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On complexity of realisation of a class of almost symmetric functions by formulas of depth 3
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S. E. Cherukhina
Published/Copyright:
May 27, 2008
Abstract
We consider the class of almost symmetric Boolean functions. For any function of this class, the values on all tiers except the second one coincide with the values of a monotone symmetric function with threshold 3. The values on the second tier are arbitrary. We study realisation of functions of this class by & ∨ &- formulas over the basis {&, ∨}.
We obtain a sharp bound for the minimum complexity of the functions of this class (the function of minimum complexity is explicitly written out) and an asymptotic estimate of complexity of a monotone symmetric function with threshold 3 which is maximal in order of complexity in the class under consideration.
Received: 2005-12-19
Published Online: 2008-05-27
Published in Print: 2008-May
© de Gruyter 2008
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Articles in the same Issue
- On approximation with given accuracy of functions of k-valued logic by polynomials
- On complexity of realisation of a class of almost symmetric functions by formulas of depth 3
- On complexity of linear operators on the class of circuits of depth 2
- On the complexity of decoding Boolean cube splitting into cube faces
- Some characteristics of dependencies in discrete random sequences
- On random 2-adjacent 0/1-polyhedra
- The intersection number of complete r-partite graphs
- On Mazurov triples of the sporadic group B and Hamiltonian cycles of the Cayley graph
- Malcev rings
