Building consensus sequences based on distributed, fault-tolerant consensus, as used for replicated state machines, typically requires a separate distributed state for every new consensus instance. Allocating and maintaining this state causes significant overhead. In particular, freeing the distributed, outdated states in a fault-tolerant way is not trivial and adds further complexity and cost to the system. In this paper, we propose an extension to the single-decree Paxos protocol that can learn a sequence of consensus decisions 'in-place', i.e. with a single set of distributed states. Our protocol does not require dynamic log structures and hence has no need for distributed log pruning, snapshotting, compaction, or dynamic resource allocation. The protocol builds a fault-tolerant atomic register that supports arbitrary read-modify-write operations. We use the concept of consistent quorums to detect whether the previous consensus still needs to be consolidated or is already finished so that the next consensus value can be safely proposed. Reading a consolidated consensus is done without state modifications and is thereby free of concurrency control and demand for serialisation. A proposer that is not interrupted reaches agreement on consecutive consensus decisions within a single message round-trip per decision by preparing the acceptors eagerly with the previous request.

General solutions of state machine replication have to ensure that all replicas apply the same commands in the same order, even in the presence of failures. Such strict ordering incurs high synchronization costs caused by distributed consensus or by the use of a leader. This paper presents a protocol for linearizable state machine replication of con ict-free replicated data types (CRDTs) that neither requires consensus nor a leader. By leveraging the properties of state-based CRDTs-in particular the monotonic growth of a join semilattice-synchronization overhead is greatly reduced. In addition, updates just need a single round trip and modify the state 'in-place' without the need for a log. Furthermore, the message size overhead for coordination consists of a single counter per message. While reads in the presence of concurrent updates are not wait-free without a coordinator, we show that more than 97 % of reads can be handled in one or two round trips under highly concurrent accesses.Our protocol achieves high throughput without auxiliary processes like command log management or leader election. It is well suited for all practical scenarios that need linearizable access on CRDT data on a ne-granular scale.

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