Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Several noteworthy classes of Boolean functions can be characterized by algebraic identities (e.g. the class of positive functions consists of all functions f satisfying the identity f(x) _ f(y) _ f(x _ y)= f( x _ y)).  give algebraic identities for several of the most frequently analyzed classes of Boolean functions (including Horn, quadratic, supermodular, and submodular functions) and proceed then to the general question of which classes of Boolean functions can be characterized by algebraic identities.  ansr this question for function classes closed under addition of inessential (irrelevant) variables. Nearly all classes of interest have this property.  show that a class with this property has a characterization by algebraic identities if and only if the class is closed under the operation of variable identication. Moreover, a single identity suces to characterize a class if and only if the number of minimal forbidden identication minors is nite. Finally,  consider characterizations by general rst-order sentences, rather than just identities.  show that a class of Boolean functions can be described by an appropriate set of such rst-order sentences if and only if it is closed under permutation of variables. c 2000 Elsevier Science B.V. All rights reserved.
['Oya Ekin', 'Stephan Foldes', 'Peter L. Hammer', 'Lisa Hellerstein']
I am writing a research paper on a idea Equational characterizations of Boolean function classes
[{"from": "human", "value": "I am writing a research paper on a idea Equational characterizations of Boolean function classes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Several noteworthy classes of Boolean functions can be characterized by algebraic identities (e.g. the class of positive functions consists of all functions f satisfying the identity f(x) _ f(y) _ f(x _ y)= f( x _ y)).  give algebraic identities for several of the most frequently analyzed classes of Boolean functions (including Horn, quadratic, supermodular, and submodular functions) and proceed then to the general question of which classes of Boolean functions can be characterized by algebraic identities.  ansr this question for function classes closed under addition of inessential (irrelevant) variables. Nearly all classes of interest have this property.  show that a class with this property has a characterization by algebraic identities if and only if the class is closed under the operation of variable identication. Moreover, a single identity suces to characterize a class if and only if the number of minimal forbidden identication minors is nite. Finally,  consider characterizations by general rst-order sentences, rather than just identities.  show that a class of Boolean functions can be described by an appropriate set of such rst-order sentences if and only if it is closed under permutation of variables. c 2000 Elsevier Science B.V. All rights reserved."}]