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Superposition Reasoning about Quantified Bitvector Formulas

David Damestani, Laura Kovacs, Martin Suda
2019 2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)  
We describe recent extensions to the first-order theorem prover Vampire for proving theorems in the theory of fixed-sized bitvectors, possibly with quantifiers.  ...  Details are given on extending both the parser of Vampire as well as the theory reasoning framework of Vampire.  ...  That is, we did not rely on Z3 to reason about ground formulas generated by AVATAR; this way, theory reasoning about QBV formulas in Vampire's AVATAR framework was performed by relying on bitvector axioms  ... 
doi:10.1109/synasc49474.2019.00022 dblp:conf/synasc/DamestaniK019 fatcat:jjxlwf4ehjgdngq7azln5djxk4

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  
Reasoning with equality and more generally theory reasoning are essential to reasoning about programs.  ...  Induction is fundamental to reason about programs.  ... 
doi:10.1145/1836089.1836090 dblp:conf/ppdp/Bonacina10 fatcat:mh3666vskfcxvgnisxp7hnwvi4

Model Generation for Quantified Formulas: A Taint-Based Approach [chapter]

Benjamin Farinier, Sébastien Bardin, Richard Bonichon, Marie-Laure Potet
2018 Lecture Notes in Computer Science  
Software verification methods have come to rely increasingly on reasoning over logical formulas modulo theory.  ...  and model generation of quantified formulas, yielding a more symmetric handling of quantified formulas in SMT.  ...  In pure first-order logic (without theories), quantifiers are mainly handled through resolution and superposition [1, 23] as done in Vampire [29, 21] and E [30] .  ... 
doi:10.1007/978-3-319-96142-2_19 fatcat:7hv63nfllfhr7gikytziwtn5ae

Towards Bit-Width-Independent Proofs in SMT Solvers [article]

Aina Niemetz, Mathias Preiner, Andrew Reynolds, Yoni Zohar, Clark Barrett, Cesare Tinelli
2019 arXiv   pre-print
These approaches, however, cannot be used directly to reason about bit-vectors of symbolic bit-width.  ...  While this logic is undecidable, this approach can still solve many formulas by capitalizing on advancements in SMT solving for non-linear arithmetic and universally quantified formulas.  ...  Reasoning about fixed-size bitvectors suffices for many applications.  ... 
arXiv:1905.10434v3 fatcat:aogwd5enzvcnlpfcilg6c6j6ra

Instantiation and Pretending to be an SMT Solver with Vampire

Giles Reger, Martin Suda, Andrei Voronkov
2017 International Workshop on Satisfiability Modulo Theories  
Secondly, it focuses on the problem of instantiation of quantified formulas and asks whether VAMPIRE needs it (it does) and whether it can directly borrow techniques from SMT solving (maybe).  ...  We discuss how Vampire reasons with problems containing both quantification and theories, the limitations this places on what it can do, and the advantages this provides over the standard SMT approach.  ...  Perhaps the most prominent of these is Hierarchic Superposition (HS) [2] , a generalisation of the superposition calculus for black-box style theory reasoning.  ... 
dblp:conf/smt/RegerSV17 fatcat:nvbolygdh5gcrahjgmpccuwwaa

Table of Contents

2019 2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)  
Reasoning about Quantified Bitvector Formulas 95 David Damestani (TU Wien, Austria), Laura Kovács (TU Wien, Austria), and Martin Suda (Czech Technical University, Czech Republic) Bicyclic Connected Graphs  ...  Károly University, Hungary), Krisztián Gajdár (Eszterházy Károly University, Hungary), and Laura Kovács (TU Wien, Austria, & Chalmers University of Technology, Sweden) Papers on Tools/Experimental Results Superposition  ... 
doi:10.1109/synasc49474.2019.00004 fatcat:wfig3ykubbclzbm6uzwa2n4epu

A Deductive Verification Framework for Circuit-building Quantum Programs [article]

Christophe Chareton, Sébastien Bardin, François Bobot, Valentin Perrelle, Benoit Valiron
2020 arXiv   pre-print
Early attempts either suffer from the lack of automation or parametrized reasoning, or target high-level abstract algorithm description languages far from the current de facto consensus of circuit-building  ...  We provide for it a set of mathematical libraries, enabling reasoning about Qbricks-Spec formulas (see Section E.2 below for further details about these).  ...  Formula ϕ,ψ : The type system of Qbricks-Spec is extended with opaque types, equipped with constant functions and relations to reason upon them.  ... 
arXiv:2003.05841v2 fatcat:4dl2f67yq5ee7og6hbeggrrzo4

An Automated Deductive Verification Framework for Circuit-building Quantum Programs

Christophe Chareton, Sébastien Bardin, François Bobot, Valentin Perrelle, Benoît Valiron
2021 European Symposium on Programming  
-A flexible symbolic representation for reasoning about quantum states, building upon the recent path-sum symbolic representation [1, 2] .  ...  Especially, first-order logic together with PPS provide a unified and powerful way to reason about many essential quantum concepts (Section 5.2) and fit well with the standard way of describing quantum  ... 
doi:10.1007/978-3-030-72019-3_6 dblp:conf/esop/CharetonBBPV21 fatcat:tzicrcp4hfgq5io2neavkv76ue

