Related papers: Quantified Linear and Polynomial Arithmetic Satisf…

In the article \The State of SAT", the authors asked whether a procedure dramatically different from DPLL can be found for handling unsatisfiable instances. This study proposes a new linear programming approach to address this issue…

Linear discriminant analysis (LDA) is a widely used technique for data classification. The method offers adequate performance in many classification problems, but it becomes inefficient when the data covariance matrix is ill-conditioned.…

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…

Existing post-training quantization methods for large language models (LLMs) offer remarkable success. However, the increasingly marginal performance gains suggest that existing quantization strategies are insufficient to support the…

Large Language Model (LLM) unlearning aims to remove targeted knowledge from a trained model, but practical deployments often require post-training quantization (PTQ) for efficient inference. However, aggressive low-bit PTQ can mask…

Modal formulae express monadic second-order properties on Kripke frames, but in many important cases these have first-order equivalents. Computing such equivalents is important for both logical and computational reasons. On the other hand,…

While large language models (LLMs) have shown progress in mathematical reasoning, they still face challenges in formalizing theorems that arise from instantiating abstract structures in concrete settings. With the goal of auto-formalizing…

The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the…

Ramsey quantifiers have recently been proposed as a unified framework for handling properties of interests in program verification involving proofs in the form of infinite cliques, which are not expressible in first-order logic. Among…

Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…

Quantization became a necessary tool for serving ever-increasing Large Language Models (LLMs). RTN (Round-to-Nearest) is perhaps the simplest quantization technique that has been around well before LLMs surged to the forefront of machine…

In program synthesis, an intelligent system takes in a set of user-generated examples and returns a program that is logically consistent with these examples. The usage of Rational Speech Acts (RSA) framework has been successful in building…

Post-training quantization (PTQ) has emerged as a promising technique to reduce the cost of large language models (LLMs). Specifically, PTQ can effectively mitigate memory consumption and reduce computational overhead in LLMs. To meet the…

#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…

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…

This paper studies the problem of synthesizing (lexicographic) polynomial ranking functions for loops that can be described in polynomial arithmetic over integers and reals. While the analogous ranking function synthesis problem for linear…

The problem of finding small unsatisfiable cores for SAT formulas has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many…

A natural and intuitive idea in model quantization is to approximate each component's quantized output to match its original. Motivated by this idea, most layer-wise post-training quantization (PTQ) methods focus on weight approximation at…

Quantization is an indispensable technique for serving Large Language Models (LLMs) and has recently found its way into LoRA fine-tuning. In this work we focus on the scenario where quantization and LoRA fine-tuning are applied together on…

Solving nonlinear SMT problems over real numbers has wide applications in robotics and AI. While significant progress is made in solving quantifier-free SMT formulas in the domain, quantified formulas have been much less investigated. We…