Counting and enumerating aggregate classifiers

peer reviewedaudience: researcherWe propose a generic model for the "weighted voting" aggregation step performed by several methods in supervised classification. Further, we construct an algorithm to count the number of distinct aggregate classifiers that arise in this model. When there are only two classes in the classification problem, we show that a class of functions that arises from aggregate classifiers coincides with the class of self-dual positive threshold Boolean functions

Modular Decomposition of Boolean Functions

Modular decomposition is a thoroughly investigated topic in many areas such as switching theory, reliability theory, game theory and graph theory. Most appli- cations can be formulated in the framework of Boolean functions. In this paper we give a uni_ed treatment of modular decomposition of Boolean functions based on the idea of generalized Shannon decomposition. Furthermore, we discuss some new results on the complexity of modular decomposition. We propose an O(mn)- algorithm for the recognition of a modular set of a monotone Boolean function f with m prime implicants and n variables. Using this result we show that the the computation of the modular closure of a set can be done in time O(mn2). On the other hand, we prove that the recognition problem for general Boolean functions is coNP-complete

Cryptography from tensor problems

We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler

Parametrised complexity of satisfiability in temporal logic

We apply the concept of formula treewidth and pathwidth to computation tree logic, linear temporal logic, and the full branching time logic. Several representations of formulas as graphlike structures are discussed, and corresponding notions of treewidth and pathwidth are introduced. As an application for such structures, we present a classification in terms of parametrised complexity of the satisfiability problem, where we make use of Courcelle's famous theorem for recognition of certain classes of structures. Our classification shows a dichotomy between W[1]-hard and fixed-parameter tractable operator fragments almost independently of the chosen graph representation. The only fragments that are proven to be fixed-parameter tractable (FPT) are those that are restricted to the X operator. By investigating Boolean operator fragments in the sense of Post's lattice, we achieve the same complexity as in the unrestricted case if the set of available Boolean functions can express the function "negation of the implication." Conversely, we show containment in FPT for almost all other clones. © ACM 2017. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in ACM Transactions on Computational Logic 18 (2017), Nr. 1, 1. DOI: https://doi.org/10.1145/3001835.DFG/ME 4279/1-