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Boolean satisfiability is a propositional logic problem of interest in multiple fields, e.g., physics, mathematics, and computer science. Beyond a field of research, instances of the SAT problem, as it is known, require efficient solution…
Boolean Satisfiability (SAT) problems are critical in fields such as artificial intelligence and cryptography, where efficient solutions are essential. Conventional probabilistic solvers often encounter scalability issues due to complex…
Building on VeriX (Verified eXplainability, arXiv:2212.01051), a system for producing optimal verified explanations for machine learning models, we present VeriX+, which significantly improves both the size and the generation time of formal…
The weighted Maximum Satisfiability problem (weighted MAX-SAT) is a NP-hard problem with numerous applications arising in artificial intelligence. As an efficient tool for heuristic design, the backbone has been applied to heuristics design…
Multiple hypothesis testing (MHT) frequently arises in scientific inquiries, and concurrent testing of multiple hypotheses inflates the risk of Type-I errors or false positives, rendering MHT corrections essential. This paper addresses MHT…
While most approaches in formal methods address system correctness, ensuring robustness has remained a challenge. In this paper we present and study the logic rLTL which provides a means to formally reason about both correctness and…
Mathematical reasoning poses a significant challenge for language models due to its complex and structured nature. In this paper, we introduce DeepSeekMath 7B, which continues pre-training DeepSeek-Coder-Base-v1.5 7B with 120B math-related…
Testing controllers in safety-critical systems is vital for ensuring their safety and preventing failures. In this paper, we address the falsification problem within learning-based closed-loop control systems through simulation. This…
We investigate practical algorithms for inconsistency-tolerant query answering over prioritized knowledge bases, which consist of a logical theory, a set of facts, and a priority relation between conflicting facts. We consider three…
We present Kwaipilot-AutoThink (KAT), an open-source 40B large language model developed to address the overthinking problem in reasoning-intensive tasks, where an automatic thinking training paradigm is proposed to dynamically switch…
Automated verification tools based on SMT solvers have made significant progress in verifying complex software systems. However, these tools face a fundamental tension between automation and performance when dealing with quantifier…
A multiple objective simulation optimization algorithm named Multiple Objective Probabilistic Branch and Bound with Single Observation (MOPBnB(so)) is presented for approximating the Pareto optimal set and the associated efficient frontier…
As multimodal large language models (MLLMs) frequently exhibit errors in complex video reasoning scenarios, correcting these errors is critical for uncovering their weaknesses and improving performance. However, existing benchmarks lack…
We develop the first two heap logics that have implicit heaplets and that admit FO-complete program verification. The notion of FO-completeness is a theoretical guarantee that all theorems that are valid when recursive definitions are…
We present a framework for training trustworthy large language model (LLM) agents for optimization modeling via a verifiable synthetic data generation pipeline. Focusing on linear and mixed-integer linear programming, our approach begins…
Machine learning applications frequently come with multiple diverse objectives and constraints that can change over time. Accordingly, trained models can be tuned with sets of hyper-parameters that affect their predictive behavior (e.g.,…
Formal specifications play a central role in ensuring software reliability and correctness. However, automatically synthesizing high-quality formal specifications remains a challenging task, often requiring domain expertise. Recent work has…
We consider the problem of constrained multi-objective blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions satisfying a set of constraints while minimizing the number…
Data errors, corruptions, and poisoning attacks during training pose a major threat to the reliability of modern AI systems. While extensive effort has gone into empirical mitigations, the evolving nature of attacks and the complexity of…
Large language models have achieved remarkable success on final-answer mathematical problems, largely due to the ease of applying reinforcement learning with verifiable rewards. However, the reasoning underlying these solutions is often…