Shared Sequencers in Distributed Systems

• Shared sequencers are mechanisms that impose a global ordering on events to maintain consistency and fairness in multi-agent and distributed environments.
• They optimize resource management and enable atomic execution in diverse systems, from concurrent programming models to high-throughput blockchain rollups.
• Research focuses on probabilistic synchronization, cryptographic verification, and incentive designs to balance performance, decentralization, and security.

A shared sequencer is a mechanism, protocol, or architectural component that enforces or exposes global ordering of events, actions, or transactions across multiple agents, threads, chains, or distributed systems. In contemporary computer systems, shared sequencers are essential primitives for consistency, atomicity, fairness, cross-domain composability, and efficient resource management. The design, analysis, and implementation of shared sequencers span concurrency theory, distributed systems, cryptographic protocol engineering, market mechanism design, and blockchain scaling solutions. Approaches to shared sequencing differ fundamentally by their treatment of resource contention, fault tolerance, randomness, probabilistic synchronization, and their trade-offs between performance, decentralization, and security.

1. Fundamental Concepts and Theoretical Models

Shared sequencing solves ordering in multi-agent or multi-resource environments where concurrent actions may cause contention, observable races, or require atomic visibility. In concurrency-theoretic language, shared sequencers restrict the partial order on actions by introducing a global schedule. In distributed systems and blockchains, shared sequencers facilitate composable execution (e.g., atomic cross-chain swaps) and fair ordering, mitigating front-running and censorship risk.

Formally, the sequentialization of parameterized concurrent programs (Torre et al., 2012) is founded upon the linear interface abstraction. A "linear interface" between rounds in a multi-process system is a mapping:

$$(\overline{u}, \overline{v}) = ((u_1, \dots, u_k), (v_1, \dots, v_k))$$

where $u_i$ and $v_i$ are shared states at round $i$'s entry and exit, respectively. This abstraction enables a transformation where only one thread's local state is tracked and only $O(k)$ copies of the shared state are needed, eliminating extra counters and non-reachable states.

Randomized and probabilistic sequencing models, such as synchronization of Bernoulli sequences on shared letters (Abbes, 2015), formalize the synchronization of randomized local actions across shared alphabets using trace monoid theory. The probability of a global trace $x = x_1 x_2 \ldots x_k$ is:

$\Pr(\uparrow x) = \prod_{\ell=1}^k t_{x_\ell}$

where

$t_a = \prod_{i \in R(a)} p_i(a)$

and $R(a)$ maps resource-sharing multiplicities.

Coordination via shared randomness (Kurri et al., 2019) quantifies communication rates to achieve distributed sampling under various access models, capturing information-theoretic limits (Wyner’s common information, total and dual total correlation), and showing the operational role for shared randomness in reducing coordination cost for distributed sequencers.

2. Assertion-Preserving Transformation and Resource Management

Assertion-preserving sequencing protocols are "lazy": they only simulate or expose reachable states of the concurrent system, thus ensuring that all preserved invariants and reachability conditions are maintained (e.g., error states in the original concurrent shared-memory program map precisely to error states in the sequentialized version). Recursive simulation and join-checks enforce the structural invariance of sequentialized execution. Resource management is optimized: only a single thread's local variables and $O(k)$ global state copies are held at any time, making it practical for large, parameterized systems.

Contrasted with whole-system replication or naive eager approaches, which can consider unreachable (spurious) states and require unbounded resources, assertion-preserving sequentialization enables scalable verification via reduction to the analysis of sequential programs, as demonstrated on device driver models.

3. Distributed Synchronization, Randomness, and Incrementality

Distributed shared sequencers may operate asynchronously or deterministically but typically rely on synchronized primitives (local clocks, pseudorandom sequences, or coordinating protocols).

Under probabilistic synchronization (Abbes, 2015), distributed agents generate local Bernoulli (or weighted random) sequences, which are incrementally stitched into global traces by online algorithms. Two central algorithms are the Probabilistic Synchronization Algorithm (PSA) and Probabilistic Full Synchronization Algorithm (PFSA). PSA is suited to linear (path) topologies; PFSA is required to circumvent deadlocks in cyclic (ring) topologies, using trial-and-reject strategies and first-hitting-time distributions (pyramidal heaps) to maintain statistical independence.

In settings where distributed agents coordinate via shared randomness (Kurri et al., 2019), optimal transmission and sampling performances are achieved by leveraging output statistics of random binning, network coding, and diverse access models: omniscient, oblivious, individually shared, “randomness-on-the-forehead,” and correlated sources. Fundamental bounds for optimal communication rates are provided, e.g.,

$$R_{\mathrm{opt}} = \min_{p(u|x,y)} \max \{ I(X; Y | U), \tfrac{1}{2}[I(X,Y;U) + I(X;Y|U)] \}$$

and region characterizations for multi-processor simulation.

