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arxiv: 2604.16571 · v1 · submitted 2026-04-17 · 💻 cs.AR · cs.SE

Recognition: unknown

EquivFusion: Unifying Hardware Equivalence Checking from Algorithms to Netlists via MLIR

Jiaying Zhu , Baoqi Zhang , Mengxia Tao , Kezhi Li , Hao Yan , Qiang Xu , Min Li
Authors on Pith no claims yet

Pith reviewed 2026-05-10 07:55 UTC · model grok-4.3

classification 💻 cs.AR cs.SE
keywords equivalence checkingMLIRhardware verificationformal methodsSMT-LIBBTOR2AIGERnetlists
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The pith

EquivFusion unifies hardware equivalence checking from algorithms to netlists using an MLIR pipeline.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents EquivFusion as a tool that brings together designs written in different languages and at different levels of abstraction for equivalence checking. It uses MLIR to create a common representation that can then be turned into standard formal verification inputs. This matters if true because it allows checking consistency between high-level models like those in PyTorch and low-level netlists without separate tools for each pair. A sympathetic reader would see this as enabling earlier verification in the design process for complex hardware.

Core claim

EquivFusion leverages a verification-oriented MLIR lowering pipeline to unify diverse entry points, including PyTorch, C/C++, Chisel, Verilog, and gate-level netlists, into a common intermediate representation. This enables automated, pairwise equivalence checking across diverse abstraction levels by rigorously translating designs into SMT-LIB, BTOR2, AIGER. It demonstrates feasibility to bridge the semantic gap between software specifications and hardware realizations.

What carries the argument

The verification-oriented MLIR lowering pipeline that converts multiple source languages into a shared intermediate form for translation to formal verification formats like SMT-LIB, BTOR2, and AIGER.

Load-bearing premise

The MLIR-based translations from each source language to the common representation and then to the formal formats preserve the original semantics without introducing or hiding discrepancies.

What would settle it

Observing a mismatch where two known equivalent designs from different levels are incorrectly flagged as non-equivalent by EquivFusion, or vice versa, would indicate a failure in the translation pipeline.

Figures

Figures reproduced from arXiv: 2604.16571 by Baoqi Zhang, Hao Yan, Jiaying Zhu, Kezhi Li, Mengxia Tao, Min Li, Qiang Xu.

Figure 1
Figure 1. Figure 1: Overview of EquivFusion. gate-level netlists. Each input is first translated by existing front￾ends into MLIR, bringing heterogeneous specifications into a com￾mon intermediate form. At the core, EqivFusion hosts a set of verification-oriented dialects on top of CIRCT: sequential designs are represented using a dedicated sequential abstraction and can be selectively unrolled to derive equivalent combinatio… view at source ↗
read the original abstract

Ensuring functional consistency between high-level algorithmic models and low-level hardware implementations is a critical challenge, particularly as modern design flows increasingly span heterogeneous abstractions--from deep learning frameworks to hardware netlists. In this paper, we present EquivFusion, an end-to-end equivalence checking tool tailored for multi-modal circuit designs. Unlike traditional flows that rely on siloed tools or ad-hoc translation, EquivFusion leverages a verification-oriented MLIR lowering pipeline to unify diverse entry points, including PyTorch, C/C++, Chisel, Verilog, and gate-level netlists, into a common intermediate representation. This architecture enables automated, pairwise equivalence checking across diverse abstraction levels by rigorously translating designs into standard formal verification formats, i.e., SMT-LIB, BTOR2, AIGER. We demonstrate EquivFusion's feasibility to bridge the semantic gap between software specifications and hardware realizations, showcasing its effectiveness in facilitating "shift-left" formal verification for datapath-intensive hardware designs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper presents EquivFusion, an end-to-end equivalence checking tool that employs a verification-oriented MLIR lowering pipeline to unify entry points from PyTorch, C/C++, Chisel, Verilog, and gate-level netlists into a common intermediate representation. This enables automated pairwise equivalence checking across abstraction levels by translating designs into SMT-LIB, BTOR2, and AIGER formats. Feasibility is shown via examples on datapath-intensive hardware designs to bridge semantic gaps between high-level algorithms and low-level implementations.

