15,033 research outputs found
On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction
The universal-algebraic approach has proved a powerful tool in the study of
the complexity of CSPs. This approach has previously been applied to the study
of CSPs with finite or (infinite) omega-categorical templates, and relies on
two facts. The first is that in finite or omega-categorical structures A, a
relation is primitive positive definable if and only if it is preserved by the
polymorphisms of A. The second is that every finite or omega-categorical
structure is homomorphically equivalent to a core structure. In this paper, we
present generalizations of these facts to infinite structures that are not
necessarily omega-categorical. (This abstract has been severely curtailed by
the space constraints of arXiv -- please read the full abstract in the
article.) Finally, we present applications of our general results to the
description and analysis of the complexity of CSPs. In particular, we give
general hardness criteria based on the absence of polymorphisms that depend on
more than one argument, and we present a polymorphism-based description of
those CSPs that are first-order definable (and therefore can be solved in
polynomial time).Comment: Extended abstract appeared at 25th Symposium on Logic in Computer
Science (LICS 2010). This version will appear in the LMCS special issue
associated with LICS 201
Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid
The two-dimensional Holstein-Hubbard model is studied by means of
continuous-time quantum Monte Carlo simulations. Using
renormalization-group-invariant correlation ratios and finite-size
extrapolation, the critical temperature of the charge-density-wave transition
is determined as a function of coupling strength, phonon frequency, and Hubbard
repulsion. The phase transition is demonstrated to be in the universality class
of the two-dimensional Ising model and detectable via the fidelity
susceptibility. The structure of the ground-state phase diagram and the
possibility of a bipolaronic metal with a single-particle gap above are
explored.Comment: 8 pages, 9 figures; expanded version including Holstein-Hubbard
result
The Complexity of Surjective Homomorphism Problems -- a Survey
We survey known results about the complexity of surjective homomorphism
problems, studied in the context of related problems in the literature such as
list homomorphism, retraction and compaction. In comparison with these
problems, surjective homomorphism problems seem to be harder to classify and we
examine especially three concrete problems that have arisen from the
literature, two of which remain of open complexity
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