A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Minimal polynomials for the conjunction of functions on disjoint variables can be very simple

1989
*
Information and Computation
*

ACKNOWLEDGMENTS We thank Hans Ulrich Simon who asked the second author (in different terminology) whether the DCSH(

doi:10.1016/0890-5401(89)90047-3
fatcat:erlme6eldfcvni3rwmro3zbgs4
*A*) holds for*minimal**polynomials*. ... The motivation for this question came from problems in the theory*of*learning within the field*of*artificial intelligence. March 14, 1988; ACCEPTED September 20, 1988 RECEIVED ...*Remark*. No explicit example is known*of**a**Boolean**function*f~ B, with C(f x f) < 2. C(f).*Remark*. ...##
###
On the Gap between the Complexity of SAT and Minimization for Certain Classes of Boolean Formulas

2014
*
International Symposium on Artificial Intelligence and Mathematics
*

It is also known that the decision version

dblp:conf/isaim/CepekG14
fatcat:kvypiio3orab7k6jzqpd2vhgka
*of**Boolean**minimization*for CNF inputs is Σ2 complete.*On*the other hand there are several subclasses*of*CNFs (e.g. ... Thus, for both the general case and the above mentioned subclasses the gap between the complexity*of*SAT and*minimization*is exactly*one*level in the*polynomial*hierarchy. ... The second author gratefully acknowledges the support*of*the Charles University Grant Agency (grant No. 1390213). ...##
###
Symbolic OBDD-Based Reachability Analysis Needs Exponential Space
[chapter]

2010
*
Lecture Notes in Computer Science
*

, y nn x j = (x j1 , . . . , x jn )

doi:10.1007/978-3-642-11266-9_19
fatcat:dibjikvj6rdhdmmwlysur2ibpu
*Boolean*encoding*of*index i j The number*of*x π(i) -nodes in the*minimal*π-OBDD for*a**Boolean**function*f is the number*of*different subfunctions f |x π(1) =b 1 ,... ... Idea:*A*π-OBDD for*a*subfunction*of**a**Boolean**function*f cannot be larger than*a*π-OBDD for f . ...*Polynomial*upper bound*on*the OBDD size*of*χ E (v i 1 ,...,in , v ℓ 1 ,... ...##
###
Minimization of pseudo-boolean functions by binary development

1974
*
Discrete Mathematics
*

An lteratlve method for zero-

doi:10.1016/s0012-365x(74)80026-9
fatcat:pcfbg2ckpbc2baofomoe33auy4
*one**minimization**of*integer*polynomials*, hnear m each variable, is outhned. ... It Js based*on*Camlon's method*of*binary developments with computations using multlphcatlon and sum mod 2. ... Rosenberg, Mmimlzatton*of*pseudo-*Boolean**functions**Remark*3.4. The*Boolean*functionsg I are expressed as*Boolean**polynomials*. ...##
###
On Quadratization of Pseudo-Boolean Functions
[article]

2014
*
arXiv
*
pre-print

We survey current term-wise techniques for quadratizing high-degree pseudo-

arXiv:1404.6538v1
fatcat:id55upbdhrdrdcrrjpwzabymya
*Boolean**functions*and introduce*a*new*one*, which allows multiple splits*of*terms. ... We also introduce the first aggregative approach, which splits*a*collection*of*terms based*on*their common parts. ...*One**of*the most frequently used technique is based*on*roof-duality [11] , and aims at finding in*polynomial*time*a*simpler form*of*the given quadratic*minimization*problem, by fixing some*of*the variables ...##
###
On quadratization of pseudo-Boolean functions

2012
*
International Symposium on Artificial Intelligence and Mathematics
*

In many applications

dblp:conf/isaim/BorosG12
fatcat:gml432m77jh55n6kun7vqljdjy
*of*pseudo-*Boolean*optimization the objective*function*(1) is*a*higher degree multilinear*polynomial*. ...*One**of*the most frequently used technique is based*on*roof-duality (Hammer, Hansen, and Simeone 1984) , and aims at finding in*polynomial*time*a*simpler form*of*the given quadratic*minimization*problem ...##
###
Horn functions and submodular boolean functions

1997
*
Theoretical Computer Science
*

After providing

doi:10.1016/s0304-3975(96)00202-2
fatcat:q5getvzelrabvd3afcenpvwyyu
*a*simple characterization*of*Horn*functions*(i.e., those*Boolean**functions*that have*a*Horn DNF), we study in detail the special class*of*submodular*functions*. ... There is*a**one*-to-*one*correspondence between the roots*of**a*submodular*function*and the ideals*of*the associated partial preorder. ... Acknowledgements The authors gratefully acknowledge the partial support by the Office*of*Naval Research (grants N0001492F1375 and N0001492F4083) and by the Air Force Office*of*Scientific Research (grant ...##
###
Reliability of Two-Stage Weighted-$bf k$-out-of-$n$Systems With Components in Common

