Diagnostic tests for discrete functions defined on rings
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Grigoriy V. Antyufeev
Abstract
The paper is concerned with sources of faults associated with commutative principal ideal rings. Tables of faults of such sources are known to correspond to Cayley multiplication tables in rings, whose elements are replaced by the values of a Boolean function of these elements. For such rings, the concepts of a diagnostic test and the Shannon function for the length of a diagnostic test are introduced in a natural way. It is shown that if A is a principal ideal ring with only one prime ideal p ≠ A, and if pn = 0 for some n ∈ ℕ, then, for this ring, the Shannon length function of a diagnostic test has the form Ldiagn(A, n) = Θ(n). We also define an easily testable functions, i.e., a function with respect to which the order of growth of the length of a diagnostic test with respect to this function is equal to the logarithm of the number of pairwise distinct columns of the table of faults. A link between easily testable functions and column separation of tables of faults for two concrete sources of faults is established.
Note: Originally published in Diskretnaya Matematika (2021) 33,№1, 3–11 (in Russian).
References
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Articles in the same Issue
- Frontmatter
- Diagnostic tests for discrete functions defined on rings
- New lower bound for the minimal number of edges of simple uniform hypergraph without the property Bk
- On some invariants under the action of an extension of GA(n, 2) on the set of Boolean functions
- On some limit properties for the power series distribution
- Estimates of lengths of shortest nonzero vectors in some lattices. I
Articles in the same Issue
- Frontmatter
- Diagnostic tests for discrete functions defined on rings
- New lower bound for the minimal number of edges of simple uniform hypergraph without the property Bk
- On some invariants under the action of an extension of GA(n, 2) on the set of Boolean functions
- On some limit properties for the power series distribution
- Estimates of lengths of shortest nonzero vectors in some lattices. I
