This paper is a contribution to the study of a quasi-order on the set Ω of Boolean functions, the simple minor quasi-order. We look at the join-irreducible members of the resulting poset Ω̃. Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those which yield...

The group of congruences and permutations of the two-colored N-dimensional Boolean cube is considered. The total number of orbits generated by these automorphisms are shown to scale as 22”/(2y+‘N!) when N tends to infinity. The probability that a randomly chosen function will belong to an orbit containing the maximum possible number of elements, 2’v+’ N!, approaches one as N goes to infinity. S...

s of Presentation: Paul Beame: Time-Space Tradeoffs and Multiparty Communication Complexity 9 Beate Bollig: Exponential Lower Bounds for Integer Multiplication Using Universal Hashing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Philipp Wölfel: On k-wise l-mixed Boolean Functions . . . . . . . . . . . . . . 10 Elizabeta Okol’nishnikova: On One Lower Bound for Branching Progra...

This paper explores lattices of Boolean functions which are built by derivative operations of the Boolean Differential Calculus [2], [8], [9]. Such operations are needed to design circuits with short delay and low power consumption [11] as well as to calculate minimal complete sets of fitting test patterns [12]. It will be shown that each derivative operation of a lattice of Boolean functions c...