arXiv subjects

Dirk Beyer

Publications and source records attributed to Dirk Beyer.

At least 19 recordsLinked to original sources

arXiv2026

Circuit-Based Program Verification: Sequential Circuits as an Intermediate Representation for Verifying C Programs

Formal verification of software programs and hardware designs shares the common goal of reasoning about state-transition systems, yet the two communities have largely developed separate intermediate representations and verification algorithms. This paper investigates sequential circuits as an intermediate representation for software verification, with the goal of enabling direct application of hardware-model-checking techniques. We present Circuit-Based Program Verification (CPV), a modular framework that translates C programs into sequential circuits and employs off-the-shelf hardware model checkers as backends. Unlike traditional software verifiers, which typically rely on path-based exploration, CPV reasons over sequential circuits, where a program's control and data flows are folded into a monolithic transition relation that can be analyzed as a whole. The framework supports reachability-safety and termination analyses and integrates multiple state-of-the-art hardware model checkers, which together provide access to diverse verification algorithms, including bounded model checking, $k$-induction, and IC3/PDR. Counterexamples found by hardware model checkers are automatically translated back into software-verification witnesses for users to interpret verification results. We conducted a comprehensive evaluation on a benchmark suite of more than 16000 tasks. Our results show that CPV achieved competitive performance against five well-established software verifiers and exhibited complementary strengths by uniquely solving tasks that other verifiers cannot handle.

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arXiv2025

SV-LIB 1.0: A Standard Exchange Format for Software-Verification Tasks

In the past two decades, significant research and development effort went into the development of verification tools for individual languages, such asC, C++, and Java. Many of the used verification approaches are in fact language-agnostic and it would be beneficial for the technology transfer to allow for using the implementations also for other programming and modeling languages. To address the problem, we propose SV-LIB, an exchange format and intermediate language for software-verification tasks, including programs, specifications, and verification witnesses. SV-LIBis based on well-known concepts from imperative programming languages and uses SMT-LIB to represent expressions and sorts used in the program. This makes it easy to parse and to build into existing infrastructure, since many verification tools are based on SMT solvers already. Furthermore, SV-LIBdefines a witness format for both correct and incorrect SV-LIB programs, together with means for specifying witness-validation tasks. This makes it possible both to implement independent witness validators and to reuse some verifiers also as validators for witnesses. This paper presents version 1.0 of the SV-LIBformat, including its design goals, the syntax, and informal semantics. Formal semantics and further extensions to concurrency are planned for future versions.

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arXiv2025

A Modular Program-Transformation Framework for Reducing Specifications to Reachability

Software verification is a complex problem, and verification tools need significant tuning to achieve high performance. Due to this, many verifiers choose to specialize on reachability properties, or invest the time to implement known transformations from the given specification to reachability on their internal representations. To improve this situation, we provide transformations as stand-alone components, modifying the input program instead of the internal representation, enabling their usage as a preprocessing step by other verifiers. This way, we separate two concerns: improving the performance of reachability analyses and implementing efficient transformations of arbitrary specifications to reachability. We implement the transformations in a framework that is based on instrumentation automata, inspired by the BLAST query language. In our initial study, we support three important concrete specifications for C programs: termination, no-overflow, and memory cleanup. Moreover, we discuss the broader expressiveness of our framework and show how general liveness properties can be transformed to reachability. We demonstrate the effectiveness and efficiency of our transformations by comparing verifiers that support the specifications natively with verifiers for reachability applied on the transformed programs. The results are very promising: Our transformations can extend existing verifiers to be effective on specifications that they do not support natively, and that the efficiency is often similar to verifiers that natively support the considered specifications.

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arXiv2024

Software Verification with CPAchecker 3.0: Tutorial and User Guide (Extended Version)

This tutorial provides an introduction to CPAchecker for users. CPAchecker is a flexible and configurable framework for software verification and testing. The framework provides many abstract domains, such as BDDs, explicit values, intervals, memory graphs, and predicates, and many program-analysis and model-checking algorithms, such as abstract interpretation, bounded model checking, Impact, interpolation-based model checking, k -induction, PDR, predicate abstraction, and symbolic execution. This tutorial presents basic use cases for CPAchecker in formal software verification, focusing on its main verification techniques with their strengths and weaknesses. It also shows further use cases of CPAchecker for test-case generation and witness-based result validation. The envisioned readers are assumed to possess a background in automatic formal verification and program analysis, but prior knowledge of CPAchecker is not required. This tutorial and user guide is based on CPAchecker in version 3.0. This user guide's latest version and other documentation are available at https://cpachecker.sosy-lab.org/doc.php.

