1,204 research outputs found
A boolean function requiring 3n network size
Paul [P] first proved a 2.5n-lower bound for the network complexity of an explicit boolean function. We modify the definition of Paul\u27s function a little and prove a 3n-lower bound for the network complexity of that function
A boolean function requiring 3n network size
Paul [P] first proved a 2.5n-lower bound for the network complexity of an explicit boolean function. We modify the definition of Paul's function a little and prove a 3n-lower bound for the network complexity of that function
On the Limits of Gate Elimination
Although a simple counting argument shows the existence of Boolean functions of exponential circuit complexity, proving superlinear circuit lower bounds for explicit functions seems to be out of reach of the current techniques. There has been a (very slow) progress in proving linear lower bounds with the latest record of 3 1/86*n-o(n). All known lower bounds are based on the so-called gate elimination technique. A typical gate elimination argument shows that it is possible to eliminate several gates from an optimal circuit by making one or several substitutions to the input variables and repeats this inductively. In this note we prove that this method cannot achieve linear bounds of cn beyond a certain constant c, where c depends only on the number of substitutions made at a single step of the induction
Robot Composite Learning and the Nunchaku Flipping Challenge
Advanced motor skills are essential for robots to physically coexist with
humans. Much research on robot dynamics and control has achieved success on
hyper robot motor capabilities, but mostly through heavily case-specific
engineering. Meanwhile, in terms of robot acquiring skills in a ubiquitous
manner, robot learning from human demonstration (LfD) has achieved great
progress, but still has limitations handling dynamic skills and compound
actions. In this paper, we present a composite learning scheme which goes
beyond LfD and integrates robot learning from human definition, demonstration,
and evaluation. The method tackles advanced motor skills that require dynamic
time-critical maneuver, complex contact control, and handling partly soft
partly rigid objects. We also introduce the "nunchaku flipping challenge", an
extreme test that puts hard requirements to all these three aspects. Continued
from our previous presentations, this paper introduces the latest update of the
composite learning scheme and the physical success of the nunchaku flipping
challenge
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