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Model Finding for Recursive Functions in SMT [chapter]

Andrew Reynolds, Jasmin Christian Blanchette, Simon Cruanes, Cesare Tinelli
2016 Lecture Notes in Computer Science  
SMT solvers have recently been extended with techniques for finding models in presence of universally quantified formulas in some restricted fragments.  ...  This paper introduces a translation which reduces axioms specifying a large class of recursive functions, including well-founded (terminating) functions, to universally quantified formulas for which these  ...  We would also like to thank Damien Busato-Gaston and Emmanouil Koukoutos for providing the initial set of benchmarks used in the evaluation, and the anonymous reviewers for their suggestions and comments  ... 
doi:10.1007/978-3-319-40229-1_10 fatcat:onkr4y3uvjdozgu2abravox65a

Using SMT Solvers to Validate Models for AI Problems [article]

Andrei Arusoaie, Ionut Pistol
2019 arXiv   pre-print
A recent addition to Z3 allowed us to describe sequences of transitions as a recursive function, thus we can check if a solution can be found in the defined model.  ...  SMT solvers use efficient decision procedures which provide proofs for the logical formulas corresponding to the AI model.  ...  The very recent addition of support for recursive functions in Z3 allowed us to look for and recover solutions, a new capability for bounded model checking.  ... 
arXiv:1903.09475v1 fatcat:uxqx5kvpczdprmbojwjnidssee

A system for SMT based constraint programming in Java

Maurice Funk
2017 Jahrestagung der Gesellschaft für Informatik  
This paper presents a system for constraint programming in Java using translation of JVM bytecode into SMT.  ...  We demonstrate that the implemented approach is able to find variable assignments for non-trivial constraints such as a Sudoku puzzle.  ...  Complex control flow (or recursion) in the constraint methods results in recursive state function definitions which cannot be correctly expressed in SMT, thus the system needs to "unroll" the definitions  ... 
doi:10.18420/in2017_260 dblp:conf/gi/Funk17 fatcat:tw6fydg7tjhsdkhrhgkih7zgcy

Unifying Compilers for SNARKs, SMT, and More [article]

Alex Ozdemir, Fraser Brown, Riad S. Wahby
2020 IACR Cryptology ePrint Archive  
CirC makes it easy to compile to new EQCs: we build support for three, R1CS (commonly used for proof systems), SMT (commonly used for verification and bug-finding), and ILP (commonly used for optimization  ...  ), in ≈2000 LOC.  ...  This work was supported in part by the NSF, the ONR, the Stanford Center for Blockchain Research, and the Simons Foundation. It was also supported by DARPA under Agreement HR00112020022.  ... 
dblp:journals/iacr/OzdemirBW20 fatcat:h7whkhhtfre2tbybjfjzpefxya

A Recursive Recurrent Neural Network for Statistical Machine Translation

Shujie Liu, Nan Yang, Mu Li, Ming Zhou
2014 Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)  
In this paper, we propose a novel recursive recurrent neural network (R 2 NN) to model the end-to-end decoding process for statistical machine translation.  ...  , like recurrent neural networks, so that language model and translation model can be integrated naturally; (2) a tree structure can be built, as recursive neural networks, so as to generate the translation  ...  in Table 3 Table 3 we can find that, the recurrent input vector is essential to SMT performance.  ... 
doi:10.3115/v1/p14-1140 dblp:conf/acl/LiuYLZ14 fatcat:jo6oeaohlbhkbb7hls3wdbwhnm

Functional SMT solving with Z3 and racket

Siddharth Agarwal, Amey Karkare
2013 2013 1st FME Workshop on Formal Methods in Software Engineering (FormaliSE)  
. 2 Z3, for instance, supports plugging in external theories via the C API, but not via the textual SMT-LIB interface.  ...  This system is expected to be useful for a wide variety of applications, from simple constraint solving to writing tools for debugging, verification, and automatic test generation for functional programs  ...  ACKNOWLEDGEMENTS We thank Leonardo de Moura at Microsoft Research for his help in understanding the Z3 C API.  ... 
doi:10.1109/formalise.2013.6612272 dblp:conf/icse/AgarwalK13 fatcat:ovesyueluva5fms4mpfd2vcqbi

CPAchecker with Support for Recursive Programs and Floating-Point Arithmetic [chapter]

Matthias Dangl, Stefan Löwe, Philipp Wendler
2015 Lecture Notes in Computer Science  
The combination of several different analyses copes well with the diversity of the verification tasks in SV-COMP.  ...  These analyses use concepts such as CEGAR, lazy abstraction, interpolation, adjustableblock encoding, bounded model checking, invariant generation, and blockabstraction memoization.  ...  of C in SMT formulae.  ... 
doi:10.1007/978-3-662-46681-0_34 fatcat:nzw7uubxufbmpdbxqidlfh6ls4

Sound reasoning about integral data types with a reusable SMT solver interface

Régis Blanc, Viktor Kuncak
2015 Proceedings of the 6th ACM SIGPLAN Symposium on Scala - SCALA 2015  
Our interface is based on the emerging SMT-LIB standard for SMT solvers, and we release a Scala library offering full support for the latest version of the standard.  ...  We leverage significant progresses recently achieved in SMT solving by developing a solver-independent interface to easily configure the back-end of Leon.  ...  >= 0) This function is defined recursively.  ... 
doi:10.1145/2774975.2774980 dblp:conf/pldi/BlancK15 fatcat:xnu7jsezjnfcjfmh5m3gxl2ecm

