Kotaro Yasui*, Kazuki Kikuchi*, Takeshi Kano*, Yumino Hayase**, Shigeru Kuroda***, Hitoshi Aonuma***,****, Ryo Kobayashi**,****, Akio Ishiguro*,**** *Research Institute of Electrical Communication, Tohoku University, Japan {k.yasui, k-kiku, tkano, ishiguro}@riec.tohoku.ac.jp **Graduate School of Science, Hiroshima University, Japan [email protected], [email protected] ***Res...

In this paper we present a constructive detection of minimal monomials in the algebraic normal form of rotation symmetric Boolean functions (immune to circular translation of indices). This helps in constructing rotation symmetric Boolean functions by respecting the rules we present here.  2003 Elsevier B.V. All rights reserved.

An algorithm for obtaining all simple disjunctive decompositions of a switching function is described. The algorithm proceeds by testing for all decompositions with a bound set of size two. Under given conditions, this test for a pair of variables will show that some larger bound sets, containing the two variables for which the test was conducted, cannot yield a decomposition. The remaining bou...

In this paper we investigate the Boolean functions with essential arity gap 2. We use Full Conjunctive Normal Forms instead of Zhegalkin’s polynomials, which allow us to simplify the proofs and to obtain several combinatorial results, concerning the Boolean functions with a given arity gap.

Finding disjunctivist versions of direct realism unexplanatory, Mark Johnston [(2004). Philosophical Studies, 120, 113–183] offers a non-disjunctive version of direct realism in its place and gives a defense of this view from the problem of hallucination. I will attempt to clarify the view that he presents and then argue that, once clarified, it either does not escape the problem of hallucinati...

A pair of clauses in a CNF formula constitutes a conflict if there is a variable that occurs positively in one clause and negatively in the other. Clearly, a CNF formula has to have conflicts in order to be unsatisfiable—in fact, there have to be many conflicts, and it is the goal of this paper to quantify how many. An unsatisfiable k-CNF has at least 2 clauses; a lower bound of 2 for the numbe...

We determine the thresholds for the number of variables, number of clauses, number of clause intersection pairs and the maximum clause degree of a k-CNF formula that guarantees satisfiability under the assumption that every two clauses share at most α variables. More formally, we call these formulas α-intersecting and define, for example, a threshold μi(k, α) for the number of clause intersecti...

Abstract The normal forms for linearly controllable quadratic system are derived and proved for single-input continuous system, single-input discrete sytem and multi-input continuous system in a constructive way.