arXiv subjects

Daniela Kaufmann

Publications and source records attributed to Daniela Kaufmann.

9 recordsLinked to original sources

arXiv2026

A Modern View on MCSat

The Model Constructing Satisfiability (MCSat) approach has shown strong performance in solving complex SMT problems, in particular in algebraic SMT theories such as non-linear integer and real arithmetic. In this paper we revisit the theory-independent MCSat framework as a proof system to provide a modern perspective that refines the original formulation of MCSat. By closely formalizing the implementation of MCSat within the Yices2 SMT solver, we incorporate design decisions that diverge from those in the seminal MCSat paper and thereby capture the current state-of-the-art in MCSat-based SMT reasoning. We present a general, theory-agnostic rule scheme for MCSat and instantiate it for several theories, including propositional logic, non-linear real arithmetic, and uninterpreted functions. We provide several detailed examples to illustrate the applicability of the presented calculus.

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arXiv2026

Avoiding Big Integers: Parallel Multimodular Algebraic Verification of Arithmetic Circuits

Word-level verification of arithmetic circuits with large operands typically relies on arbitrary-precision arithmetic, which can lead to significant computational overhead as word sizes grow. In this paper, we present a hybrid algebraic verification technique based on polynomial reasoning that combines linear and nonlinear rewriting. Our approach relies on multimodular reasoning using homomorphic images, where computations are performed in parallel modulo different primes, thereby avoiding any large-integer arithmetic. We implement the proposed method in the verification tool TalisMan2.0 and evaluate it on a suite of multiplier benchmarks. Our results show that hybrid multimodular reasoning significantly improves upon existing approaches.

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arXiv2025

ReVEAL: GNN-Guided Reverse Engineering for Formal Verification of Optimized Multipliers

We present ReVEAL, a graph-learning-based method for reverse engineering of multiplier architectures to improve algebraic circuit verification techniques. Our framework leverages structural graph features and learning-driven inference to identify architecture patterns at scale, enabling robust handling of large optimized multipliers. We demonstrate applicability across diverse multiplier benchmarks and show improvements in scalability and accuracy compared to traditional rule-based approaches. The method integrates smoothly with existing verification flows and supports downstream algebraic proof strategies.

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arXiv2025

Recycling Algebraic Proof Certificates

Proof certificates can be used to validate the correctness of algebraic derivations. However, in practice, we frequently observed that the exact same proof steps are repeated for different sets of variables, which leads to unnecessarily large proofs. To overcome this issue we extend the existing Practical Algebraic Calculus with linear combinations (LPAC) with two new proof rules that allow us to capture and reuse parts of the proof to derive a more condensed proof certificate. We integrate these rules into the proof checker Pacheck 2.0. Our experimental results demonstrate that the proposed extension helps to reduce both proof size and verification time.

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arXiv2024

Extracting Linear Relations from Gr\"obner Bases for Formal Verification of And-Inverter Graphs

Formal verification techniques based on computer algebra have proven highly effective for circuit verification. The circuit, given as an and-inverter graph, is encoded as a set of polynomials that automatically generates a Gr\"obner basis with respect to a lexicographic term ordering. Correctness of the circuit can be derived by computing the polynomial remainder of the specification. However, the main obstacle is the monomial blow-up during the rewriting of the specification, which leads to the development of dedicated heuristics to overcome this issue. In this paper, we investigate an orthogonal approach and focus the computational effort on rewriting the Gr\"obner basis itself. Our goal is to ensure the basis contains linear polynomials that can be effectively used to rewrite the linearized specification. We first prove the soundness and completeness of this technique and then demonstrate its practical application. Our implementation of this method shows promising results on benchmarks related to multiplier verification.

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arXiv2024

PolySAT: Word-level Bit-vector Reasoning in Z3

PolySAT is a word-level decision procedure supporting bit-precise SMT reasoning over polynomial arithmetic with large bit-vector operations. The PolySAT calculus extends conflict-driven clause learning modulo theories with two key components: (i) a bit-vector plugin to the equality graph, and (ii) a theory solver for bit-vector arithmetic with non-linear polynomials. PolySAT implements dedicated procedures to extract bit-vector intervals from polynomial inequalities. For the purpose of conflict analysis and resolution, PolySAT comes with on-demand lemma generation over non-linear bit-vector arithmetic. PolySAT is integrated into the SMT solver Z3 and has potential applications in model checking and smart contract verification where bit-blasting techniques on multipliers/divisions do not scale.

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arXiv2024

MCSat-based Finite Field Reasoning in the Yices2 SMT Solver

This system description introduces an enhancement to the Yices2 SMT solver, enabling it to reason over non-linear polynomial systems over finite fields. Our reasoning approach fits into the model-constructing satisfiability (MCSat) framework and is based on zero decomposition techniques, which find finite basis explanations for theory conflicts over finite fields. As the MCSat solver within Yices2 can support (and combine) several theories via theory plugins, we implemented our reasoning approach as a new plugin for finite fields and extended Yices2's frontend to parse finite field problems, making our implementation the first MCSat-based reasoning engine for finite fields. We present its evaluation on finite field benchmarks, comparing it against cvc5. Additionally, our work leverages the modular architecture of the MCSat solver in Yices2 to provide a foundation for the rapid implementation of further reasoning techniques for this theory.

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arXiv2024

Life span of SAT techniques

In this paper we take 4 different features of the SAT solver CaDiCaL, blocked clause elimination, vivification, on-the-fly self subsumption, and increasing the bound of variable elimination over the SAT Competitions benchmarks between 2009 and 2022. We study these features by both activating them one-by-one and deactivating them one-by-one. We have three hypothesis regarding the experiments: (i) disabling features is always harmful; (ii) the life span of the techniques is limited; and (iii) features simulate each other. Our experiments cannot confirm any of the hypothesis.

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arXiv2023

SMT Solving over Finite Field Arithmetic

Non-linear polynomial systems over finite fields are used to model functional behavior of cryptosystems, with applications in system security, computer cryptography, and post-quantum cryptography. Solving polynomial systems is also one of the most difficult problems in mathematics. In this paper, we propose an automated reasoning procedure for deciding the satisfiability of a system of non-linear equations over finite fields. We introduce zero decomposition techniques to prove that polynomial constraints over finite fields yield finite basis explanation functions. We use these explanation functions in model constructing satisfiability solving, allowing us to equip a CDCL-style search procedure with tailored theory reasoning in SMT solving over finite fields. We implemented our approach and provide a novel and effective reasoning prototype for non-linear arithmetic over finite fields.

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