5,416 research outputs found
Unary Pushdown Automata and Straight-Line Programs
We consider decision problems for deterministic pushdown automata over a
unary alphabet (udpda, for short). Udpda are a simple computation model that
accept exactly the unary regular languages, but can be exponentially more
succinct than finite-state automata. We complete the complexity landscape for
udpda by showing that emptiness (and thus universality) is P-hard, equivalence
and compressed membership problems are P-complete, and inclusion is
coNP-complete. Our upper bounds are based on a translation theorem between
udpda and straight-line programs over the binary alphabet (SLPs). We show that
the characteristic sequence of any udpda can be represented as a pair of
SLPs---one for the prefix, one for the lasso---that have size linear in the
size of the udpda and can be computed in polynomial time. Hence, decision
problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP
can be converted in logarithmic space into a udpda, and this forms the basis
for our lower bound proofs. We show coNP-hardness of the ordered matching
problem for SLPs, from which we derive coNP-hardness for inclusion. In
addition, we complete the complexity landscape for unary nondeterministic
pushdown automata by showing that the universality problem is -hard, using a new class of integer expressions. Our techniques have
applications beyond udpda. We show that our results imply -completeness for a natural fragment of Presburger arithmetic and coNP lower
bounds for compressed matching problems with one-character wildcards
Independent Set, Induced Matching, and Pricing: Connections and Tight (Subexponential Time) Approximation Hardnesses
We present a series of almost settled inapproximability results for three
fundamental problems. The first in our series is the subexponential-time
inapproximability of the maximum independent set problem, a question studied in
the area of parameterized complexity. The second is the hardness of
approximating the maximum induced matching problem on bounded-degree bipartite
graphs. The last in our series is the tight hardness of approximating the
k-hypergraph pricing problem, a fundamental problem arising from the area of
algorithmic game theory. In particular, assuming the Exponential Time
Hypothesis, our two main results are:
- For any r larger than some constant, any r-approximation algorithm for the
maximum independent set problem must run in at least
2^{n^{1-\epsilon}/r^{1+\epsilon}} time. This nearly matches the upper bound of
2^{n/r} (Cygan et al., 2008). It also improves some hardness results in the
domain of parameterized complexity (e.g., Escoffier et al., 2012 and Chitnis et
al., 2013)
- For any k larger than some constant, there is no polynomial time min
(k^{1-\epsilon}, n^{1/2-\epsilon})-approximation algorithm for the k-hypergraph
pricing problem, where n is the number of vertices in an input graph. This
almost matches the upper bound of min (O(k), \tilde O(\sqrt{n})) (by Balcan and
Blum, 2007 and an algorithm in this paper).
We note an interesting fact that, in contrast to n^{1/2-\epsilon} hardness
for polynomial-time algorithms, the k-hypergraph pricing problem admits
n^{\delta} approximation for any \delta >0 in quasi-polynomial time. This puts
this problem in a rare approximability class in which approximability
thresholds can be improved significantly by allowing algorithms to run in
quasi-polynomial time.Comment: The full version of FOCS 201
Charge-dependent nucleon-nucleon potential from chiral effective field theory
We discuss charge symmetry and charge independence breaking in a chiral
effective field theory approach for few-nucleon systems based on a modified
Weinberg power counting. We construct a two-nucleon potential with bound and
scattering states generated by means of a properly regularized
Lippmann-Schwinger equation. We systematically introduce strong
isospin-violating and electromagnetic operators in the theory. We use standard
procedures to treat the Coulomb potential between two protons in momentum
space. We present results for phase shifts in the proton-proton, the
neutron-proton and the neutron-neutron systems. We discuss the various
contributions to charge dependence and charge symmetry breaking observed in the
nucleon-nucleon scattering lengths.Comment: 28 pages, 11 figure
Some results on triangle partitions
We show that there exist efficient algorithms for the triangle packing
problem in colored permutation graphs, complete multipartite graphs,
distance-hereditary graphs, k-modular permutation graphs and complements of
k-partite graphs (when k is fixed). We show that there is an efficient
algorithm for C_4-packing on bipartite permutation graphs and we show that
C_4-packing on bipartite graphs is NP-complete. We characterize the cobipartite
graphs that have a triangle partition
The problem with the SURF scheme
There is a serious problem with one of the assumptions made in the security
proof of the SURF scheme. This problem turns out to be easy in the regime of
parameters needed for the SURF scheme to work.
We give afterwards the old version of the paper for the reader's convenience.Comment: Warning : we found a serious problem in the security proof of the
SURF scheme. We explain this problem here and give the old version of the
paper afterward
The Impact of Flavour Changing Neutral Gauge Bosons on B->X_s gamma
The branching ratio of the rare decay B->X_s gamma provides potentially
strong constraints on models beyond the Standard Model. Considering a general
scenario with new heavy neutral gauge bosons, present in particular in Z' and
gauge flavour models, we point out two new contributions to the B->X_s gamma
decay. The first one originates from one-loop diagrams mediated by gauge bosons
and heavy exotic quarks with electric charge -1/3. The second contribution
stems from the QCD mixing of neutral current-current operators generated by
heavy neutral gauge bosons and the dipole operators responsible for the B->X_s
gamma decay. The latter mixing is calculated here for the first time. We
discuss general sum rules which have to be satisfied in any model of this type.
We emphasise that the neutral gauge bosons in question could also significantly
affect other fermion radiative decays as well as non-leptonic two-body B
decays, epsilon'/epsilon, anomalous (g-2)_mu and electric dipole moments.Comment: 31 pages, 5 figures; version published on JHEP; added magic QCD
numbers for flavour-violating Z gauge boson contribution to B -> X_s gamm
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