Redundancy Criteria and Simplification at Work [chapter]

Thomas Hillenbrand, Ruzica Piskac, Uwe Waldmann, Christoph Weidenbach
2013 Lecture Notes in Computer Science  
complexities for the completion of conditional rewrite systems, rewriting with equivalences for theorem proving in set theory, soft typing for the exploration of sort information in the context of equations  ...  We present Harald Ganzinger's work in the light of the simplification and redundancy techniques that have been developed for concrete problem areas.  ...  Each of the propositions that Nipkow showed with Isabelle/HOL encapsulates a single induction or is already deductive, at least modulo the arithmetic reasoning in the background; and in the former case  ... 
doi:10.1007/978-3-642-37651-1_7 fatcat:fr4uqtwvubbtvgjepamaamojeu

How to Get an Efficient yet Verified Arbitrary-Precision Integer Library [chapter]

Raphaël Rieu-Helft, Claude Marché, Guillaume Melquiond
2017 Lecture Notes in Computer Science  
The GNU Multi-Precision library is a widely used, safetycritical, library for arbitrary-precision arithmetic.  ...  Its source code is written in C and assembly, and includes intricate state-of-the-art algorithms for the sake of high performance.  ...  We gratefully thank Pascal Cuoq, Jean-Christophe Filliâtre and Mário Pereira for their comments on preliminary versions of this article.  ... 
doi:10.1007/978-3-319-72308-2_6 fatcat:dumc7tclvjahpl5tokwwsv6tze

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality [chapter]

Jasmin Christian Blanchette, Mathias Fleury, Christoph Weidenbach
2016 Lecture Notes in Computer Science  
We developed a formal framework for CDCL (conflict-driven clause learning) in Isabelle/HOL.  ...  Through a chain of refinements, an abstract CDCL calculus is connected to a SAT solver expressed in a functional programming language, with total correctness guarantees.  ...  Andrei Popescu gave us his permission to reuse, in a slightly adapted form, the succinct description of locales he cowrote on a different occasion [7] .  ... 
doi:10.1007/978-3-319-40229-1_4 fatcat:5xhbugmxdbazpnnszokuyovxou
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