Definition
A run in a binary sequence is a set of consecutive 0s or 1s. A run of 0s is often denoted a 0-run or a gap and a run of 1s is often denoted a 1-run or a block. A gap of length k is a set of k consecutive 0s flanked by 1s. A block of length k is a set of k consecutive 1s flanked by 0s. A run of length k is a gap of length k or a block of length k.
Applications
The number of runs in a sequence is important in Golomb’s randomness postulates [1] to evaluate the randomness of a sequence.
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Golomb SW (1967) Shift register sequences. Holden-Day series in information systems. Holden-Day. San Francisco. Revised ed., Aegean Park Press, Laguna Hills
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Helleseth, T. (2011). Run. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_367
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DOI: https://doi.org/10.1007/978-1-4419-5906-5_367
Publisher Name: Springer, Boston, MA
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