Significance. If the translations are semantics-preserving, the unified MLIR-based approach could meaningfully advance shift-left formal verification in heterogeneous design flows by reducing reliance on siloed tools. The modular architecture leveraging MLIR dialects for multiple source languages and formal backends is a practical strength that could support broader adoption in hardware verification.

major comments (2)
  1. The central claim that the MLIR lowering pipeline produces semantics-preserving translations from diverse sources to the common IR and then to SMT-LIB/BTOR2/AIGER is load-bearing for all equivalence results. The manuscript supplies no formal semantics for the custom dialects, no machine-checked proofs of the lowering rules, and no systematic validation (e.g., differential testing against reference simulators or comparison to independently verified translations). This assumption is stated in the abstract and the architecture description but left unaddressed in the provided examples.
  2. The evaluation demonstrates feasibility on datapath designs but reports no quantitative results on verification success rates, scalability limits, or direct comparisons to existing equivalence checkers. Without such data in the results section, it is difficult to assess whether the unified pipeline delivers practical advantages over ad-hoc translations.
minor comments (2)
  1. Clarify the exact MLIR dialect definitions and lowering passes with concrete code snippets or pseudocode in the main text or an appendix to aid reproducibility.
  2. Add citations to prior work on MLIR for hardware modeling and multi-level equivalence checking to better situate the contribution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and for recognizing the potential of a unified MLIR-based approach for cross-abstraction equivalence checking. We address each major comment below, indicating where revisions will be made to clarify the manuscript's contributions and limitations.

read point-by-point responses

  1. Referee: The central claim that the MLIR lowering pipeline produces semantics-preserving translations from diverse sources to the common IR and then to SMT-LIB/BTOR2/AIGER is load-bearing for all equivalence results. The manuscript supplies no formal semantics for the custom dialects, no machine-checked proofs of the lowering rules, and no systematic validation (e.g., differential testing against reference simulators or comparison to independently verified translations). This assumption is stated in the abstract and the architecture description but left unaddressed in the provided examples.

    Authors: We acknowledge that the manuscript does not include formal semantics definitions for the custom dialects or machine-checked proofs of the lowering rules. The pipeline extends established MLIR dialects (e.g., arith, scf, hw) whose semantics are documented in the MLIR ecosystem, and the lowering passes to SMT-LIB, BTOR2, and AIGER are implemented to maintain behavioral equivalence by construction for the supported operations. The examples demonstrate end-to-end equivalence on datapath designs, providing empirical evidence rather than exhaustive validation. To strengthen this, we will add a new subsection discussing semantic preservation arguments based on the dialect extensions and include differential testing results against reference simulators for the presented examples. revision: partial

  2. Referee: The evaluation demonstrates feasibility on datapath designs but reports no quantitative results on verification success rates, scalability limits, or direct comparisons to existing equivalence checkers. Without such data in the results section, it is difficult to assess whether the unified pipeline delivers practical advantages over ad-hoc translations.

    Authors: The evaluation section prioritizes demonstrating the unification of multiple source languages and abstraction levels, which is the core contribution, rather than performance benchmarking. Quantitative data such as translation and solving times for the examples can be extracted from the current implementation. We will incorporate these metrics into the results section along with a discussion of observed scalability on the datapath designs. Direct comparisons to existing tools are inherently limited because no single prior tool supports the same range of entry points (PyTorch through netlists); we will add a qualitative comparison table highlighting this distinction. revision: yes

Circularity Check

0 steps flagged

No circularity: systems description of MLIR pipeline with no derivations or self-referential claims

full rationale

The paper describes an end-to-end tool architecture that lowers multiple hardware/software entry points through custom MLIR dialects to SMT-LIB/BTOR2/AIGER for pairwise equivalence checking. No equations, fitted parameters, predictions, or first-principles derivations appear in the provided text or abstract. The central claim is feasibility of the translation pipeline demonstrated on datapath examples; semantic preservation is stated as an operating assumption rather than derived from any internal definition or self-citation chain. No load-bearing steps reduce to inputs by construction, satisfying the criteria for a score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a systems/tool paper. No free parameters, mathematical axioms, or invented entities are introduced; the approach rests on the standard semantics of MLIR and existing formal verification back-ends.

pith-pipeline@v0.9.0 · 5483 in / 1161 out tokens · 50714 ms · 2026-05-10T07:55:47.208206+00:00 · methodology

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Reference graph

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