On the decidability of homomorphism equivalence for languages

AbstractWe consider decision problems of the following type. Given a language L and two homomorphisms h1 and h2, one has to determine to what extent h1 and h2 agree on L. For instance, we say that h1 and h2 are equivalent on L if h1(ω) = h2(ω) holds for each ω ε L. In our main theorem we present an algorithm for deciding whether two given homomorphisms are equivalent on a given context-free language. This result also gives an algorithm for deciding whether the translations defined by two deterministic gsm mappings agree on a given context-free language

Rewrite Closure and CF Hedge Automata

We introduce an extension of hedge automata called bidimensional context-free hedge automata. The class of unranked ordered tree languages they recognize is shown to be preserved by rewrite closure with inverse-monadic rules. We also extend the parameterized rewriting rules used for modeling the W3C XQuery Update Facility in previous works, by the possibility to insert a new parent node above a given node. We show that the rewrite closure of hedge automata languages with these extended rewriting systems are context-free hedge languages

Incomplete Transition Complexity of Basic Operations on Finite Languages

The state complexity of basic operations on finite languages (considering complete DFAs) has been in studied the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of boolean operations, concatenation, star, and reversal. For all operations we give tight upper bounds for both description measures. We correct the published state complexity of concatenation for complete DFAs and provide a tight upper bound for the case when the right automaton is larger than the left one. For all binary operations the tightness is proved using family languages with a variable alphabet size. In general the operational complexities depend not only on the complexities of the operands but also on other refined measures.Comment: 13 page

Additive decomposability of functions over abelian groups

Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables with arity gap 2.Comment: 17 page

Spectrum of bound fermion states on vortices in 3^3He-B

We study subgap spectra of fermions localized within vortex cores in $^3$He-B. We develop an analytical treatment of the low-energy states and consider the characteristic properties of fermion spectra for different types of vortices. Due to the removed spin degeneracy the spectra of all singly quantized vortices consist of two different anomalous branches crossing the Fermi level. For singular $o$ and $u$ vortices the anomalous branches are similar to the standard Caroli-de Gennes -Matricon ones and intersect the Fermi level at zero angular momentum yet with different slopes corresponding to different spin states. On the contrary the spectral branches of nonsingular vortices intersect the Fermi level at finite angular momenta which leads to the appearance of a large number of zero modes, i.e. energy states at the Fermi level. Considering the $v$, $w$ and $uvw$ vortices with superfluid cores we show that the number of zero modes is proportional to the size of the vortex core.Comment: 6 pages, 1 figur

Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates

The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates (BEC) by solving the Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both the BdG and TDGP approaches allows one to unambiguously identify every observed mode.Comment: 5 pages, 4 figure

Propagating chain-free normal forms for EOL systems

We establish two types of normal forms for EOL systems. We first show that each ε-free EOL language can be generated by a propagating EOL system in which each derivation tree is chain-free. By this we mean that it contains at least one path from the root to the grandfather of a leaf in which each node has more than one son. We use this result to prove that each ε-free EOL language can be generated by a propagating EOL system in which each production has a right side of length at most two and which does not contain nonterminal chainproductions, i.e., productions A → B for nonterminals A and B. As applications of our results we give a simple proof for the decidability of the finiteness problem for EOL systems and solve an open problem concerning completeness of EOL forms

Unconventional Vortices and Phase Transitions in Rapidly Rotating Superfluid ^{3}He

This paper studies vortex-lattice phases of rapidly rotating superfluid ^3He based on the Ginzburg-Landau free-energy functional. To identify stable phases in the p-Omega plane (p: pressure; Omega: angular velocity), the functional is minimized with the Landau-level expansion method using up to 3000 Landau levels. This system can sustain various exotic vortices by either (i) shifting vortex cores among different components or (ii) filling in cores with components not used in the bulk. In addition, the phase near the upper critical angular velocity Omega_{c2} is neither the A nor B phases, but the polar state with the smallest superfluid density as already shown by Schopohl. Thus, multiple phases are anticipated to exist in the p-Omega plane. Six different phases are found in the present calculation performed over 0.0001 Omega_{c2} <= Omega <= Omega_{c2}, where Omega_{c2} is of order (1- T/T_c) times 10^{7} rad/s. It is shown that the double-core vortex experimentally found in the B phase originates from the conventional hexagonal lattice of the polar state near Omega_{c2} via (i) a phase composed of interpenetrating polar and Scharnberg-Klemm sublattices; (ii) the A-phase mixed-twist lattice with polar cores; (iii) the normal-core lattice found in the isolated-vortex calculation by Ohmi, Tsuneto, and Fujita; and (iv) the A-phase-core vortex discovered in another isolated-vortex calculation by Salomaa and Volovik. It is predicted that the double-core vortex will disappear completely in the experimental p-T phase diagram to be replaced by the A-phase-core vortex for Omega >~ 10^{3} ~ 10^{4} rad/s. C programs to minimize a single-component Ginzburg-Landau functional are available at {http://phys.sci.hokudai.ac.jp/~kita/index-e.html}.Comment: 13 pages, 9 figure

Vortex core transitions in superfluid 3He in globally anisotropic aerogels

Core structures of a single vortex in A-like and B-like phases of superfluid 3He in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although any uniaxial deformation leads to a wider A-like phase with the axial pairing in the pressure-temperature phase diagram, the vortex core states in the two phases in aerogel depend highly on the type of deformation. In a compressed aerogel, the first-order vortex core transition (VCT) previously seen in the bulk B phase appears at any pressure in the B-like phase while no strange vortex core is expected in the corresponding A-like phase. By contrast, in a stretched aerogel, the VCT in the B-like phase is lost while another VCT is expected to occur between a nonunitary core and a polar one in the A-like phase. Experimental search for these results is hoped to understand correlation between superfluid 3He and aerogel structure.Comment: 7 pages, 6 figures Text was changed. Resubmitted versio

The Need for Effective Early Behavioral Family Interventions for Children with Attention Deficit Hyperactivity Disorder (ADHD)

There is a pressing need for the development of effective early family intervention programs for children showing Attention Deficit Hyperactivity Disorder (ADHD) behaviours with Conduct Disorder (CD) or Oppositional Defiant Disorder (ODD) behaviours. Previous research has indicated that children with ADHD are at risk of developing comorbid CD or ODD behaviours. In addition, it has been shown that ODD or CD behaviours in childhood tend to persist and to have adverse effects on later social adjustment. However, ODD or CD behaviours are not necessary concomitants of ADHD, and it has been demonstrated that behavioural intervention can have both short- and long term beneficial effects for children showing early signs of ODD or CD behaviours. In short term, behavioural family interventions may be able to reduce oppositional behaviour, particularly in the preschool years. In the long term, early intervention has shown to reduce the incidence of later antisocial behaviour in children at risk for this developmental trajectory. In this paper, it will be argued that behavioural family interventions have not been effectively utilised or promulgated in the community for children with ADHD despite the demonstrated efficacy of these types of interventions. A model of a multilevel system of intervention that can be tailored to the individual family’s needs is presented