Compact quadratizations for pseudo-Boolean functions
نویسندگان
چکیده
منابع مشابه
Quadratizations of symmetric pseudo-Boolean functions: sub-linear bounds on the number of auxiliary variables
The problem of minimizing a pseudo-Boolean function with no additional constraints arises in a variety of applications. A quadratization is a quadratic reformulation of the nonlinear problem obtained by introducing a set of auxiliary binary variables which can be optimized using quadratic optimization techniques. Using the well-known result that a pseudoBoolean function can be uniquely expresse...
متن کاملLocally monotone Boolean and pseudo-Boolean functions
We propose local versions of monotonicity for Boolean and pseudoBoolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if none of its partial derivatives changes in sign on tuples which differ in less than p positions. As it turns out, this parameterized notion provides a hierarchy of monotonicities for pseudo-Boolean (Boolean) functions. Local monotonicities are ...
متن کاملRepresenting Boolean Functions as Linear Pseudo-Boolean Constraints
A linear pseudo-Boolean constraint (LPB) is an expression of the form a1 · l1 + . . .+am · lm ≥ d, where each li is a literal (it assumes the value 1 or 0 depending on whether a propositional variable xi is true or false) and the a1, . . . , am, d are natural numbers. The formalism can be viewed as a generalisation of a propositional clause. It has been said that LPBs can be used to represent B...
متن کاملPermutation Independent Comparison of Pseudo Boolean Functions
We address the problem of permutation independent comparison of two pseudo Boolean functions given by multiplicative binary moment diagrams (∗Bmds), i. e., the problem of deciding whether there exists a permutation of the input variables such that the two ∗Bmds are equal. The analogous problem has already been investigated for binary decision diagrams (Bdds) in detail [5, 7, 8, 9, 10]. All thes...
متن کاملQuadratization of Symmetric Pseudo-Boolean Functions
A pseudo-Boolean function is a real-valued function f(x) = f(x1, x2, . . . , xn) of n binary variables; that is, a mapping from {0, 1}n to R. For a pseudo-Boolean function f(x) on {0, 1}n, we say that g(x, y) is a quadratization of f if g(x, y) is a quadratic polynomial depending on x and on m auxiliary binary variables y1, y2, . . . , ym such that f(x) = min{g(x, y) : y ∈ {0, 1}m} for all x ∈ ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2019
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-019-00511-0