It is commonly understood that a verification tool should provide a counterexample to witness a specification violation. Until recently, software verifiers dumped error witnesses in proprietary formats, which are often neither human-nor machine-readable, and an exchange of witnesses between different verifiers was impossible. To close this gap in softwareverification technology, we have defined an exchange format for error witnesses that is easy to write and read by verification tools (for further processing, e.g., witness validation) and that is easy to convert into visualizations that conveniently let developers inspect an error path. To eliminate manual inspection of false alarms, we develop the notion of stepwise testification: in a first step, a verifier finds a problematic program path and, in addition to the verification result false, constructs a witness for this path; in the next step, another verifier re-verifies that the witness indeed violates the specification. This process can have more than two steps, each reducing the state space around the error path, making it easier to validate the witness in a later step. An obvious application for testification is the setting where we have two verifiers: one that is efficient but imprecise and another one that is precise but expensive. We have implemented the technique of error-witness-driven program analysis in two state-of-the-art verification tools, CPAchecker and Ultimate Automizer, and show by experimental evaluation that the approach is applicable to a large set of verification tasks.

k-induction is a promising technique to extend bounded model checking from falsification to verification. In software verification, k-induction works only if auxiliary invariants are used to strengthen the induction hypothesis. The problem that we address is to generate such invariants (1) automatically without user-interaction, (2) efficiently such that little verification time is spent on the invariant generation, and (3) that are sufficiently strong for a k-induction proof. We boost the k-induction approach to significantly increase effectiveness and efficiency in the following way: We start in parallel to k-induction a data-flow-based invariant generator that supports dynamic precision adjustment and refine the precision of the invariant generator continuously during the analysis, such that the invariants become increasingly stronger. The k-induction engine is extended such that the invariants from the invariant generator are injected in each iteration to strengthen the hypothesis. The new method solves the above-mentioned problem because it (1) automatically chooses an invariant by step-wise refinement, (2) starts always with a lightweight invariant generation that is computationally inexpensive, and (3) refines the invariant precision more and more to inject stronger and stronger invariants into the induction system. We present and evaluate an implementation of our approach, as well as all other existing approaches, in the open-source verification-framework CPACHECKER. Our experiments show that combining k-induction with continuously-refined invariants significantly increases effectiveness and efficiency, and outperforms all existing implementations of k-induction-based verification of C programs in terms of successful results.

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After many years of successful development of new approaches for software verification, there is a need to consolidate the knowledge about the different abstract domains and algorithms. The goal of this paper is to provide a compact and accessible presentation of four SMT-based verification approaches in order to study them in theory and in practice. We present and compare the following different “schools of thought” of software verification: bounded model checking, k-induction, predicate abstraction, and lazy abstraction with interpolants. Those approaches are well-known and successful in software verification and have in common that they are based on SMT solving as the back-end technology. We reformulate all four approaches in the unifying theoretical framework of configurable program analysis and implement them in the verification framework CPAchecker. Based on this, we can present an evaluation that thoroughly compares the different approaches, where the core differences are expressed in configuration parameters and all other variables are kept constant (such as parser front end, SMT solver, used theory in SMT formulas). We evaluate the effectiveness and the efficiency of the approaches on a large set of verification tasks and discuss the conclusions.

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Property-directed reachability (PDR) is a SAT/SMT-based reachability algorithm that incrementally constructs inductive invariants. After it was successfully applied to hardware model checking, several adaptations to software model checking have been proposed. We contribute a replicable and thorough comparative evaluation of the state of the art: We (1) implemented a standalone PDR algorithm and, as improvement, a PDR-based auxiliary-invariant generator for k -induction, and (2) performed an experimental study on the largest publicly available benchmark set of C verification tasks, in which we explore the effectiveness and efficiency of software verification with PDR. The main contribution of our work is to establish a reproducible baseline for ongoing research in the area by providing a well-engineered reference implementation and an experimental evaluation of the existing techniques. 1 extern void __VERIFIER_error() __attribute__ ֒→ ((__noreturn__)); 2 extern unsigned int __VERIFIER_nondet_uint(void); 3 void __VERIFIER_assert(int cond) { 4 if (!(cond)) { 5 ERROR: __VERIFIER_error(); 6 } 7 return; 8 } 9 int main(void) { 10 unsigned int w = __VERIFIER_nondet_uint(); 11 unsigned int x = w; 12 unsigned int y = w + 1; 13 unsigned int z = x + 1; 14 while (__VERIFIER_nondet_uint()) { 15 y++; 16 z++; 17 } 18 __VERIFIER_assert(y == z);