2005
*
IEEE Transactions on Reliability
*

This paper extends the existing

doi:10.1109/tr.2005.853274
fatcat:bndh7t3ytbgplgupudd2neixi4
*one*-stage weighted--out-*of*-model to two-stage weighted-k-out-*of*-models with components in common. ... Reliability bounds for systems with -dependent component failures are investigated based*on*the generated*minimal*cuts &*minimal*paths. ... 1 The singular and plural*of*an acronym are always spelled the same. if it is*functioning**a*term*of**a*cut*polynomial*, which represents an -component*minimal*cut consisting*of*components .*a*term*of**a*...##
###
Efficient Determination of Gibbs Estimators with Submodular Energy Functions
[article]

2003
*
arXiv
*
pre-print

For that the decomposition

arXiv:math/0304041v1
fatcat:reidej2mpbdwnlkhgmp4lged4a
*of*the*functions*by*Boolean**polynomials*is used. The modified SFM algorithm for*minimization**of*submodular*Boolean**polynomials*is described. ... Combinatorial algorithms for*minimization**of**functions**of*many variables, which take their values in finite totally ordered sets, are developed. ... After we represent the*function*V (j) by*a**Boolean**polynomial*and then*minimize*the*polynomial*. ...##
###
Approximate evaluations of characteristic polynomials of Boolean functions

2001
*
Theoretical Computer Science
*

Let k( ; n) denote the

doi:10.1016/s0304-3975(00)00151-1
fatcat:ak4cawhrczcv3eq2662ntlbqkq
*minimal*number*of**Boolean**function*evaluations needed to reduce the initial error by*a*factor*of*where n is the number*of**Boolean*variables. ... Motivated by combinational circuit veriÿcation and testing, we study the approximate evaluation*of*characteristic*polynomials**of**Boolean**functions*. ... Suppose that we use k*Boolean**function*values for an approximate evaluation*of**a*characteristic*polynomial**of**a**Boolean**function**of*n variables. ...##
###
Page 3364 of Mathematical Reviews Vol. , Issue 91F
[page]

1991
*
Mathematical Reviews
*

*A*

*remark*

*on*

*minimal*

*polynomials*

*of*

*Boolean*

*functions*. CSL ’88 (Duisburg, 1988), 372-383, Lecture Notes in Comput. Sci., 385, Springer, Berlin, 1989. ... that for the case

*of*f and g being symmetric

*Boolean*

*functions*the

*minimal*DNF

*of*f(x)

*A*g(y) is given by multiplying the

*minimal*DNF representations

*of*f(x) and g(y). ...

##
###
Representing Boolean Functions Using Polynomials: More Can Offer Less
[chapter]

2011
*
Lecture Notes in Computer Science
*

For this purpose, instead

doi:10.1007/978-3-642-21111-9_32
fatcat:diytlldimbfcrbea2twre6funm
*of*an exact*polynomial*representation, usually the sign representation*of**a**Boolean**function*is considered. ... In this paper, the basic methods*of*representing*a**Boolean**function*by*polynomials*are examined, and an alternative approach to this problem is proposed. ... is appropriate for the type*of*applications under consideration, or to use*a*combined approach to achieve the best result. ...##
###
Representing Boolean Functions Using Polynomials: More Can Offer Less
[article]

2013
*
arXiv
*
pre-print

For this purpose, instead

arXiv:1307.1157v1
fatcat:t34h3t5yorbo5gecyf6piq5zu4
*of*an exact*polynomial*representation, usually the sign representation*of**a**Boolean**function*is considered. ... In this paper, the basic methods*of*representing*a**Boolean**function*by*polynomials*are examined, and an alternative approach to this problem is proposed. ... is appropriate for the type*of*applications under consideration, or to use*a*combined approach to achieve the best result. ...##
###
Incremental polynomial time dualization of quadratic functions and a subclass of degree-k functions

2009
*
Annals of Operations Research
*

We consider the problem

doi:10.1007/s10479-009-0637-x
fatcat:2dke6pd2cbfx3g6233xjxbkegq
*of*dualizing*a**Boolean**function*f represented by*a*DNF. ... In its most general form, this problem is commonly believed not to be solvable by*a*quasi-*polynomial*total time algorithm. ... The author also acknowledges the support from the Turkish Academy*of*Science. ...##
###
The Complexity of Minimizing FBDDs
[chapter]

1999
*
Lecture Notes in Computer Science
*

Free Binary Decision Diagrams (FBDDs) are

doi:10.1007/3-540-48340-3_23
fatcat:hmbdh6p5mvgtxa4bqd4ecr35we
*a*data structure for the representation and manipulation*of**Boolean**functions*. ... In this paper it is shown that the existence*of**polynomial*time approximation schemes for optimizing graph orderings or for*minimizing*FBDDs implies NP ZPP or NP P, respectively, and so such algorithms ... We*remark*that for OBDDs there are similar optimization problems, namely the computation*of**a**minimal*size OBDD for*a**function*given by an OBDD and the computation*of*an optimal variable ordering for*a*...
« Previous

*Showing results 1 — 15 out of 21,096 results*