Certificates for decision problems in temporal logic using context-based tableaux and sequent calculi.

115 p.Esta tesis trata de resolver problemas de Satisfactibilidad y Model Checking, aportando certificados del resultado. En ella, se trabaja con tres lógicas temporales: Propositional Linear Temporal Logic (PLTL), Computation Tree Logic (CTL) y Extended Computation Tree Logic (ECTL). Primero se presenta el trabajo realizado sobre Certified Satisfiability. Ahí se muestra una adaptación del ya existente método dual de tableaux y secuentes basados en contexto para satisfactibilidad de fórmulas PLTL en Negation Normal Form. Se ha trabajado la generación de certificados en el caso en el que las fórmulas son insactisfactibles. Por último, se aporta una prueba de soundness del método. Segundo, se ha optimizado con Sat Solvers el método de Certified Satisfiability para el contexto de Certified Model Checking. Se aportan varios ejemplos de sistemas y propiedades. Tercero, se ha creado un nuevo método dual de tableaux y secuentes basados en contexto para realizar Certified Satisfiability para fórmulas CTL yECTL. Se presenta el método y un algoritmo que genera tanto el modelo en el caso de que las fórmulas son satisfactibles como la prueba en el caso en que no lo sean. Por último, se presenta una implementación del método para CTL y una experimentación comparando el método propuesto con otro método de similares características

Towards Certified Model Checking for PLTL using One-pass Tableaux

The standard model checking setup analyses whether the given system specification satisfies a dedicated temporal property of the system, providing a positive answer here or a counter-example. At the same time, it is often useful to have an explicit proof that certifies the satisfiability. This is exactly what the {\it certified model checking (CMC)} has been introduced for. The paper argues that one-pass (context-based) tableau for PLTL can be efficiently used in the CMC setting, emphasising the following two advantages of this technique. First, the use of the context in which the eventualities occur, forces them to fulfil as soon as possible. Second, a dual to the tableau sequent calculus can be used to formalise the certificates. The combination of the one-pass tableau and the dual sequent calculus enables us to provide not only counter-examples for unsatisfied properties, but also proofs for satisfied properties that can be checked in a proof assistant. In addition, the construction of the tableau is enriched by an embedded solver, to which we dedicate those (propositional) computational tasks that are costly for the tableaux rules applied solely. The combination of the above techniques is particularly helpful to reason about large (system) specifications

Correctness Witness Validation by Abstract Interpretation

Witnesses record automated program analysis results and make them exchangeable. To validate correctness witnesses through abstract interpretation, we introduce a novel abstract operation unassume. This operator incorporates witness invariants into the abstract program state. Given suitable invariants, the unassume operation can accelerate fixpoint convergence and yield more precise results. We demonstrate the feasibility of this approach by augmenting an abstract interpreter with unassume operators and evaluating the impact of incorporating witnesses on performance and precision. Using manually crafted witnesses, we can confirm verification results for multi-threaded programs with a reduction in effort ranging from 7% to 47% in CPU time. More intriguingly, we discover that using witnesses from model checkers can guide our analyzer to verify program properties that it could not verify on its own.Comment: 29 pages, 4 figures, 2 tables, extended version of the paper which is to appear at VMCAI 202

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers

Verified Propagation Redundancy and Compositional UNSAT Checking in CakeML

Modern SAT solvers can emit independently-checkable proof certificates to validate their results. The state-of-the-art proof system that allows for compact proof certificates is propagation redundancy (PR). However, the only existing method to validate proofs in this system with a formally verified tool requires a transformation to a weaker proof system, which can result in a significant blowup in the size of the proof and increased proof validation time. This article describes the first approach to formally verify PR proofs on a succinct representation. We present (i) a new Linear PR (LPR) proof format, (ii) an extension of the DPR-trim tool to efficiently convert PR proofs into LPR format, and (iii) cake_lpr, a verified LPR proof checker developed in CakeML. We also enhance these tools with (iv) a new compositional proof format designed to enable separate (parallel) proof checking. The LPR format is backwards compatible with the existing LRAT format, but extends LRAT with support for the addition of PR clauses. Moreover, cake_lpr is verified using CakeML ’s binary code extraction toolchain, which yields correctness guarantees for its machine code (binary) implementation. This further distinguishes our clausal proof checker from existing checkers because unverified extraction and compilation tools are removed from its trusted computing base. We experimentally show that: LPR provides efficiency gains over existing proof formats; cake_lpr ’s strong correctness guarantees are obtained without significant sacrifice in its performance; and the compositional proof format enables scalable parallel proof checking for large proofs