MINIMAL NON-INTEGER ALPHABETS ALLOWING PARALLEL ADDITION

Authors

  • Jan Legerský Research Institute for Symbolic Computation, Johannes Kepler University, Altenbergerstra{\ss}e 69, A-4040 Linz, Austria Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Czech Republic http://orcid.org/0000-0002-8122-668X

DOI:

https://doi.org/10.14311/AP.2018.58.0285

Keywords:

numeration system, parallel addition, minimal alphabet

Abstract

Parallel addition, i.e., addition with limited carry propagation has been so far studied for complex bases and integer alphabets. We focus on alphabets consisting of integer combinations of powers of the base. We give necessary conditions on the alphabet allowing parallel addition. Under certain assumptions, we prove the same lower bound on the size of the generalized alphabet that is known for alphabets consisting of consecutive integers. We also extend the characterization of bases allowing parallel addition to numeration systems with non-integer alphabets.

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Published

2018-10-31

How to Cite

Legerský, J. (2018). MINIMAL NON-INTEGER ALPHABETS ALLOWING PARALLEL ADDITION. Acta Polytechnica, 58(5), 285–291. https://doi.org/10.14311/AP.2018.58.0285

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Articles