Apr 29, 2009 questions in bounded model checking of timed automata along with questions of circuit timing analysis can be answered with this logic. Smt solvers and applications vijay ganesh university of waterloo winter 20 wednesday, 16 january. Ian johnson basics of smt solving algorithms and theories april 29, 2009 17 24. We discuss uses of smt solvers for scalable static analysis in section 1. Smt generalizes sat by adding equality reasoning, arithmetic, and other useful. Bounded model checking of software using smt solvers instead of sat solvers alessandro armando, jacopo mantovani, and lorenzo platania. Bounded model checking of software using smt solvers instead of sat solvers. It traces its roots to logic and theorem proving, both to provide the conceptual framework in which to formalize the fundamental questions and to provide algorithmic procedures for the analysis of logical questions. C bounded model checking cbmc is one of the leading approaches to automatic software analysis. Mar 19, 2010 bounded model checking of multithreaded software using smt solvers. Na vely solvable using an iterative bellmanford method, but better negativeweight cycle detection algorithms are known. In our approach, we puts the os model in the checking algorithm in order to avoid the states of the os model to be verified, and the stateoftheart smt solver z3 is employed to perform the verification. The combined decision procedure for inductive datatypes and linear. Bounded model checking of multithreaded software using smt solvers.
Test generation with satisfiability modulo theories. These theories often model ubiquitous data types, such as integers, bitvectors, arrays, algebraic data. In software model checking, that means that only program traces up to a given length are considered. This is gophersat, a sat and pseudoboolean solver written purely in go. Automatic abstraction in smtbased unbounded software model. The key idea is to i build a propositional formula whose models correspond to program traces of bounded length that violate some given property and ii use stateoftheart sat solvers to check the resulting. A novel approach to model checking using smt and the theory of lists. Model checking software, solving horn clauses and ic3. More than 40 million people use github to discover, fork, and contribute to over 100 million projects. Application of this idea to software model checking. We use the vericon tool as starting point for illustrating verification condition generation.
Citeseerx document details isaac councill, lee giles, pradeep teregowda. Symbolic bounded model checking of abstract state machines. In the first lecture we examine connections from program logics to smt solving. Bounded model checking of software using smt solvers instead. The paper presents a good overview of the state of the art in software model checking. Smtbased bounded model checking for embedded ansic software. Verifying ctllive properties of infinite state models using. Satsmt solvers and applications university of waterloo. Instead, we proposed to focus on the socalled decision problem, which relaxes the standard decision problem. Existing solvers support many theories useful for program analysis. The lecture takes as starting point the stateofthe art smt solver z3, developed at microsoft research and the use of it for software verification. Pdf bounded model checking of multithreaded software. Bounded model checking of software using smt solvers instead of.
This is the largest computational usage ever for any smt solver, with over 4 billion constraints processed to date. Modeling languages programming languages model checking systematic testing statespace exploration. Model checking of symbolic transition systems with smt. These efforts make our approach more efficient and scalable. Examples of theories typically used in computer science are the theory of real numbers, the theory of integers, and the theories of various data. Software model checking is the algorithmic analysis of programs to prove. Symbolic software model checking, discussed in section 1. In smtbased bounded model checking, we unroll the transition system m and the property. A smt solver for the theory of records is described in 9.
Sat solvers, able to efficiently solve huge numbers of small problems. In symbolic execution and bounded model checking, program executions are encoded succinctly as a formula. Symbolic model checking with efficient data structures bdds, sat. For the finitestate case, nuxmv features a strong verification engine based on stateoftheart satbased algorithms.