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arXiv2024

MoXIchecker: An Extensible Model Checker for MoXI

MoXI is a new intermediate verification language introduced in 2024 to promote the standardization and open-source implementations for symbolic model checking by extending the SMT-LIB 2 language with constructs to define state-transition systems. The tool suite of MoXI provides a translator from MoXI to Btor2, which is a lower-level intermediate language for hardware verification, and a translation-based model checker, which invokes mature hardware model checkers for Btor2 to analyze the translated verification tasks. The extensibility of such a translation-based model checker is restricted because more complex theories, such as integer or real arithmetics, cannot be precisely expressed with bit-vectors of fixed lengths in Btor2. We present MoXIchecker, the first model checker that solves MoXI verification tasks directly. Instead of translating MoXI to lower-level languages, MoXIchecker uses the solver-agnostic library PySMT for SMT solvers as backend for its verification algorithms. MoXIchecker is extensible because it accommodates verification tasks involving more complex theories, not limited by lower-level languages, facilitates the implementation of new algorithms, and is solver-agnostic by using the API of PySMT. In our evaluation, MoXIchecker uniquely solved tasks that use integer or real arithmetics, and achieved a comparable performance against the translation-based model checker from the MoXI tool suite.

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arXiv2024

Augmenting Interpolation-Based Model Checking with Auxiliary Invariants (Extended Version)

Software model checking is a challenging problem, and generating relevant invariants is a key factor in proving the safety properties of a program. Program invariants can be obtained by various approaches, including lightweight procedures based on data-flow analysis and intensive techniques using Craig interpolation. Although data-flow analysis runs efficiently, it often produces invariants that are too weak to prove the properties. By contrast, interpolation-based approaches build strong invariants from interpolants, but they might not scale well due to expensive interpolation procedures. Invariants can also be injected into model-checking algorithms to assist the analysis. Invariant injection has been studied for many well-known approaches, including k-induction, predicate abstraction, and symbolic execution. We propose an augmented interpolation-based verification algorithm that injects external invariants into interpolation-based model checking (McMillan, 2003), a hardware model-checking algorithm recently adopted for software verification. The auxiliary invariants help prune unreachable states in Craig interpolants and confine the analysis to the reachable parts of a program. We implemented the proposed technique in the verification framework CPAchecker and evaluated it against mature SMT-based methods in CPAchecker as well as other state-of-the-art software verifiers. We found that injecting invariants reduces the number of interpolation queries needed to prove safety properties and improves the run-time efficiency. Consequently, the proposed invariant-injection approach verified difficult tasks that none of its plain version (i.e., without invariants), the invariant generator, or any compared tools could solve.

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arXiv2022

Interpolation and SAT-Based Model Checking Revisited: Adoption to Software Verification

The article "Interpolation and SAT-Based Model Checking" (McMillan, 2003) describes a formal-verification algorithm, which was originally devised to verify safety properties of finite-state transition systems. It derives interpolants from unsatisfiable BMC queries and collects them to construct an overapproximation of the set of reachable states. Although 20 years old, the algorithm is still state-of-the-art in hardware model checking. Unlike other formal-verification algorithms, such as k-induction or PDR, which have been extended to handle infinite-state systems and investigated for program analysis, McMillan's interpolation-based model-checking algorithm from 2003 has not been used to verify programs so far. Our contribution is to close this significant, two decades old gap in knowledge by adopting the algorithm to software verification. We implemented it in the verification framework CPAchecker and evaluated the implementation against other state-of-the-art software-verification techniques on the largest publicly available benchmark suite of C safety-verification tasks. The evaluation demonstrates that McMillan's interpolation-based model-checking algorithm from 2003 is competitive among other algorithms in terms of both the number of solved verification tasks and the run-time efficiency. Our results are important for the area of software verification, because researchers and developers now have one more approach to choose from.

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arXiv2021

Towards a Benchmark Set for Program Repair Based on Partial Fixes

Software bugs significantly contribute to software cost and increase the risk of system malfunctioning. In recent years, many automated program-repair approaches have been proposed to automatically fix undesired program behavior. Despite of their great success, specific problems such as fixing bugs with partial fixes still remain unresolved. A partial fix to a known software issue is a programmer's failed attempt to fix the issue the first time. Even though it fails, this fix attempt still conveys important information such as the suspicious software region and the bug type. In this work we do not propose an approach for program repair with partial fixes, but instead answer a preliminary question: Do partial fixes occur often enough, in general, to be relevant for the research area of automated program repair? We crawled 1500 open-source C repositories on GitHub for partial fixes. The result is a benchmark set of 2204 benchmark tasks for automated program repair based on partial fixes. The benchmark set is available open source and open to further contributions and improvement.

