506 research outputs found
An extensive English language bibliography on graph theory and its applications
Bibliography on graph theory and its application
Complexity of Problems of Commutative Grammars
We consider commutative regular and context-free grammars, or, in other
words, Parikh images of regular and context-free languages. By using linear
algebra and a branching analog of the classic Euler theorem, we show that,
under an assumption that the terminal alphabet is fixed, the membership problem
for regular grammars (given v in binary and a regular commutative grammar G,
does G generate v?) is P, and that the equivalence problem for context free
grammars (do G_1 and G_2 generate the same language?) is in
On 2-form gauge models of topological phases
We explore various aspects of 2-form topological gauge theories in (3+1)d.
These theories can be constructed as sigma models with target space the second
classifying space of the symmetry group , and they are classified by
cohomology classes of . Discrete topological gauge theories can typically
be embedded into continuous quantum field theories. In the 2-form case, the
continuous theory is shown to be a strict 2-group gauge theory. This embedding
is studied by carefully constructing the space of -form connections using
the technology of Deligne-Beilinson cohomology. The same techniques can then be
used to study more general models built from Postnikov towers. For finite
symmetry groups, 2-form topological theories have a natural lattice
interpretation, which we use to construct a lattice Hamiltonian model in (3+1)d
that is exactly solvable. This construction relies on the introduction of a
cohomology, dubbed 2-form cohomology, of algebraic cocycles that are identified
with the simplicial cocycles of as provided by the so-called
-construction of Eilenberg-MacLane spaces. We show algebraically and
geometrically how a 2-form 4-cocycle reduces to the associator and the braiding
isomorphisms of a premodular category of -graded vector spaces. This is used
to show the correspondence between our 2-form gauge model and the Walker-Wang
model.Comment: 78 page
An extensive English language bibliography on graph theory and its applications, supplement 1
Graph theory and its applications - bibliography, supplement
Fault-tolerant Hamiltonian laceability of Cayley graphs generated by transposition trees
AbstractA bipartite graph is Hamiltonian laceable if there exists a Hamiltonian path joining every pair of vertices that are in different parts of the graph. It is well known that Cay(Sn,B) is Hamiltonian laceable, where Sn is the symmetric group on {1,2,…,n} and B is a generating set consisting of transpositions of Sn. In this paper, we show that for any F⊆E(Cay(Sn,B)), if |F|≤n−3 and n≥4, then there exists a Hamiltonian path in Cay(Sn,B)−F joining every pair of vertices that are in different parts of the graph. The result is optimal with respect to the number of edge faults
Local stabilizer codes in three dimensions without string logical operators
We suggest concrete models for self-correcting quantum memory by reporting
examples of local stabilizer codes in 3D that have no string logical operators.
Previously known local stabilizer codes in 3D all have string-like logical
operators, which make the codes non-self-correcting. We introduce a notion of
"logical string segments" to avoid difficulties in defining one dimensional
objects in discrete lattices. We prove that every string-like logical operator
of our code can be deformed to a disjoint union of short segments, and each
segment is in the stabilizer group. The code has surface-like logical operators
whose partial implementation has unsatisfied stabilizers along its boundary.Comment: 18 pages, 12 figures; clarified intermidiate steps in the proo
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