Satisfiability Modulo Recursive Programs [chapter]

Philippe Suter, Ali Sinan Köksal, Viktor Kuncak
2011 Lecture Notes in Computer Science  
We present a semi-decision procedure for checking satisfiability of expressive correctness properties of recursive first-order functional programs.  ...  In our approach, both properties and programs are expressed in the same language, a subset of Scala. We implemented our procedure and integrated it with the Z3 SMT solver and the Scala compiler.  ...  We thank Nikolaj Bjørner and Leonardo de Moura for their help with Z3. We thank Mirco Dotta and Swen Jacobs for preliminary versions of some of the benchmarks.  ... 
doi:10.1007/978-3-642-23702-7_23 fatcat:msorndfrk5d4zj7pbcvxtssoxu

Analyzing Alloy Formulas using an SMT Solver: A Case Study [article]

Aboubakr Achraf El Ghazi, Mana Taghdiri
2015 arXiv   pre-print
Current analysis of Alloy models - as performed by the Alloy Analyzer - is based on SAT solving and thus, is done only with respect to finitized types.  ...  This paper also reports on our experimental results that compare the performance of our analysis to that of the Alloy Analyzer for various versions of the address book problem.  ...  Investigating whether Yices can analyze such models in a high-enough scope to find the counterexample, will be left for future.  ... 
arXiv:1505.00672v1 fatcat:fishw63rbfbtngwcpuodslg2xy

How to Exploit Structure while Solving Weighted Model Integration Problems

Samuel Kolb, Pedro Zuidberg Dos Martires, Luc De Raedt
2019 Conference on Uncertainty in Artificial Intelligence  
Weighted model counting (WMC) is a stateof-the-art technique for probabilistic inference in discrete domains.  ...  WMC has recently been extended towards weighted model integration (WMI) in order to handle discrete and continuous distributions alike.  ...  We thank Stefano Teso for his helpful comments.  ... 
dblp:conf/uai/KolbMR19 fatcat:ift6q5wavvbvxfkabicic53kyi

Satisfiability Modulo Bounded Checking [chapter]

Simon Cruanes
2017 Lecture Notes in Computer Science  
We describe a new approach to find models for a computational higher-order logic with datatypes. The goal is to find counterexamples for conjectures stated in proof assistants.  ...  The architecture is reminiscent of that of an SMT solver. We present the rules of the calculus, an implementation, and some promising experimental results.  ...  Acknowledgments The author would like to thank Jasmin Blanchette, Martin Brain, Raphaël Cauderlier, Koen Claessen, Pascal Fontaine, Andrew Reynolds, and Martin Riener, and the anonymous reviewers, for  ... 
doi:10.1007/978-3-319-63046-5_8 fatcat:llkw2d2mdrca3k67zsiqizntjq

SMT-Friendly Formalization of the Solidity Memory Model [article]

Ákos Hajdu, Dejan Jovanović
2020 arXiv   pre-print
Solidity is the dominant programming language for Ethereum smart contracts. This paper presents a high-level formalization of the Solidity language with a focus on the memory model.  ...  In addition, the formalization we provide is effective: all but few features can be encoded in the quantifier-free fragment of standard SMT theories.  ...  For each parameter p i and return value r i of a function, we add declarations p i : T (type(p i )) and r i : T (type(r i )) in the SMT program.  ... 
arXiv:2001.03256v1 fatcat:zhblyr3dgfdypp53erjb7wbkrm

Semantic Importance Sampling for Statistical Model Checking [chapter]

Jeffery P. Hansen, Lutz Wrage, Sagar Chaki, Dionisio de Niz, Mark Klein
2015 Lecture Notes in Computer Science  
Using an SMT solver, SIS recursively constructs an abstract indicator function that over-approximates the input-event region, and then uses this abstract indicator function to perform SMC with IS.  ...  Statistical Model Checking (SMC) is a technique, based on Monte-Carlo simulations, for computing the bounded probability that a specific event occurs during a stochastic system's execution.  ...  The #include on Line 1, allows the model include the special osmosis functions to be compiled by a standard compiler such as gcc for use in the SMC phase. SMT Generation.  ... 
doi:10.1007/978-3-662-46681-0_21 fatcat:3zcemvlyevevtb33efpxjyhnbe

SMT-based Verification Applied to Non-convex Optimization Problems

Rodrigo Araujo, Iury Bessa, Lucas Carvalho Cordeiro, Joao Edgar Chaves Filho
2016 2016 VI Brazilian Symposium on Computing Systems Engineering (SBESC)  
This paper presents a novel, complete, and flexible optimization algorithm, which relies on recursive executions that re-constrains a model-checking procedure based on Satisfiability Modulo Theories (SMT  ...  This SMT-based optimization technique is able to optimize a wide range of functions, including non-linear and non-convex problems using fixed-point arithmetic.  ...  ACKNOWLEDGMENT The authors thank Nikolaj Bjorner for reviewing a draft version of this paper.  ... 
doi:10.1109/sbesc.2016.010 dblp:conf/sbesc/AraujoBCF16 fatcat:b2sydqypsvayxn5bjopzdogioa
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