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تسجيل مستخدم جديدOn Consistency of Operational Transformation Approach
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Aurel Randolph
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The Operational Transformation (OT) approach, used in many collaborative editors, allows a group of users to concurrently update replicas of a shared object and exchange their updates in any order. The basic idea of this approach is to transform any received update operation before its execution on a replica of the object. This transformation aims to ensure the convergence of the different replicas of the object, even though the operations are executed in different orders. However, designing transformation functions for achieving convergence is a critical and challenging issue. Indeed, the transformation functions proposed in the literature are all revealed incorrect. In this paper, we investigate the existence of transformation functions for a shared string altered by insert and delete operations. From the theoretical point of view, two properties - named TP1 and TP2 - are necessary and sufficient to ensure convergence. Using controller synthesis technique, we show that there are some transformation functions which satisfy only TP1 for the basic signatures of insert and delete operations. As a matter of fact, it is impossible to meet both properties TP1 and TP2 with these simple signatures.
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OT (Operational Transformation) was invented for supporting real-time co-editors in the late 1980s and has evolved to become a core technique used in todays working co-editors and adopted in major industrial products. CRDT (Commutative Replicated Dat
a Type) for co-editors was first proposed around 2006, under the name of WOOT (WithOut Operational Transformation). Follow-up CRDT variations are commonly labeled as post-OT techniques capable of making concurrent operations natively commutative in co-editors. On top of that, CRDT solutions have made broad claims of superiority over OT solutions, and routinely portrayed OT as an incorrect, complex and inefficient technique. Over one decade later, however, OT remains the choice for building the vast majority of co-editors, whereas CRDT is rarely found in working co-editors. Contradictions between the reality and CRDTs purported advantages have been the source of much confusion and debate in co-editing communities. Have the vast majority of co-editors been unfortunate in choosing the faulty and inferior OT, or those CRDT claims are false? What are the real differences between OT and CRDT for co-editors? What are the key factors and underlying reasons behind the choices between OT and CRDT in the real world? To seek truth from facts, we set out to conduct a comprehensive and critical review on representative OT and CRDT solutions and working co-editors based on them. From this work, we have made important discoveries about OT and CRDT, and revealed facts and evidences that refute CRDT claims over OT on all accounts. We report our discoveries in a series of three articles and the current article is the first one in this series. We hope the discoveries from this work help clear up common misconceptions and confusions surrounding OT and CRDT, and accelerate progress in co-editing technology for real world applications.
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rtant tool to save time and cost when exploring the identification capability of quantum probes and experimentally implementing quantum identification schemes. In this paper, we generalize the identifiability test based on the Similarity Transformation Approach (STA) in classical control theory and extend it to the domain of quantum Hamiltonian identification. We employ STA to prove the identifiability of spin-1/2 chain systems with arbitrary dimension assisted by single-qubit probes. We further extend the traditional STA method by proposing a Structure Preserving Transformation (SPT) method for non-minimal systems. We use the SPT method to introduce an indicator for the existence of economic quantum Hamiltonian identification algorithms, whose computational complexity directly depends on the number of unknown parameters (which could be much smaller than the system dimension). Finally, we give an example of such an economic Hamiltonian identification algorithm and perform simulations to demonstrate its effectiveness.
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