125,253 research outputs found
A New Technique for Reachability of States in Concatenation Automata
We present a new technique for demonstrating the reachability of states in
deterministic finite automata representing the concatenation of two languages.
Such demonstrations are a necessary step in establishing the state complexity
of the concatenation of two languages, and thus in establishing the state
complexity of concatenation as an operation. Typically, ad-hoc induction
arguments are used to show particular states are reachable in concatenation
automata. We prove some results that seem to capture the essence of many of
these induction arguments. Using these results, reachability proofs in
concatenation automata can often be done more simply and without using
induction directly.Comment: 23 pages, 1 table. Added missing affiliation/funding informatio
Error suppression via complementary gauge choices in Reed-Muller codes
Concatenation of two quantum error correcting codes with complementary sets
of transversal gates can provide a means towards universal fault-tolerant
computation. We first show that it is generally preferable to choose the inner
code with the higher pseudo-threshold in order to achieve lower logical failure
rates. We then explore the threshold properties of a wide range of
concatenation schemes. Notably, we demonstrate that the concatenation of
complementary sets of Reed-Muller codes can increase the code capacity
threshold under depolarizing noise when compared to extensions of previously
proposed concatenation models. We also analyze the properties of logical errors
under circuit level noise, showing that smaller codes perform better for all
sampled physical error rates. Our work provides new insights into the
performance of universal concatenated quantum codes for both code capacity and
circuit level noise.Comment: 11 pages + 4 appendices, 6 figures. In v2, Fig.1 was added to conform
to journal specification
Operational State Complexity of Deterministic Unranked Tree Automata
We consider the state complexity of basic operations on tree languages
recognized by deterministic unranked tree automata. For the operations of union
and intersection the upper and lower bounds of both weakly and strongly
deterministic tree automata are obtained. For tree concatenation we establish a
tight upper bound that is of a different order than the known state complexity
of concatenation of regular string languages. We show that (n+1) (
(m+1)2^n-2^(n-1) )-1 vertical states are sufficient, and necessary in the worst
case, to recognize the concatenation of tree languages recognized by (strongly
or weakly) deterministic automata with, respectively, m and n vertical states.Comment: In Proceedings DCFS 2010, arXiv:1008.127
Graph Concatenation for Quantum Codes
Graphs are closely related to quantum error-correcting codes: every
stabilizer code is locally equivalent to a graph code, and every codeword
stabilized code can be described by a graph and a classical code. For the
construction of good quantum codes of relatively large block length,
concatenated quantum codes and their generalizations play an important role. We
develop a systematic method for constructing concatenated quantum codes based
on "graph concatenation", where graphs representing the inner and outer codes
are concatenated via a simple graph operation called "generalized local
complementation." Our method applies to both binary and non-binary concatenated
quantum codes as well as their generalizations.Comment: 26 pages, 12 figures. Figures of concatenated [[5,1,3]] and [[7,1,3]]
are added. Submitted to JM
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
On the simplicity of multigerms
We prove several results regarding the simplicity of germs and multigerms
obtained via the operations of augmentation, simultaneous augmentation and
concatenation and generalised concatenation. We also give some results in the
case where one of the branches is a non stable primitive germ. Using our
results we obtain a list which includes all simple multigerms from to .Comment: 26 pages, to appear in Mathematica Scandinavica. Second version adds
two families that were missing in Table
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