Theory decision by decomposition

Maria Paola Bonacina, Mnacho Echenim
2010 Journal of symbolic computation  
The topic of this article is decision procedures for satisfiability modulo theories (SMT) of arbitrary quantifier-free formulae.  ...  We propose an approach that decomposes the formula in such a way that its definitional part, including the theory, can be compiled by a rewrite-based first-order theorem prover, and the residual problem  ...  born to reason about quantifiers and non-ground equalities.  ... 
doi:10.1016/j.jsc.2008.10.008 fatcat:wkrfe3ritjhcvdbjfb2ese2tfy

Interpolation Systems for Ground Proofs in Automated Deduction: a Survey

Maria Paola Bonacina, Moa Johansson
2015 Journal of automated reasoning  
We analyze interpolation in the presence of equality, and we demonstrate the color-based approach by giving a complete interpolation system for ground proofs by superposition.  ...  This does not imply that interpolants are quantifier-free. A theory is quantifier-free interpolating if quantifier-free input formulae are guaranteed to have quantifier-free interpolants.  ...  Since most reasoners transform closed formulae into sets, or conjunctions, of clauses, from now on we assume that A and B are disjoint sets of clauses.  ... 
doi:10.1007/s10817-015-9325-5 fatcat:tdwepokjfvcjxfx2ieykouexee

Analyzing Network Management Effects with SPIN and cTLA [chapter]

Gerrit Rothmaier, Andre Pohl, Heiko Krumm
2004 Security and Protection in Information Processing Systems  
Due to cTLA's connection to the temporal logic of actions TLA, formal analysis can resort to symbolic reasoning. Supplementarily, automated analysis can be applied.  ...  The semantics of cTLA specifications is directly defined by TLA formulas [Lam93] and the TLA methods for symbolic logical reasoning can be applied.  ...  In particular, superposition supports the so-called structured verification.  ... 
doi:10.1007/1-4020-8143-x_5 dblp:conf/sec/RothmaierPK04 fatcat:lwymxpk3vzgj7bvrdovgaxfwka

Inductive verification of data model invariants in web applications using first-order logic

Ivan Bocić, Tevfik Bultan, Nicolás Rosner
2018 Automated Software Engineering : An International Journal  
Manysorted logic allows us to specify type information explicitly, thus lightening the burden of reasoning about type information during theorem proving.  ...  We noticed that the theorem prover did an excessive number of deductions solely to reason about the types of quantified variables and objects.  ...  We noticed that the theorem prover performed an excessive number of deductions solely to reason about the types of quantified variables and objects.  ... 
doi:10.1007/s10515-018-0249-2 fatcat:2sfo6vslpjgglgttjwyygnyoha

On a Rewriting Approach to Satisfiability Procedures: Extension, Combination of Theories and an Experimental Appraisal [chapter]

Alessandro Armando, Maria Paola Bonacina, Silvio Ranise, Stephan Schulz
2005 Lecture Notes in Computer Science  
Contrary to the folklore that a general-purpose prover cannot compete with specialized reasoners, the experiments are overall favorable to the theorem prover, showing that the rewriting approach is both  ...  Any combination of the theories above, and with the quantifier-free theory of equality and arrays (with or without extensionality), is covered.  ...  (arbitrary quantifier-free formulae), whether by integration with a SAT solver (as explored first in [10] ), or by using the prover's ability to handle first-order clauses.  ... 
doi:10.1007/11559306_4 fatcat:mar73gtjkzhcne5scewq6xi2su

Efficient Interpolation for the Theory of Arrays [article]

Jochen Hoenicke, Tanja Schindler
2018 arXiv   pre-print
Existing techniques for Craig interpolation for the quantifier-free fragment of the theory of arrays are inefficient for computing sequence and tree interpolants: the solver needs to run for every partitioning  ...  ., integer or bitvector theory for reasoning about numeric variables and array theory for reasoning about pointers.  ...  Johansson [4] for superposition calculus.  ... 
arXiv:1804.07173v2 fatcat:ehtv5wckurbvjplvb7hzvko5oa

Horn Clause Solvers for Program Verification [chapter]

Nikolaj Bjørner, Arie Gurfinkel, Ken McMillan, Andrey Rybalchenko
2015 Lecture Notes in Computer Science  
Automatic program verification and symbolic model checking tools interface with theorem proving technologies that check satisfiability of formulas.  ...  Solving Horn clauses amounts to establishing Existential positive Fixed-point Logic formulas, a perspective that was promoted by Blass and Gurevich.  ...  In the world of constraint logic programming, CLP, expressing programs as Horn clauses and reasoning about Horn clauses has been pursued for several years, spearheaded by Joxan Jaffar and collaborators  ... 
doi:10.1007/978-3-319-23534-9_2 fatcat:hsmmbrr35nfsveszovx67isifq
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