The initial majority identification task is a fundamental test problem in cellular automaton research. To pass the test, two-state has to attain uniform configuration consisting of only state that was initially majority. It does so solely through its local, internal dynamics—i.e., success an example emergent computation. Finding new, better-performing automata continues be interest for what add...

In this paper we examine the problem of computing majority functionMAJn on n bits by depthtwo formula, where each gate is a majority function on at most k inputs. We present such formula that gives the first nontrivial upper bound for this problem, with k = 2 3n + 4. This answers an open question in [7]. We also look at this problem in adaptive setting — when we are allowed to query for value o...

Although it may seem easy to compare states in terms of the number of their citizens and the size and shape of their countries, the connection between the democratic state and the numerical and spatial considerations is more subtle and complex, for theoretical views of society and the state tend to diverge into opposing positions that explore themutually exclusive extremes ofatomism and holism....

in this paper, we study the existence of coupled coincidence andcoupled common fixed points for single-valued and fuzzy mappingsunder a contractive condition in metric space. presented theoremsextend and improve the main results of abbas and$acute{c}$iri$acute{c}$ {itshape et al.} [m. abbas, l.$acute{c}$iri$acute{c}$, {itshape et al.}, coupled coincidenceand common fixed point theorems for hybr...

We study the construction of prediction algorithms in a situation in which a learner faces a sequence of trials with a prediction to be made in each and the goal of the learner is to make few mistakes We are interested in the case that the learner has reason to believe that one of some pool of known algorithms will perform well but the learner does not know which one A simple and e ective metho...