Atomic Arbitrage Transactions

• Atomic Arbitrage transactions are indivisible multi-step operations that ensure either all trades execute successfully or none do, eliminating partial execution risks.
• They employ coordination contracts, state checkpointing, and BLS threshold signatures to enforce strict atomicity even in asynchronous and adversarial environments.
• These mechanisms underpin efficient arbitrage in DeFi and DEXes, reducing MEV risks and optimizing cross-chain and multi-market trades while addressing throughput tradeoffs.

Atomic Arbitrage (AA) transactions are indivisible multi-step operations—executed across one or more blockchains or markets—that guarantee either the successful completion of all constituent trades or the rollback of all, thereby eliminating the risks of partial execution. Originally conceptualized in the context of crosschain or multi-market asset swaps, AA transactions have become foundational to decentralized finance (DeFi), market design, and cross-domain interoperability as they enforce strong atomicity and consistency properties even in asynchronous, adversarial, or high-latency environments.

1. Formal Principles of Atomic Arbitrage Transactions

AA transactions ensure “all-or-nothing” semantics in arbitrage, codified by the requirement that for a composite operation $T$ with sub-actions $\{S_1, S_2, \ldots, S_n\}$ across $n$ markets or blockchains,

$$A(T) = \begin{cases} \text{commit} & \text{if } \bigwedge_{i=1}^{n} S_i \text{ commits} \ \text{rollback} & \text{else} \end{cases}$$

as formalized in (Robinson et al., 2020) and (Robinson et al., 2020). These semantics are essential for markets where any exposure induced by non-atomic multi-step arbitrage can lead to significant adversarial risk—specifically, price slippage, partial fills, or race conditions with other market participants.

In contemporary smart contract environments, atomicity is achieved via explicit transaction locking, state checkpointing, or design patterns such as “commit/abort” phases, often utilizing multi-chain coordination contracts or threshold signature schemes (e.g., BLS signatures as in (Robinson et al., 2020)). The mathematics of the protocol guarantee safety (no inconsistent or partially executed state is reachable) and liveness (all locks are eventually resolved via commit or abort, see (Robinson et al., 2020)).

2. Core Technical Architectures and Protocols

2.1 Cross-Chain Atomicity Mechanisms

• Coordination Contracts and Locking: A coordination contract on a designated blockchain (the “coordination blockchain”) orchestrates the entire crosschain transaction, defining a global timeout ($B_\text{timeout} = B_\text{start} + \Delta$) and maintaining the state (Started, Committed, Ignored) (Robinson et al., 2019, Robinson et al., 2020).
• Locking Semantics: Each affected contract maintains a lock status,

$$L = \begin{cases} 1, & \text{if } \text{State} = \text{Started} \wedge B_\text{current} \leq B_\text{timeout} \ 0, & \text{otherwise} \end{cases}$$

ensuring contracts are intransigent until a global commit/ignore (Robinson et al., 2019).

• BLS Threshold Signatures: Validators on each blockchain use threshold signatures to jointly attest to readiness and outcomes, producing a single combinatorial signature ($\sigma = \operatorname{Combine}(\{\sigma_i\})$) as authoritative evidence for crosschain progress (Robinson et al., 2020).
• Witness Networks: Protocols like AC³WN (Zakhary et al., 2019) enhance atomicity by employing a permissionless network of witnesses mediating a “global commit” decision, decoupling individual steps’ deadlines and allowing resilience to asynchronous/split-brain events.

2.2 Advanced Transaction Models

• Call Execution Trees: General frameworks (e.g., GPACT in (Robinson et al., 2020)) represent multi-chain atomic operations as rooted execution trees, with provisional updates at each “segment” and a signaling phase governing final commit/abort.
• Algebraic Topology Abstraction: An alternative is the algebraic-topological “simplicial complex” model (Zhao, 2020), in which an AA transaction is a high-dimensional simplex linking all participating ledgers, with atomicity enforced by the topology: the simplex is only “filled” if all faces succeed.

Protocol/Model	Atomicity Guarantee	Coordination Mechanism
Coordination Contract	Strong (timeout-based rollback)	Central contract + locks
AC³WN Witness Network	Strong (witness-based)	Open network consensus
Simplicial Complexes	Strong (topological)	Protocols over simplex structure
GPACT	Strong (tree-structured)	Start/Segment/Root/Signalling

3. Implementation in Practice: DeFi and DEXes

AA transactions underpin the most sophisticated forms of arbitrage in decentralized exchanges (DEXes), especially under the Automated Market Maker (AMM) paradigm.

