String smt solvers are specialised software tools for solving the satisfiability modulo. Smt solvers are widely used as core engines in many applications. Tools and algorithms for the construction and analysis of systems 4963 budapest, april 2008, 337340. Smt solver as a small part of an larger set of algorithms. However, systems are usually designed and modeled at a higher level than the boolean level and the translation to boolean logic can be expensive. Detecting critical bugs in smt solversusing blackbox. The tool can handle various nonlinear real functions such as polynomials, trigonometric. Successful commercial computer systems contain tens of millions of lines of handwritten software, all of which is subject to change as competitive pressures motivate the addition of new features in each release. An example conjunction of loatingpoint constraints in the smtlibv2. It is not directed at experts but at potential users and developers of. And store a i v returns a new array identical to a, but on position i it contains the value v. A familiarity with the basic idea of smt solvers would be useful. To improve this situation, we propose to complement traditional testing techniques with grammarbased blackbox. In computer science and mathematical logic, the satisfiability modulo theories smt problem is a decision problem for logical formulas with respect to combinations of background theories expressed in classical firstorder logic with equality.
Z3 is a satisfiability modulo theories smt solver that integrates several decision procedures. To this end, we present a reinforcement learning driven fuzzing system banditfuzz that zeroes in on the grammatical constructs of wellformed solver inputs that are the root cause of performance or correctness issues in solversundertest. Smtracker is a matlabbased graphical user interface gui for automatically quantifying, visualising and managing smt data via five interactive panels, allowing the user to interactively explore tracking data from several conditions, movies and cells on a trackby track basis. Smt solvers are useful both for verification, proving the correctness of programs, software testing based on symbolic execution, and for synthesis, generating program fragments by searching over the space of possible programs. There are different ways that fuzzing tools generate inputs to pass to the target program. We describe the opensource tool dreal, an smt solver for nonlinear formulas over the reals. Boolector is an smt solver for the theory of bitvectors and the extensional theory of arrays over bitvectors.
Fuzzing has been used to test all kinds of software including sat solvers 10. It is used in several program analysis, verification, and test case generation projects at microsoft and was awarded the 2015 acm sigplan programming languages software award, which is given for software systems that have had a lasting influence. Fuzzing is a powerful testing technique which is typically used in the domains of software security and quality. Over the last few years having seen some of the presentations by pablo sole on deplib, blogposts by sean heelan, and having messed around a little bit with the reil in binnavi we were really curious to get a. Stateoftheart testing techniques for smt solvers do not reliably detect such errors. Nov 19, 20 smt solvers for software security array operations in smt lib 2. Georgy nosenko an introduction to the use smt solvers. Earlier this summer beans attended the weeklong smt solver summer school held at mit campus in boston, mass. At microsoft, fuzzing is mandatory for every untrusted interface of every product, as prescribed in the security development lifecycle, 7 which documents recommendations on how to develop.
Btor format 8, the smtlib format 26 distinguishes b etw een type b o ole an and bitve ctor of bitwidth one. Smt solvers perform great once the problem domain has been defined. Effectively, the sum tota l of knowledge possessed by. Fuzzing for smt solvers kyle dewey, mehmet emre, ben hardekopf.
Care must be taken to avoid socalled matching loops, which may prevent termination of the solver. Fuzzing and deltadebugging smt solvers proceedings of the. Fuzzing and deltadebugging smt solvers software testing. They focus on testing controlflow reachability properties of programs. Contribute to ppmxsudoku solver development by creating an account on github.
This chapter covers some of these areas where smt solvers have been used. Typically, fuzzers are used to test programs that take structured inputs. This is the largest computational usage ever for any smt solver, with over 4 billion constraints processed to date. It is not a comprehensive survey, but a basic and rigorous introduction to some of the key ideas. Full verification of smt solvers, however, is difficult due to their complex nature and still an open question. By design, such avoidance limits the extent to which the smt solver is able to apply the. It is not directed at experts but at potential users and developers of smt solvers. Several of our applications are in the context of the z3 smt solver available from microsoft research. Inspired by the utility of fuzzers, we introduce stringfuzz and. In this case, the fuzzer takes a legal input provided by the operator and mutates it, using that as an input instead. To the best of our knowledge, banditfuzz is the first machinelearning based fuzzer for smt solvers. Since 2008, sage has been running in production for over 1,000 machineyears, automatically fuzzing hundreds of applications.
As with many other successful applications of smt solvers, there is a focus on reducing the number of queries that most be made. Therefore, robustness and correctness are essential criteria. The concolic execution technique for python programs used in this chapter was pioneered by. The casp solver ezsmt, the main software product of this work, is inspired by earlier solvers of this kind including systems clingcon gebser et al. Theories solvers for software security, in particular for. Expression select a i returns the value stored at position i of the array a. So lets use a smt solver z3 for example to express a solved sudoku puzzle and to solve it actually. Grammarbased blackbox fuzzing test smt solver with randomsmt formulas for speci.
Jan 11, 2012 blackbox fuzzing is a simple yet effective technique for finding security vulnerabilities in software. Examples of theories typically used in computer science are the theory of real numbers, the theory of integers, and the theories of various data. Clarke carnegie mellon university, pittsburgh, pa 152 abstract. Thousands of security bugs have been found this way. Floatingpoint arithmetic is an essential ingredient of embedded systems, such as in the avionics and automotive industries. Fuzzing and deltadebugging smt solvers proceedings of. To improve this situation, we propose to complement traditional testing techniques with grammarbased blackbox fuzz testing, combined with deltadebugging.
