Abstract
Membrane systems represent a new abstract model inspired by cell biology. This new model works with multisets. In this paper we deal with various number encodings over multisets. We present the natural encoding and a most compact encoding, and study their properties using elements of combinatorics over multisets. We construct the membrane systems implementing the arithmetic operations using these encodings. For each encoding and operation we present its complexity. With respect to their complexity, we compare the encodings and we remark a transfer from the usual encoding lengths and time complexities of order log b n to lengths and complexities of order \(^b\sqrt{n}\).
Work partially supported by the CEEX Programme, project “ForMol” 47/2005
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Bonchiş, C., Ciobanu, G., Izbaşa, C. (2006). Encodings and Arithmetic Operations in Membrane Computing. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_59
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DOI: https://doi.org/10.1007/11750321_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34021-8
Online ISBN: 978-3-540-34022-5
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