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arXiv2020

Software Verification with PDR: Implementation and Empirical Evaluation of the State of the Art

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.

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arXiv2019

Verification Artifacts in Cooperative Verification: Survey and Unifying Component Framework

The goal of cooperative verification is to combine verification approaches in such a way that they work together to verify a system model. In particular, cooperative verifiers provide exchangeable information (verification artifacts) to other verifiers or consume such information from other verifiers with the goal of increasing the overall effectiveness and efficiency of the verification process. This paper first gives an overview over approaches for leveraging strengths of different techniques, algorithms, and tools in order to increase the power and abilities of the state of the art in software verification. Second, we specifically outline cooperative verification approaches and discuss their employed verification artifacts. We formalize all artifacts in a uniform way, thereby fixing their semantics and providing verifiers with a precise meaning of the exchanged information.

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arXiv2016

A Light-Weight Approach for Verifying Multi-Threaded Programs with CPAchecker

Verifying multi-threaded programs is becoming more and more important, because of the strong trend to increase the number of processing units per CPU socket. We introduce a new configurable program analysis for verifying multi-threaded programs with a bounded number of threads. We present a simple and yet efficient implementation as component of the existing program-verification framework CPAchecker. While CPAchecker is already competitive on a large benchmark set of sequential verification tasks, our extension enhances the overall applicability of the framework. Our implementation of handling multiple threads is orthogonal to the abstract domain of the data-flow analysis, and thus, can be combined with several existing analyses in CPAchecker, like value analysis, interval analysis, and BDD analysis. The new analysis is modular and can be used, for example, to verify reachability properties as well as to detect deadlocks in the program. This paper includes an evaluation of the benefit of some optimization steps (e.g., changing the iteration order of the reachability algorithm or applying partial-order reduction) as well as the comparison with other state-of-the-art tools for verifying multi-threaded programs.

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arXiv2015

Domain-Type-Guided Refinement Selection Based on Sliced Path Prefixes

Abstraction is a successful technique in software verification, and interpolation on infeasible error paths is a successful approach to automatically detect the right level of abstraction in counterexample-guided abstraction refinement. Because the interpolants have a significant influence on the quality of the abstraction, and thus, the effectiveness of the verification, an algorithm for deriving the best possible interpolants is desirable. We present an analysis-independent technique that makes it possible to extract several alternative sequences of interpolants from one given infeasible error path, if there are several reasons for infeasibility in the error path. We take as input the given infeasible error path and apply a slicing technique to obtain a set of error paths that are more abstract than the original error path but still infeasible, each for a different reason. The (more abstract) constraints of the new paths can be passed to a standard interpolation engine, in order to obtain a set of interpolant sequences, one for each new path. The analysis can then choose from this set of interpolant sequences and select the most appropriate, instead of being bound to the single interpolant sequence that the interpolation engine would normally return. For example, we can select based on domain types of variables in the interpolants, prefer to avoid loop counters, or compare with templates for potential loop invariants, and thus control what kind of information occurs in the abstraction of the program. We implemented the new algorithm in the open-source verification framework CPAchecker and show that our proof-technique-independent approach yields a significant improvement of the effectiveness and efficiency of the verification process.

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arXiv2015

Combining k-Induction with Continuously-Refined Invariants

Bounded model checking (BMC) is a well-known and successful technique for finding bugs in software. k-induction is an approach to extend BMC-based approaches from falsification to verification. Automatically generated auxiliary invariants can be used to strengthen the induction hypothesis. We improve this approach and further increase effectiveness and efficiency in the following way: we start with light-weight invariants and refine these invariants continuously during the analysis. We present and evaluate an implementation of our approach 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 software verification in terms of successful verification results.