3.1 Cyclic Arbitrage and Smart Contract Atomicity

In DEXes such as Uniswap V2 (Wang et al., 2021), cyclic arbitrage is implemented by chaining swaps across pools (A₁ → A₂ → ⋯ → Aₙ → A₁) within a single on-chain atomic transaction. Arbitrage is only possible if: $$\frac{a_{2,1} a_{3,2} \dots a_{1,n}}{a_{1,2} a_{2,3} \dots a_{n,1}} > \frac{1}{r_1^n r_2^n}$$ with $a_{i,j}$ denoting reserves and $r_k$ the fee-adjustment factors.

Optimal input volumes $\delta_1^{(\text{op})}$ maximize net return, and atomicity ensures that either all swaps execute at the initial observed prices, or none do—protecting the arbitrageur from price impact caused by external trades during execution. Empirically, over 99.9% of DEX cyclic arbitrages are executed atomically, minimizing the high failure rate and negative outcomes associated with sequential strategies (Wang et al., 2021).

3.2 On-Chain Integrations: Automated Arbitrage Market Makers (A2MM)

Protocols like A2MM (Zhou et al., 2021) integrate routing and arbitrage across multiple underlying AMMs within one atomic smart contract call. This approach batch-executes swaps and price-leveling arbitrage pathways, reducing redundant network traffic, mitigating MEV extraction via frontrunning/sandwich attacks, and lowering transaction costs—as measured by empirical reductions of up to 32.8% block-space and 90% swap fees.

4. Performance, Scalability, and Tradeoffs

The cryptographic and coordination overhead associated with AA transactions manifests as a significant reduction in system throughput (Robinson, 2020). For instance, on Hyperledger Besu, aggregate tps drops from 375 to 39.5 for crosschain atomicity scenarios where BLS pairing verifications and extra signaling transactions dominate processing. However, distributing the role of coordinators or optimizing signature aggregation can yield higher throughput (approaching 65 tps or more in non-coordinating nodes).

These cost factors must be weighed against the risk elimination AA transactions provide; for latency-sensitive, high-frequency arbitrage, the impact can be material and informs decisions on batching, consensus-layer integration, or hardware acceleration.

5. Extensions: Emerging Contexts and Limitations

5.1 Layer 2, Cross-Rollup, and Shared Sequencing

On Layer-2 (L2) rollups, atomic arbitrage remains challenging due to execution risk and timing mismatch across domains. Non-atomic arbitrage is subject to price drifts during execution, necessitating metrics such as Loss Versus Rebalancing (LVR) to quantify arbitrage opportunity and prevent double counting opportunities persisting over multiple blocks (Gogol et al., 4 Jun 2024). Under atomic execution, the window for opportunity narrows to a single point, and the realized maximal arbitrage value per block more closely tracks theoretical upper bounds.

However, atomicity is not uniformly profit-maximizing: models show that under certain failure probability regimes, atomic bundling can actually reduce expected arbitrage profits compared to non-atomic strategies, since partial execution against an external reference price may sometimes be more advantageous (Silva et al., 15 Oct 2024). This subtlety is central in the design of shared sequencer systems.

5.2 Beyond AMMs: DAOs, Prediction Markets, and Grassroots Systems

AA transaction concepts generalize to a wide range of domains:

• DAOs and Speculative Exits: In repeated auction models for governance tokens, “atomic exits” (where instant forks are allowed) enable arbitrageurs to immediately redeem treasury value, mandating careful design in DAO governance to disincentivize speculative exploitation (Eschenbaum et al., 27 May 2025).
• Prediction Markets: In platforms like Polymarket (Saguillo et al., 5 Aug 2025), atomic (multi-market, position-balanced) arbitrage exploits mispricing among semantically linked outcome tokens, with empirical evidence of over $40M in realized profits. Market rebalancing and combinatorial arbitrage are computationally detected using heuristic reductions from$O(2^{n+m})</sup>comparisons,leveragingLLMsandsemanticclustering.</li><li><strong>GrassrootsPlatforms</strong>:Indistributedtransitionsystems(<ahref="/papers/2502.11299"title=""rel="nofollow"data−turbo="false"class="assistant−link"x−datax−tooltip.raw="">Shapiro,16Feb2025</a>),atomictransactionsaredefinedasclosure−preserving,multi−agentupdateswithwell−specifiedinvariants,encompassingbothassetswapsandarbitrageoperations.</li></ul><h3class=′paper−heading′id=′high−frequency−and−near−instant−cross−chain−arbitrage′>5.3High−FrequencyandNear−InstantCross−ChainArbitrage</h3><p>Emergingprotocolsusingpre−signedadaptorsignaturesandPTLCsratherthanHTLCsenableatomicswapsbetweenchainswithexecutiontimesreducedtoapproximately15seconds—and,withLayer2extensions,potentiallyaslowas2seconds(<ahref="/papers/2503.12719"title=""rel="nofollow"data−turbo="false"class="assistant−link"x−datax−tooltip.raw="">Francollaetal.,17Mar2025</a>).ThisallowsHFTstrategiesondecentralizedrails,significantlyreducingexposuretointerimpricemovementsandcompressingarbitragespreads.</p><h2class=′paper−heading′id=′identification−searcher−dynamics−and−mev−implications′>6.Identification,SearcherDynamics,andMEVImplications</h2><p>AAtransactionsaresystematicallyidentifiedbyconditionssuchas:</p><ul><li>Multi−swapinclusion(</sup> comparisons, leveraging LLMs and semantic clustering.</li> <li><strong>Grassroots Platforms</strong>: In distributed transition systems (<a href="/papers/2502.11299" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Shapiro, 16 Feb 2025</a>), atomic transactions are defined as closure-preserving, multi-agent updates with well-specified invariants, encompassing both asset swaps and arbitrage operations.</li> </ul> <h3 class='paper-heading' id='high-frequency-and-near-instant-cross-chain-arbitrage'>5.3 High-Frequency and Near-Instant Cross-Chain Arbitrage</h3> <p>Emerging protocols using pre-signed adaptor signatures and PTLCs rather than HTLCs enable atomic swaps between chains with execution times reduced to approximately 15 seconds—and, with Layer 2 extensions, potentially as low as 2 seconds (<a href="/papers/2503.12719" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Francolla et al., 17 Mar 2025</a>). This allows HFT strategies on decentralized rails, significantly reducing exposure to interim price movements and compressing arbitrage spreads.</p> <h2 class='paper-heading' id='identification-searcher-dynamics-and-mev-implications'>6. Identification, Searcher Dynamics, and MEV Implications</h2> <p>AA transactions are systematically identified by conditions such as:</p> <ul> <li>Multi-swap inclusion (N \geq 2$)
• Non-negative net asset change for each asset (sufficiency)
• Positive net profit versus transaction and bidding costs (Vostrikov et al., 29 Aug 2025)

On platforms such as Polygon, searcher behavior—spanning both spam-based and auction-based transaction ordering strategies—reveals the evolving economics of AA. Spam-based approaches contribute to congestion and lower average MEV per transaction; auction-based mechanisms such as FastLane achieve higher profit with greater network efficiency (Vostrikov et al., 29 Aug 2025). The dynamic raises concerns regarding fairness, centralization (validators capturing fees), and calls for protocol innovation in transaction ordering and intent-based bundling.

Strategy Type	Prevalence	MEV Extraction Efficiency
Spam-Based	High	Lower per transaction
Auction-Based	Growing	Higher per transaction

The emergence of composable solvers—bundling all available operations into a single atomic transaction—may ultimately reduce the MEV landscape to a contest over blockspace and protocol-level prioritization, fundamentally shifting incentives.

7. Mathematical and Theoretical Perspectives

Beyond implementation, the theoretical apparatus for AA leverages formal atomicity conditions found in distributed systems, such as strict serializability, write-ahead logging, checkpoint-restore semantics, and (in markets with concave transaction costs) asymptotic arbitrage over sequences of discrete trades (Rygiel et al., 30 Sep 2024, Shapiro, 16 Feb 2025). Algebraic-topological representations provide alternative rigor for modeling multi-party agreements as high-dimensional complexes, ensuring that all internal dependencies are respected.

Summary

Atomic Arbitrage transactions provide a mathematically and operationally robust solution for carrying out riskless multi-domain financial operations, enforcing strong atomicity guarantees across blockchains, markets, and computational contexts. Their implementation underpins market efficiency, fair MEV extraction, and interoperability in decentralized systems, while introducing new tradeoffs relating to system throughput, complexity, and economic incentives. Theoretical and practical research continues to refine these mechanisms, tailoring them to evolving network architectures, market structures, and application domains.