65,668 research outputs found
Pebbling Arguments for Tree Evaluation
The Tree Evaluation Problem was introduced by Cook et al. in 2010 as a
candidate for separating P from L and NL. The most general space lower bounds
known for the Tree Evaluation Problem require a semantic restriction on the
branching programs and use a connection to well-known pebble games to generate
a bottleneck argument. These bounds are met by corresponding upper bounds
generated by natural implementations of optimal pebbling algorithms. In this
paper we extend these ideas to a variety of restricted families of both
deterministic and non-deterministic branching programs, proving tight lower
bounds under these restricted models. We also survey and unify known lower
bounds in our "pebbling argument" framework
Weyl semimetals from noncentrosymmetric topological insulators
We study the problem of phase transitions from 3D topological to normal
insulators without inversion symmetry. In contrast with the conclusions of some
previous work, we show that a Weyl semimetal always exists as an intermediate
phase regardless of any constriant from lattice symmetries, although the
interval of the critical region is sensitive to the choice of path in the
parameter space and can be very narrow. We demonstrate this behavior by
carrying out first-principles calculations on the noncentrosymmetric
topological insulators LaBiTe and LuBiTe and the trivial insulator
BiTeI. We find that a robust Weyl-semimetal phase exists in the solid solutions
LaBiSbTe and LuBiSbTe for
\% and \% respectively. A
low-energy effective model is also constructed to describe the critical
behavior in these two materials. In BiTeI, a Weyl semimetal also appears with
applied pressure, but only within a very small pressure range, which may
explain why it has not been experimentally observed.Comment: 10 pages, 11 figure
Universal Witnesses for State Complexity of Basic Operations Combined with Reversal
We study the state complexity of boolean operations, concatenation and star
with one or two of the argument languages reversed. We derive tight upper
bounds for the symmetric differences and differences of such languages. We
prove that the previously discovered bounds for union, intersection,
concatenation and star of such languages can all be met by the recently
introduced universal witnesses and their variants.Comment: 18 pages, 8 figures. LNCS forma
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