Related papers: Determinism in the Certification of UNSAT Proofs
Boolean Satisfiability (SAT) solvers are now routinely used in the verification of large industrial problems. However, their application in safety-critical domains such as the railways, avionics, and automotive industries requires some form…
Verification methods based on SAT, SMT, and Theorem Proving often rely on proofs of unsatisfiability as a powerful tool to extract information in order to reduce the overall effort. For example a proof may be traversed to identify a minimal…
Modern high-performance SAT solvers quickly solve large satisfiability instances that occur in practice. If the instance is satisfiable, then the SAT solver can provide a witness which can be checked independently in the form of a…
We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms…
Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…
Functional verification constitutes one of the most challenging tasks in the development of modern hardware systems, and simulation-based verification techniques dominate the functional verification landscape. A dominant paradigm in…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about arrays. Yet the satisfiability of such formulas is, in…
Our recently proposed certification framework for bit-level k-induction-based model checking has been shown to be quite effective in increasing the trust of verification results even though it partially involved quantifier reasoning. In…
Constrained-random simulation is the predominant approach used in the industry for functional verification of complex digital designs. The effectiveness of this approach depends on two key factors: the quality of constraints used to…
Clausal proofs have become a popular approach to validate the results of SAT solvers. However, validating clausal proofs in the most widely supported format (DRAT) is expensive even in highly optimized implementations. We present a new…
Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity.…
Many procedures for SAT-related problems, in particular for those requiring the complete enumeration of satisfying truth assignments, rely their efficiency and effectiveness on the detection of (possibly small) partial assignments…
Modern SAT or QBF solvers are expected to produce correctness certificates. However, certificates have worst-case exponential size (unless NP=coNP), and at recent SAT competitions the largest certificates of unsatisfiability are starting to…
Certifying verification algorithms not only return whether a given property holds or not, but also provide an accompanying independently checkable certificate and a corresponding witness. The certificate can be used to easily validate the…
The dramatic improvements in combinatorial optimization algorithms over the last decades have had a major impact in artificial intelligence, operations research, and beyond, but the output of current state-of-the-art solvers is often hard…
We discuss the topic of unsatisfiability proofs in SMT, particularly with reference to quantifier free non-linear real arithmetic. We outline how the methods here do not admit trivial proofs and how past formalisation attempts are not…
Commonly used proof strategies by automated reasoners organise proof search either by ordering-based saturation or by reducing goals to subgoals. In this paper, we combine these two approaches and advocate a SAT-based method with symmetry…
As state-of-the-art neural networks are deployed on reasoning and algorithmic tasks, exactness guarantees become increasingly important. However, high average-case accuracy can still mask inconsistent behaviors. This motivates exact…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…