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Engineering Theories with Z3 [chapter]

Nikolaj Bjørner
2011 Lecture Notes in Computer Science  
We here explore different theories that extend Microsoft Research's SMT solver Z3's basic support. Some can be directly encoded or axiomatized, others make use of user theory plug-ins.  ...  They are a good fit for the domain of software and hardware engineering because they support many domains that are commonly used by the tools.  ...  It comes with built-in support for the theory of equality, uninterpreted functions, arithmetic, arrays, bit-vectors, and even first-order quantification.  ... 
doi:10.1007/978-3-642-25318-8_3 fatcat:oyhhz3bzwrh4nkuahyllkodg7u

Engineering Theories with Z3 [chapter]

Nikolaj Bjørner
2011 Lecture Notes in Computer Science  
We here explore different theories that extend Microsoft Research's SMT solver Z3's basic support. Some can be directly encoded or axiomatized, others make use of user theory plug-ins.  ...  They are a good fit for the domain of software and hardware engineering because they support many domains that are commonly used by the tools.  ...  It comes with built-in support for the theory of equality, uninterpreted functions, arithmetic, arrays, bit-vectors, and even first-order quantification.  ... 
doi:10.1007/978-3-642-25379-9_1 fatcat:inayuog7nvaefpf7hfwkv7k4ua

IDP-Z3: a reasoning engine for FO(.) [article]

Pierre Carbonnelle, Simon Vandevelde, Joost Vennekens, Marc Denecker
2022 arXiv   pre-print
We have developed a new reasoning engine, IDP-Z3, that removes this limitation, and we put it to the test in four knowledge-intensive industrial use cases. This paper describes FO(.)  ...  (aka FO-dot), the language used to represent knowledge in the IDP3 and IDP-Z3 system.  ...  The authors thank Ingmar Dasseville and Jo Devriendt for their contributions to the development of IDP-Z3.  ... 
arXiv:2202.00343v2 fatcat:ds3eufzawneyrbzkqulqftqeua

Scala to the Power of Z3: Integrating SMT and Programming [chapter]

Ali Sinan Köksal, Viktor Kuncak, Philippe Suter
2011 Lecture Notes in Computer Science  
We describe a system that integrates the SMT solver Z3 with the Scala programming language.  ...  Using Z3's mechanism of theory extensions, our system also helps users construct custom constraint solvers where the interpretation of predicates and functions is given as Scala code.  ...  A definition such as the following is all that is needed to add a theory solver to Z3's DPLL engine: class BAPATheory(val z3: Z3Context) extends Z3Theory(z3, "Sets with cardialities") { // User−defined  ... 
doi:10.1007/978-3-642-22438-6_30 fatcat:rgpberf7mrdjle4btwkrnfmrki

Z3: An Efficient SMT Solver [chapter]

Leonardo de Moura, Nikolaj Bjørner
2008 Lecture Notes in Computer Science  
Satisfiability Modulo Theories (SMT) problem is a decision problem for logical first order formulas with respect to combinations of background theories such as: arithmetic, bit-vectors, arrays, and uninterpreted  ...  Z3 is a new and efficient SMT Solver freely available from Microsoft Research. It is used in various software verification and analysis applications.  ...  Front-ends interact with Z3 by using either a textual format or a binary API.  ... 
doi:10.1007/978-3-540-78800-3_24 fatcat:xq4pou3gdnbdpk4mdrtzzhtwee

PIPE+Verifier - A Tool for Analyzing High Level Petri Nets

Su Liu, Xudong He
2015 Proceedings of the 27th International Conference on Software Engineering and Knowledge Engineering  
the backend engine.  ...  In our prior work, we have developed a method based on BMC and a supporting tool PIPE+Verifier to analyze high level Petri nets using a state of the art satisfiability modulo theories (SMT) solver Z3 as  ...  The connector consists of four components: • Solver Invoker: the invoker links to the tool to the backend engine Z3, which contains some scripts to automatically launch Z3 with proper parameters.  ... 
doi:10.18293/seke2015-60 dblp:conf/seke/LiuH15 fatcat:anpac22fpnbaveixy4ztf46tzm

Z3-str: a z3-based string solver for web application analysis

Yunhui Zheng, Xiangyu Zhang, Vijay Ganesh
2013 Proceedings of the 2013 9th Joint Meeting on Foundations of Software Engineering - ESEC/FSE 2013  
In this paper, we develop a general purpose string solver, called Z3-str, as an extension of the Z3 SMT solver through its plug-in interface.  ...  The string-sorted terms include string constants and variables of arbitrary length, with functions such as concatenation, sub-string, and replace.  ...  Z3 is recently open-sourced. We are looking into if Z3-str can communicate with the integer theory better to improve performance.  ... 
doi:10.1145/2491411.2491456 dblp:conf/sigsoft/ZhengZG13 fatcat:jsr7kptgw5erxbtw77e5krqhyu