4. Shared Sequencers in High-Throughput and Cryptographic Devices

Shared sequencer architectures underpin high-performance implementations such as ThundeRiNG (Tan et al., 2021), which uses a single, resource-intensive root state generator and many lightweight leaf state output units (SOUs) on FPGA; these SOUs receive offsets and permutation to decorrelate output streams. Decorrelation exploits XOR fusion with secondary pseudo-random sources, with Yao’s XOR lemma justifying multiplicative diminution of correlation coefficients:

$|\rho_Z| \approx |\rho_X| \cdot |\rho_{I,J}|$

Scalability is achieved with constant DSP usage for hundreds (to thousands) of simultaneous sequences.

Cellular automata-based generators (Cardell, 23 Jun 2025) produce multiple interleaved (shared) high-quality sequences via vertical column reads of evolved CA. Interleaving $t$ shifted PN-sequences yields period $T \leq 2^t (2^L-1)$ and linear complexity $LC \leq 2^t L$. Regular cyclic and hybrid CA (rules 102, 60, 150, 90) provide parallelism, structural regularity, and robust cryptographic properties for parallel shared keystream generation, with Zech logarithms enabling precise algebraic control over shift and combination.

5. Shared Sequencers in Blockchain, Smart Contracts, and Rollup Architectures

Blockchain scaling relies on sequencer infrastructure to maintain throughput and fairness under decentralization, as articulated in studies of decentralized and shared sequencer networks for rollups (Motepalli et al., 2023). The property framework encompasses liveness, Byzantine fault tolerance ($n = 3f + 1$), fairness, and atomic cross-rollup composability. Consensus protocols (HotStuff, Tendermint, DAGs) and committee selection (restaking, cryptographic sortition), alongside reward, data availability, and governance mechanisms, structure the evolving architecture of sequencer networks.

In Sui smart contracts (Overko, 21 Jun 2024), shared objects (as opposed to owned objects) necessitate consensus-based sequencing. Metrics such as density (fraction of total transactions involving shared objects) and contention degree quantify operational workloads. Case studies reveal extensive use (density values up to 0.9) but overall low contention, supporting scalable multi-writer primitives with manageable overhead.

Formal models of atomic composability (Sarkar, 2023) introduce structured operations (publish, buffer, resolve, verify) and cryptographic primitives (zk-SNARKs/STARKs) to ensure atomic cross-rollup execution, with shared sequencers integrated as off-chain orderers feeding into decentralized validation. Timestamp constraints and buffer management underpin concurrency control, ensuring resilience against manipulation. However, complexity and centralization risks remain.

6. Market Mechanism Design, MEV, and Sequencer Economics

Economic analysis of shared sequencing (Mamageishvili et al., 2023) elucidates incentive and efficiency trade-offs in cross-chain arbitrage and MEV extraction. Under First Come First Serve (FCFS), shared sequencing increases arbitrage realization probability but induces more aggressive (and wasteful) latency investment:

$$C'(s^*) = f(0) v\, \text{(shared)} \quad \text{vs.}\quad C'(s^*) = f(0) v/2\, \text{(separate)}$$

For bidding-based ordering (e.g., TimeBoost), equilibrium bid and protocol revenue depend intricately on cost function curvature, cap parameters, and arbitrage value. Contrary to expectation, shared sequencing does not always increase protocol revenue and under some regimes separate sequencing yields higher revenue.

Atomic execution in shared sequencers (Silva et al., 15 Oct 2024) may further reduce arbitrage profits by eliminating "half-success" cases available in non-atomic execution of cross-rollup swaps, especially under intermediate failure probabilities and partial execution. Thus, atomicity alone is insufficient for systematic MEV profit enhancement, implying that additional incentive or bridging properties are required.

7. Future Directions, Challenges, and Comparisons

Set-theoretic approaches (Setchain, grow-only sets) propose alternative models wherein only epoch boundaries are totally ordered, relaxing monolithic sequential consistency and offering dramatic throughput improvements for decentralized applications (Capretto et al., 8 Sep 2025). Byzantine-tolerant mechanisms and formal fraud-proof games (implemented in LEAN4) represent advanced security models for shared sequencer and data availability committee operations, focusing on pred-etermined algorithms and mechanized correctness proofs rather than generic transaction validity.

A plausible implication is that the future evolution of shared sequencers will involve hybrid designs combining assertion-preserving sequentialization, distributed randomness/coordination, cryptographic verification, and market-compatible incentive mechanisms. Integration into multi-rollup and cross-chain systems is constrained by centralization risks, protocol revenue trade-offs, and increasing operational complexity, demanding continued research in both foundational theory and scalable engineering.