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Journal of the ACM (JACM)
On the significance of the directed acyclic word graph in cryptology
AUSCRYPT '90 Proceedings of the international conference on cryptology on Advances in cryptology
On the construction of run permuted sequences
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
The shortest feedback shift register that can generate a given sequence
CRYPTO '89 Proceedings on Advances in cryptology
Synthesis of parallel binary machines
Proceedings of the International Conference on Computer-Aided Design
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In this paper we extend the theory of maximum order complexity from a single sequence to an ensemble of sequences. In particular, the maximum order complexity of an ensemble of sequences is defined and its properties discussed. Also, an algorithm is given to determine the maximum order complexity of an ensemble of sequences linear in time and memory. It is also shown how to determine the maximum order feedback shift register equivalent of a given ensmble of sequences, i.e. including a feedback function. Hence, the problem of finding the absolutely shortest (possibly nonlinear) feedback shift register, that can generate two or more given sequences with characters from some arbitrary finite alphabet, is solved. Finally, the consequences for sequence prediction based on the minimum number of observations are discussed.