34 research outputs found
Strong inapproximability of the shortest reset word
The \v{C}ern\'y conjecture states that every -state synchronizing
automaton has a reset word of length at most . We study the hardness
of finding short reset words. It is known that the exact version of the
problem, i.e., finding the shortest reset word, is NP-hard and coNP-hard, and
complete for the DP class, and that approximating the length of the shortest
reset word within a factor of is NP-hard [Gerbush and Heeringa,
CIAA'10], even for the binary alphabet [Berlinkov, DLT'13]. We significantly
improve on these results by showing that, for every , it is NP-hard
to approximate the length of the shortest reset word within a factor of
. This is essentially tight since a simple -approximation
algorithm exists.Comment: extended abstract to appear in MFCS 201
Checking Whether an Automaton Is Monotonic Is NP-complete
An automaton is monotonic if its states can be arranged in a linear order
that is preserved by the action of every letter. We prove that the problem of
deciding whether a given automaton is monotonic is NP-complete. The same result
is obtained for oriented automata, whose states can be arranged in a cyclic
order. Moreover, both problems remain hard under the restriction to binary
input alphabets.Comment: 13 pages, 4 figures. CIAA 2015. The final publication is available at
http://link.springer.com/chapter/10.1007/978-3-319-22360-5_2
Top Compositeness at the Tevatron and LHC
We explore the possibility that the right-handed top quark is composite. We
examine the consequences that compositeness would have on
production at the Tevatron, and derive a weak constraint on the scale of
compositeness of order a few hundred GeV from the inclusive cross
section. More detailed studies of differential properties of
production could potentially improve this limit. We find that a composite top
can result in an enhancement of the production rate at
the LHC (of as much as compared to the Standatd Model four top rate). We
explore observables which allow us to extract the four top rate from the
backgrounds, and show that the LHC can either discover or constrain top
compositeness for wide ranges of parameter space.Comment: 9 pages, 4 figure
A Fast Algorithm Finding the Shortest Reset Words
In this paper we present a new fast algorithm finding minimal reset words for
finite synchronizing automata. The problem is know to be computationally hard,
and our algorithm is exponential. Yet, it is faster than the algorithms used so
far and it works well in practice. The main idea is to use a bidirectional BFS
and radix (Patricia) tries to store and compare resulted subsets. We give both
theoretical and practical arguments showing that the branching factor is
reduced efficiently. As a practical test we perform an experimental study of
the length of the shortest reset word for random automata with states and 2
input letters. We follow Skvorsov and Tipikin, who have performed such a study
using a SAT solver and considering automata up to states. With our
algorithm we are able to consider much larger sample of automata with up to
states. In particular, we obtain a new more precise estimation of the
expected length of the shortest reset word .Comment: COCOON 2013. The final publication is available at
http://link.springer.com/chapter/10.1007%2F978-3-642-38768-5_1
Algebraic synchronization criterion and computing reset words
We refine a uniform algebraic approach for deriving upper bounds on reset
thresholds of synchronizing automata. We express the condition that an
automaton is synchronizing in terms of linear algebra, and obtain upper bounds
for the reset thresholds of automata with a short word of a small rank. The
results are applied to make several improvements in the area.
We improve the best general upper bound for reset thresholds of finite prefix
codes (Huffman codes): we show that an -state synchronizing decoder has a
reset word of length at most . In addition to that, we prove
that the expected reset threshold of a uniformly random synchronizing binary
-state decoder is at most . We also show that for any non-unary
alphabet there exist decoders whose reset threshold is in .
We prove the \v{C}ern\'{y} conjecture for -state automata with a letter of
rank at most . In another corollary, based on the recent
results of Nicaud, we show that the probability that the \v{C}ern\'y conjecture
does not hold for a random synchronizing binary automaton is exponentially
small in terms of the number of states, and also that the expected value of the
reset threshold of an -state random synchronizing binary automaton is at
most .
Moreover, reset words of lengths within all of our bounds are computable in
polynomial time. We present suitable algorithms for this task for various
classes of automata, such as (quasi-)one-cluster and (quasi-)Eulerian automata,
for which our results can be applied.Comment: 18 pages, 2 figure
Color-Octet-Electroweak-Doublet Scalars and the CDF Dijet Anomaly
We study the phenomenology of color-octet scalars in the (8, 2)1/2
representation in the context of the 3.2\sigma excess, in the dijet invariant
mass spectrum of the W+jj final state, recently observed by the CDF
collaboration. We consider the region of parameter space with a sizable mass
splitting between the charged and neutral color-octet scalars and consistent
with electroweak precision data. We implement the principle of Minimal Flavor
Violation (MFV) in order to suppress FCNC currents and reduce the number of
free parameters. The excess in the W+jj channel corresponds to the charged
current decay of the heavier neutral octet scalar into its lighter charged
partner which decays into the two jets. In the MFV scenario, the production of
the neutral color-octet is dominated by gluon fusion due to the Yukawa
suppression of production via initial state quarks. As a result, no visible
excess is expected in the \gamma+jj channel due to Yukawa and CKM suppression.
