Related papers: Formalizing the Soundness of the Encoding Methods …

Large language models (LLMs) are increasingly used for tasks that implicitly reduce to Boolean satisfiability (SAT), yet their reasoning ability on SAT remains unclear. We present a systematic study of LLMs on 2-SAT and 3-SAT, together with…

The search for increased trustworthiness of SAT solvers is very active and uses various methods. Some of these methods obtain a proof from the provers then check it, normally by replicating the search based on the proof's information.…

Many state-of-the-art Satisfiability Modulo Theories (SMT) solvers for the theory of fixed-size bit-vectors employ an approach called bit-blasting, where a given formula is translated into a Boolean satisfiability (SAT) problem and…

CoqQ is a framework for reasoning about quantum programs in the Coq proof assistant. Its main components are: a deeply embedded quantum programming language, in which classic quantum algorithms are easily expressed, and an expressive…

We investigate here a new version of the Calculus of Inductive Constructions (CIC) on which the proof assistant Coq is based: the Calculus of Congruent Inductive Constructions, which truly extends CIC by building in arbitrary first-order…

Model checking is an automatic formal verification technique that is widely used in hardware verification. The state-of-the-art complete model-checking techniques, based on IC3/PDR and its general variant CAR, are based on computing…

Individual clinical Knowledge Artifacts (KA) are designed to be used in Clinical Decision Support (CDS) systems at the point of care for delivery of safe, evidence-based care in modern healthcare systems. For formal authoring of a KA,…

Static analyzers based on abstract interpretation are complex pieces of software implementing delicate algorithms. Even if static analysis techniques are well understood, their implementation on real languages is still error-prone. This…

We describe an embedding of the QWIRE quantum circuit language in the Coq proof assistant. This allows programmers to write quantum circuits using high-level abstractions and to prove properties of those circuits using Coq's theorem proving…

This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…

We present the design, implementation, and foundation of a verifier for higher-order functional programs with generics and recursive data types. Our system supports proving safety and termination using preconditions, postconditions and…

Implicit Chain-of-Thought (CoT) methods offer a token-efficient alternative to explicit CoT reasoning in Large Language Models (LLMs), but a persistent performance gap has limited their adoption. We identify a core latent instability issue…

Satisfiability Modulo Theories (SMT) and SAT solvers are critical components in many formal software tools, primarily due to the fact that they are able to easily solve logical problem instances with millions of variables and clauses. This…

Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…

This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…

This work is a part of an ongoing effort to prove the correctness of invertibility conditions for the theory of fixed-width bit-vectors, which are used to solve quantified bit-vector formulas in the Satisfiability Modulo Theories (SMT)…

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 present an executable formally verified SAT encoding of classical AI planning. We use the theorem prover Isabelle/HOL to perform the verification. We experimentally test the verified encoding and show that it can be used for reasonably…

Error Detection and Correction Codes (ECCs) are often used in digital designs to protect data integrity. Especially in safety-critical systems such as automotive electronics, ECCs are widely used and the verification of such complex logic…