This paper shows a method to represent interval functions by using head-tail expressions. The head-tail expressions represent
greater-than GT(
X:
A) functions,
less-than LT(
X:
B) functions, and interval functions
IN0(
X:
A,
B) more efficiently than sum-of-products expressions. Let
n be the number of bits to represent the largest value in the interval (
A,
B). This paper proves that a head-tail expression (HT) represents an interval function with at most
n words in a ternary content addressable memory (TCAM) realization. It also shows the average numbers of factors to represent interval functions by HTs for up to
n=16, which were obtained by a computer simulation. It also conjectures that, for sufficiently large
n, the average number of factors to represent
n-variable interval functions by HTs is at most 2/3
n-5/9. Experimental results also show that, for n≥10, to represent interval functions, HTs require at least 20% fewer factors than MSOPs, on the average.
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