A Is an Integer Valued Symmetric Matrix

We first observe that if Oj Z, f = 1, 2. n, then, for all Vi Z, aiVi [2 ] if and only if aiVi [2 ] — where (2 ] is the least integer greater than or equal to X. This means that if A is an integer matrix, we can always assume that the individual components of the threshold vector h are of the form bi = Zi +, Zi Z. Using this form for 6, we see from equation 5.129 that 

Corollary 1 [goles87a] If A is an n x n integer-valued symmetric matrix, then the transient length of the generalized threshold rule defined in equation 5.121 is bounded by 

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