Characterizing Arithmetic Read-Once Formulae
نویسندگان
چکیده
منابع مشابه
How Do Read-Once Formulae Shrink?
Let f be a de Morgan read-once function of n variables. Let f " be the random restriction obtained by independently assigning to each variable of f, the value 0 with probability (1 ? ")=2, the value 1 with the same probability, and leaving it unassigned with probability ". We show that f " depends, on the average, on only O(" n + "n 1==) variables, where = log p 5?1 2 ' 3:27. This result is asy...
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We give an alternative proof to a characterization theorem of Gurvich for Boolean functions whose formula size is exactly the number of variables. Those functions are called Read-Once. We use methods of combinatorial optimization and give as a corollary an alternative proof for some results of Seymour.
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Moore and Shannon have shown that relays with arbitrarily high reliability can be built from relays with arbitrarily poor reliability. Valiant used similar methods to construct monotone read-once formulae of size O(n +2) (where = log p 5?1 2 ' 3:27) that amplify (? 1 n ; + 1 n) (where = p 5?1 2 ' 0:62) to (2 ?n ; 1 ? 2 ?n) and deduced as a consequence the existence of monotone formulae of the s...
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A formula is read-once if each variable appears at most once in it. An arithmetic read-once formula is one in which the operations are addition, subtraction, multiplication, and division (and constants are allowed). We present a randomized (Las Vegas) parallel algorithm for the exact interpolation of arithmetic read-once formulas over suuciently large elds. More speciically, for n-variable read...
متن کاملOn the Communication Complexity of Read-Once AC Formulae
We study the 2-party randomized communication complexity of read-once AC formulae. For balanced AND-OR trees T with n inputs and depth d, we show that the communication complexity of the function f (x, y) = T (x◦y) is Ω(n/4) where (x◦y)i is defined so that the resulting tree also has alternating levels of AND and OR gates. For each bit of x, y, the operation ◦ is either AND or OR depending on t...
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ژورنال
عنوان ژورنال: ACM Transactions on Computation Theory
سال: 2016
ISSN: 1942-3454,1942-3462
DOI: 10.1145/2858783