Contributions to the Z+jj final state are suppressed for a mass spectrum where
the decay of the heavier color-octet to this final state is mediated by an
off-shell neutral color-octet partner. MFV allows one to control fraction of
bottom quarks in the final state jets by a single ratio of two free parameters.Comment: 14 pages, 6 figures, typos corrected, references added, text and
figures modified in some places for better clarity, version to appear in
Physics Letters
New Physics Models of Direct CP Violation in Charm Decays
In view of the recent LHCb measurement of Delta A_CP, the difference between
the time-integrated CP asymmetries in D --> K+K- and D --> pi+pi- decays, we
perform a comparative study of the possible impact of New Physics degrees of
freedom on the direct CP asymmetries in singly Cabibbo suppressed D meson
decays. We systematically discuss scenarios with a minimal set of new degrees
of freedom that have renormalizable couplings to the SM particles and that are
heavy enough such that their effects on the D meson decays can be described by
local operators. We take into account both constraints from low energy flavor
observables, in particular D0-D0bar mixing, and from direct searches. While
models that explain the large measured value for Delta A_CP with chirally
enhanced chromomagnetic penguins are least constrained, we identify a few
viable models that contribute to the D meson decays at tree level or through
loop induced QCD penguins. We emphasize that such models motivate direct
searches at the LHC.Comment: 24 pages, 13 figures. v2: typos corrected, reference added, published
versio
Color & Weak triplet scalars, the dimuon asymmetry in decay, the top forward-backward asymmetry, and the CDF dijet excess
The new physics required to explain the anomalies recently reported by the D0
and CDF collaborations, namely the top forward-backward asymmetry (FBA), the
like-sign dimuon charge asymmetry in semileptonic b decay, and the CDF dijet
excess, has to feature an amount of flavor symmetry in order to satisfy the
severe constrains arising from flavor violation. In this paper we show that,
once baryon number conservation is imposed, color & weak triplet scalars with
hypercharge can feature the required flavor structure as a consequence
of standard model gauge invariance. The color & weak triplet model can
simultaneously explain the top FBA and the dimuon charge asymmetry or the
dimuon charge asymmetry and the CDF dijet excess. However, the CDF dijet excess
appears to be incompatible with the top FBA in the minimal framework. Our model
for the dimuon asymmetry predicts the observed pattern in the
region of parameter space required to explain the top FBA, whereas our model
for the CDF dijet anomaly is characterized by the absence of beyond the SM
b-quark jets in the excess region. Compatibility of the color & weak triplet
with the electroweak constraints is also discussed. We show that a Higgs boson
mass exceeding the LEP bound is typically favored in this scenario, and that
both Higgs production and decay can be significantly altered by the triplet.
The most promising collider signature is found if the splitting among the
components of the triplet is of weak scale magnitude.Comment: references added, published versio
Lepton Number Violation from Colored States at the LHC
The possibility to search for lepton number violating signals at the Large
Hadron Collider (LHC) in the colored seesaw scenario is investigated. In this
context the fields that generate neutrino masses at the one-loop level are
scalar and Majorana fermionic color-octets of SU(3). Due to the QCD strong
interaction these states may be produced at the LHC with a favorable rate. We
study the production mechanisms and decays relevant to search for lepton number
violation signals in the channels with same-sign dileptons. In the simplest
case when the two fermionic color-octets are degenerate in mass, one could use
their decays to distinguish between the neutrino spectra. We find that for
fermionic octets with mass up to about 1 TeV the number of same-sign dilepton
events is larger than the standard model background indicating a promising
signal for new physics.Comment: minor corrections, added reference
Colored Resonant Signals at the LHC: Largest Rate and Simplest Topology
We study the colored resonance production at the LHC in a most general
approach. We classify the possible colored resonances based on group theory
decomposition, and construct their effective interactions with light partons.
The production cross section from annihilation of valence quarks or gluons may
be on the order of 400 - 1000 pb at LHC energies for a mass of 1 TeV with
nominal couplings, leading to the largest production rates for new physics at
the TeV scale, and simplest event topology with dijet final states. We apply
the new dijet data from the LHC experiments to put bounds on various possible
colored resonant states. The current bounds range from 0.9 to 2.7 TeV. The
formulation is readily applicable for future searches including other decay
modes.Comment: 29 pages, 9 figures. References updated and additional K-factors
include