Theories smt problem with string contraints, which is a type of constraint. Our sat solver precosat won three medals in the sat competition 2009. Detecting critical bugs in smt solvers using blackbox mutational. Hack, art, and science, which presents an overview of the main automated testing techniques in use today for finding security vulnerabilities in software fuzzing means automatic test generation and execution with the goal of finding security. Introduction fuzzing and symbolic execution often do not achieve high coverage, not only at the source code, binary, or any intermediate code levels but also at the component level. In this paper, the source language used is dafny 19, the ivl is boogie 2 20, and the smt solver is z3 9, but the tactic described is applicable to other program veri. Such legal inputs might be human produced or automated, for example from a grammar or smt solver query. It is used in various software verification and analysis applications. Grammarbased blackbox input fuzzing proved to be effective to uncover bugs in smt solvers but is entirely inputbased and. The advantage of smt is that many things that are obvious in smt can take a long time for an equivalent sat solver to rediscover. This can be used as an argument to z3 or other smt solvers. Microsoft launches cloud fuzzing service i programmer.
Casp and smt formalisms, which is the main theoretical contribution of the thesis. Again, i would say that for a first version you should get pretty far with an external integration where you let the smt solver deal with propositional sat and uninterpreted functions and arithmetic if you need this. In the process, sage found many new security vulnerabilities missed by blackbox fuzzing and static program analysis and. Whitebox fuzzing for security testing sage has had a remarkable impact at microsoft. Pdf smt solvers for software security researchgate. For example, smt solvers are used to generate test cases, to nd bugs 5,11,12,30,31, and to verify systems 2,6,19,20,21,23. Detecting critical bugs in smt solversusing blackbox mutational. Solving floatingpoint constraints using coverageguided fuzzing. Diffusion parameters and motion behaviour is analysed by several methods.
T ry to pip e cat devurandom to an arbitrary smt solver. Vulnerability checking exploit generation copy protection analysis overall workflow. Satisfiability modulo theories smt solvers are fundamental tools in the broad context of software engineering and security research. Many applications use satis ability modulo theories smt solvers as core decision engines. A brief introduction to fuzzing and why its an important. Fuzzing and deltadebugging smt solvers robert brummayer and armin biere institute for formal models and veri. The program is then monitored for exceptions such as crashes, failing builtin code assertions, or potential memory leaks. For example, if an smt solver concludes unsat although the input.
Fuzzing and deltadebugging smt solvers institute for formal. In proceedings of the 27th acm joint european software engineer. Im looking at doing some verification work where ive got regular tree grammars as an underlying theory. An smt solver will then return a satisfying assignm ent, if one exists, such as b 0 in this case. The software running on your pc has been affected by sage. Predicting smt solver performance for software veri. Satsmt solvers and applications university of waterloo. Fuzzing or fuzz testing is an automated software testing technique that involves providing invalid, unexpected, or random data as inputs to a computer program.
Verification back ends such as smt solvers are typically highly complex pieces of software with performance, correctness and robustness as key requirements. Btor format 8, the smt lib format 26 distinguishes b etw een type b o ole an and bitve ctor of bitwidth one. A crashing smt solver may lead to a crash of the application, or even worse, an incorrect solver may lead to wrong results. Georgy nosenko an introduction to the use smt solvers for. A fuzzer for string smt solvers uwspace university. G and try to derive a contradiction i assume the inequality a 0 i register thelemma. More specifically, they synthesize valid branch reachability properties using concrete. Solving fp constraints using coverageguided fuzzing esecfse 19, august 26s30, 2019, tallinn, estonia listing 1. Smt solvers for software security array operations in smtlib 2. Detecting critical bugs in smt solvers using blackbox mutational fuzzing.
An smt solver for nonlinear theories over the reals. Dec 18, 2010 smt solvers are widely used as core engines in many applications. Solverbased debuggers solverbased type systems solverbased concurrency bug. Satisfiability modulo theories smt solvers that support quantifier instantiations via matching triggers can be programmed to give practical support for userdefined theories. All satisfiable constraints are mapped to n new inputs, which are tested and ranked according to incremental instruction coverage. Satisfiability modulo theories smt problem is a decision problem for logical first order formulas with respect to combinations of background theories such as. Z3 lets you define your own stuff with uninterpreted functions, but that doesnt tend to work well any time your decision procedures are recursive. Fuzzing 16 generates formulas that may crash the solvers or reveal performance issues, but do not reliably detect soundness problems. Satisfiability modulo theories smt solvers have made tremendous progress over the last decade 25 and now underpin many im portant software engineering. By nature, many of these applications are safetycritical, requiring rigorous mathematical methods such as model checking to verify the adherence to safety standards. Vijay ganesh 1,000 constraints 10,000 constraints 100,000 constraints 1,000,000 constraints 1998 2001 2004 2007 2010 solverbased programming languages compiler optimizations using solvers solverbased debuggers solverbased type systems solverbased concurrency bug. Z3 is a new and efficient smt solver freely available from microsoft research. It won first places in the prestigious bitvector and bitvector with arrays tracks in the smt competition. As a result, they are frequently used as the engine behind veri.
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