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arXiv2013

Reusing Precisions for Efficient Regression Verification

Continuous testing during development is a well-established technique for software-quality assurance. Continuous model checking from revision to revision is not yet established as a standard practice, because the enormous resource consumption makes its application impractical. Model checkers compute a large number of verification facts that are necessary for verifying if a given specification holds. We have identified a category of such intermediate results that are easy to store and efficient to reuse: abstraction precisions. The precision of an abstract domain specifies the level of abstraction that the analysis works on. Precisions are thus a precious result of the verification effort and it is a waste of resources to throw them away after each verification run. In particular, precisions are small and thus easy to store; they are easy to process and have a large impact on resource consumption. We experimentally show the impact of precision reuse on industrial verification problems, namely, 59 device drivers with 1119 revisions from the Linux kernel.

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arXiv2013

Domain Types: Selecting Abstractions Based on Variable Usage

The success of software model checking depends on finding an appropriate abstraction of the subject program. The choice of the abstract domain and the analysis configuration is currently left to the user, who may not be familiar with the tradeoffs and performance details of the available abstract domains. We introduce the concept of domain types, which classify the program variables into types that are more fine-grained than standard declared types, such as int or long, in order to guide the selection of an appropriate abstract domain for a model checker. Our implementation determines the domain type for each variable in a pre-processing step, based on the variable usage in the program, and then assigns each variable to an abstract domain. The model-checking framework that we use supports to specify a separate analysis precision for each abstract domain, such that we can freely configure the analysis. We experimentally demonstrate a significant impact of the choice of the abstract domain per variable. We consider one explicit (hash tables for integer values) and one symbolic (binary decision diagrams) domain. The experiments are based on standard verification tasks that are taken from recent competitions on software verification. Each abstract domain has unique advantages in representing the state space of variables of a certain domain type. Our experiments show that software model checkers can be improved with a domain-type guided combination of abstract domains.

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arXiv2012

Explicit-Value Analysis Based on CEGAR and Interpolation

Abstraction, counterexample-guided refinement, and interpolation are techniques that are essential to the success of predicate-based program analysis. These techniques have not yet been applied together to explicit-value program analysis. We present an approach that integrates abstraction and interpolation-based refinement into an explicit-value analysis, i.e., a program analysis that tracks explicit values for a specified set of variables (the precision). The algorithm uses an abstract reachability graph as central data structure and a path-sensitive dynamic approach for precision adjustment. We evaluate our algorithm on the benchmark set of the Competition on Software Verification 2012 (SV-COMP'12) to show that our new approach is highly competitive. In addition, we show that combining our new approach with an auxiliary predicate analysis scores significantly higher than the SV-COMP'12 winner.

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arXiv2011

Conditional Model Checking

Software model checking, as an undecidable problem, has three possible outcomes: (1) the program satisfies the specification, (2) the program does not satisfy the specification, and (3) the model checker fails. The third outcome usually manifests itself in a space-out, time-out, or one component of the verification tool giving up; in all of these failing cases, significant computation is performed by the verification tool before the failure, but no result is reported. We propose to reformulate the model-checking problem as follows, in order to have the verification tool report a summary of the performed work even in case of failure: given a program and a specification, the model checker returns a condition P ---usually a state predicate--- such that the program satisfies the specification under the condition P ---that is, as long as the program does not leave states in which P is satisfied. We are of course interested in model checkers that return conditions P that are as weak as possible. Instead of outcome (1), the model checker will return P = true; instead of (2), the condition P will return the part of the state space that satisfies the specification; and in case (3), the condition P can summarize the work that has been performed by the model checker before space-out, time-out, or giving up. If complete verification is necessary, then a different verification method or tool may be used to focus on the states that violate the condition. We give such conditions as input to a conditional model checker, such that the verification problem is restricted to the part of the state space that satisfies the condition. Our experiments show that repeated application of conditional model checkers, using different conditions, can significantly improve the verification results, state-space coverage, and performance.

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arXiv2011

Feature-Aware Verification

A software product line is a set of software products that are distinguished in terms of features (i.e., end-user--visible units of behavior). Feature interactions ---situations in which the combination of features leads to emergent and possibly critical behavior--- are a major source of failures in software product lines. We explore how feature-aware verification can improve the automatic detection of feature interactions in software product lines. Feature-aware verification uses product-line verification techniques and supports the specification of feature properties along with the features in separate and composable units. It integrates the technique of variability encoding to verify a product line without generating and checking a possibly exponential number of feature combinations. We developed the tool suite SPLverifier for feature-aware verification, which is based on standard model-checking technology. We applied it to an e-mail system that incorporates domain knowledge of AT&T. We found that feature interactions can be detected automatically based on specifications that have only feature-local knowledge, and that variability encoding significantly improves the verification performance when proving the absence of interactions.

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