InSPeCT: Iterated Local Search for Solving Path Conditions

Fuxiang Chen, Aldy Gunawan, David Lo, Sunghun Kim
2019 2019 IEEE 15th International Conference on Automation Science and Engineering (CASE)  
It also generates tests with higher test coverage than both MLB and Z3.  ...  To generate test cases, many Symbolic Execution approaches first produce Path Conditions (PCs), a set of constraints, and pass them to a Satisfiability Modulo Theories (SMT) solver.  ...  Fig. 3 . 3 Time (ms) spent by InSPeCT, MLB & Z3 , in Software Engineering (aka.  ... 
doi:10.1109/coase.2019.8843039 dblp:conf/case/ChenGL019 fatcat:qvs3lpciongf5a6c2yhpvefdvu

Static analysis of functionally graded composite shells on elastic foundations with nonlocal elasticity theory

Mohammad Arefi, O. Civalek
2020 Archives of Civil and Mechanical Engineering  
Third-order shear deformation theory is developed for modelling the kinematic relations, and nonlocal elasticity theory is developed for size-dependent analysis.  ...  The aim of this present work is to study the higher-order modelling of a cylindrical nano-shell resting on Pasternak's foundation based on nonlocal elasticity theory.  ...  The numerical results have been compared with those results based on Eringen nonlocal elasticity theory, strain gradient theory, modified couple stress theory and classical theories.  ... 
doi:10.1007/s43452-020-00032-2 fatcat:kowkan42z5bvrmlm3cilgpnnvy

FrankenBit: Bit-Precise Verification with Many Bits [chapter]

Arie Gurfinkel, Anton Belov
2014 Lecture Notes in Computer Science  
In this paper, we present FrankenBit -a tool that combines bit-precise invariant synthesis with BMC counterexample search.  ...  As the name suggests, FrankenBit combines a large variety of existing verification tools and techniques, including LLBMC, UFO, Z3, Boolector, MiniSAT and STP.  ...  Finally, the safety of the weakened invariant is checked again with Z3 (Z3 safety), and, if necessary, strengthened using the bit-precise version of Z3/PDR. Counterexamples.  ... 
doi:10.1007/978-3-642-54862-8_32 fatcat:aablpvf2w5b7pe24ywxkzadmxy

An Empirical Study of Path Feasibility Queries [article]

Asankhaya Sharma
2013 arXiv   pre-print
Our path condition formulas are generated in a theory of quantifier free bit vectors with arrays (QF_ABV).  ...  We show that among the different SMT solvers, STP is better than Z3 by an order of magnitude for such kind of queries.  ...  Our results indicate a much bigger gap between performance of Z3 and STP (about 10 times); it can be further explained by the fact that Z3 supports existential theory of arrays while in STP the theory  ... 
arXiv:1302.4798v1 fatcat:auzhlzu7bbb4fcci7eea7t4xl4

A reverse thermal cloak design method based on inverse problem theory

Jun Guo, MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, 710049, China, Zhiguo Qu, Xueliang Wang, MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, 710049, China, MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, 710049, China
2020 ES Energy & Environment  
A reverse thermal cloak design method is developed based on inverse problem theory.  ...  The maximum deviation between background temperature with and without cloak position is no larger than 0.9% for background with uniform gradient and no larger than 5% for background with non-uniform gradient  ...  Thermal conductivity of Z3 should be calculated by the reverse design method based on inverse problem theory.  ... 
doi:10.30919/esee8c375 fatcat:n5hxat425zfgjauuzlinqvq2mu

Encoding Floating-Point Numbers Using the SMT Theory in ESBMC: An Empirical Evaluation over the SV-COMP Benchmarks [chapter]

Mikhail Y. R. Gadelha, Lucas C. Cordeiro, Denis A. Nicole
2017 Lecture Notes in Computer Science  
This paper describes the support for encoding C/C++ programs using the SMT theory of floating-point numbers in ESBMC: an SMT-based context-bounded model checker that provides bit-precise verification of  ...  The experimental results show that our encoding based on MathSAT is able to outperform not only Z3, but also other existing approaches that participated in the most recent edition of SV-COMP.  ...  This paper presents a BMC approach to encoding C programs using SMT floating-point theory, evaluates the encoding using the SMT solvers that support this theory, and compares our approach with other existing  ... 
doi:10.1007/978-3-319-70848-5_7 fatcat:t2defnoaeravteynwclsjgmdyy

Page 1735 of American Society of Civil Engineers. Collected Journals Vol. 116, Issue EM8 [page]

1990 American Society of Civil Engineers. Collected Journals  
; (2) that they are properly cor- related with one another; and (3) that they average to the parent value, (1/2)(Z} + Z3) = Z°.  ...  + Z3) = Z}; and (4) that they are properly correlated with Z} and Zj. The third criterion implies conditioning of the distributions of Z} and Z} on the value of Z}.  ... 

Functional SMT solving with Z3 and racket

Siddharth Agarwal, Amey Karkare
2013 2013 1st FME Workshop on Formal Methods in Software Engineering (FormaliSE)  
, for instance, supports plugging in external theories via the C API, but not via the textual SMT-LIB interface.  ...  We present an attempt to make using SMT solvers simpler by integrating the Z3 solver into a host language, Racket.  ...  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
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