24,982 research outputs found
Testing the Equivalence of Regular Languages
The minimal deterministic finite automaton is generally used to determine
regular languages equality. Antimirov and Mosses proposed a rewrite system for
deciding regular expressions equivalence of which Almeida et al. presented an
improved variant. Hopcroft and Karp proposed an almost linear algorithm for
testing the equivalence of two deterministic finite automata that avoids
minimisation. In this paper we improve the best-case running time, present an
extension of this algorithm to non-deterministic finite automata, and establish
a relationship between this algorithm and the one proposed in Almeida et al. We
also present some experimental comparative results. All these algorithms are
closely related with the recent coalgebraic approach to automata proposed by
Rutten
Radiative corrections in bumblebee electrodynamics
We investigate some quantum features of the bumblebee electrodynamics in flat
spacetimes. The bumblebee field is a vector field that leads to a spontaneous
Lorentz symmetry breaking. For a smooth quadratic potential, the massless
excitation (Nambu-Goldstone boson) can be identified as the photon, transversal
to the vacuum expectation value of the bumblebee field. Besides, there is a
massive excitation associated with the longitudinal mode and whose presence
leads to instability in the spectrum of the theory. By using the
principal-value prescription, we show that no one-loop radiative corrections to
the mass term is generated. Moreover, the bumblebee self-energy is not
transverse, showing that the propagation of the longitudinal mode can not be
excluded from the effective theory.Comment: Revised version: contains some more elaborated interpretation of the
results. Conclusions improve
Tameness of pseudovariety joins involving R
2000 Mathematics Subject Classification: 20M07 (primary); 20M05, 20M35, 68Q70 (secondary).In this paper, we establish several decidability results for pseudovariety joins of the form VvW, where V is a subpseudovariety of J or the pseudovariety R. Here, J (resp. R) denotes the pseudovariety of all J-trivial (resp. R-trivial) semigroups. In particular, we show that the pseudovariety VvW is (completely) kappa-tame when V is a subpseudovariety of J with decidable kappa-word problem and W is (completely) kappa-tame. Moreover, if W is a kappa-tame pseudovariety which satisfies the pseudoidentity x_1...x_ry^{\omega+1}zt^\omega = x_1... x_ryzt^\omega, then we
prove that RvW is also kappa-tame.
In particular the joins RvAb, RvG, RvOCR,
and RvCR are decidable.União Europeia (UE). Fundo Europeu de Desenvolvimento Regional (FEDER) - POCTI/32817/MAT/2000.International Association for the Promotion of Co-operation with Scientists from the New Independent States (NIS) of the Former Soviet Union (INTAS) - project 99-1224.Fundação para a Ciência e a Tecnologia (FCT)
Reducibility of pointlike problems
We show that the pointlike and the idempotent pointlike problems are reducible with respect to natural signatures in the following cases: the pseudovariety of all fi nite semigroups in which the order of every subgroup is a product of elements of a fi xed set of primes; the pseudovariety of all fi nite semigroups in which every regular J-class is the product of a rectangular band by a group from a fixed pseudovariety of groups that is reducible for the pointlike problem, respectively graph reducible. Allowing only trivial groups, we obtain omega-reducibility of the pointlike and idempotent pointlike problems, respectively for the
pseudovarieties of all finite aperiodic semigroups (A) and of all finite semigroups in which all regular elements are idempotents (DA).ANR 2010 BLAN 0202 01 FRE
Re-entrant magnetic field induced charge and spin gaps in the coupled dual-chain quasi-one dimensional organic conductor Perylene[Pt(mnt)]
An inductive method is used to follow the magnetic field-dependent
susceptibility of the coupled charge density wave (CDW) and spin-Peierls (SP)
ordered state behavior in the dual chain organic conductor
Perylene[Pt(mnt)]. In addition to the coexisting SP-CDW state phase
below 8 K and 20 T, the measurements show that a second spin-gapped phase
appears above 20 T that coincides with a field-induced insulating phase. The
results support a strong coupling of the CDW and SP order parameters even in
high magnetic fields, and provide new insight into the nature of the magnetic
susceptibility of dual-chain spin and charge systems.Comment: 6 pages, 6 figure
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