Software model checking is the algorithmic analysis of programs to prove properties of their executions. We have built a pro totype implementation of our technique that uses a satisfiability modulo. Vulnerability checking exploit generation copy protection analysis overall workflow. The number of loop iterations and recursive calls occurring in the program is then bounded by the given number k. Questions in bounded model checking of timed automata along with questions of circuit timing analysis can be answered with this logic. Automated program analysis with software model checking. Pdf bounded model checking of software using smt solvers. C bounded model checking cbmc has proven to be a successful approach to automatic software analysis. Model checking software with first order logic specifications. The approachamounts to i building a propositional formula whosemodels correspondto programtraces of bounded length violating some given propertyandii using stateoftheartsat solvers to check the resulting formulae for satis. By querying the smt solver, the model checker either finds a counterexample to an invariant, or proves that there is no counterexample up to given computation length.
Takeaways symbolic software model checking smt for horn clauses simplification and preprocessing a solver using clues from ic3 an algorithmic overview separate slides. Section 9 relates model checking to software testing and type systems, and section 10 presents a general conclusion. Some such solver is embedded as a background validity checker in most veri. Now, in model checking, you can conjunct the model and the negation of the property to give you one formula. In the purely boolean case, a model is a truth assignment to the boolean variables. Theories solvers for software security, in particular for. For our application of equivalence checking to verify the proper working of a deobfuscator for a virtualization obfuscator, the use of an smt solver is easily feasible. The dominating approach to smt t, called lazy approach, is based on the integration of a sat solver and of a decision procedure able to handle sets of atomic constraints in t tsolver, handling respectively the boolean and the theoryspecific components of reasoning. This is the largest computational usage ever for any smt solver, with over 4. In this paper, we investigate the applicability of ic3 to software model checking. Smt solver, but rather, how to generate the constraint system from the program and which constraint system to generate in the. Getting unsat would mean your model satisfies the propertyspecification. Section 8, liveness and termination, briefly offers some hints for working in this area. For our application of equivalence checking to verify the proper working of a deobfuscator for a virtualization obfuscator.
I wrote the following code using the python z3 api, mirroring the code described in the paper. Smt solvers perform great once the problem domain has been defined. Automatic abstraction in smtbased unbounded software. Lazy theorem proving for bounded model checking over. If it gives you a solution, it would mean the property is sometimes violated since you conjuncted the negated property. As an alternative, cbmc has featured support for external smt solvers since version 3. Smt solvers enable application of bounded model checking to in. The key idea is to i build a propositional formula whose models correspond to program traces of bounded length that violate some given property and ii use stateoftheart sat solvers to check the resulting formulae for satisfiability.
On verifying atl transformations using offtheshelf smt solvers. Theories smt solver to solve the resulting formulae. Lazy theorem proving for bounded model checking over infinite. Clarke carnegie mellon university, pittsburgh, pa, usa abstract. Model checking is always up to some bound limited often finite input domain, for specific properties, under some environment assumptions ex. Early attempts for solving smt instances involved translating them to boolean sat instances e. Software or hardware systems can be often represented as a state transition. Citeseerx bounded model checking of software using smt. Model checking of symbolic transition systems with smt solvers. An smt solver for nonlinear theories over the reals. In order to cope with increasing software complexity. Automatic abstraction in smtbased unbounded software model checking. International journal on software tools for technology transfer 2009. Bounded model checking of multithreaded software using.
Software model checkers based on underapproximations and smt solvers are very successful at verifying safety i. Vijay ganesh talk outline 2 topics covered in lecture on sat solvers motivation for satsmt solvers in software engineering. Model checking using smt and theory of lists to prove facts about a simple machine. Bounded model checking of multithreaded software using smt. C bounded model checking cbmc has proved to be a successful approach to automatic software analysis. Static verification techniques leverage boolean formula satisfiability solvers such as sat and smt solvers that operate on conjunctive normal form and first order. The verification is performed by unwinding the loops in the program and passing the. The application of bounded model checking to software poses new chal. Model checking software or hardware systems can be often represented as a state transition system, or model, m s,i,t,l m is a model both in 1. Bounded model checking of software using smt solvers. Smtbased bounded model checking for embedded ansic. 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.
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