104 research outputs found
Bisimilarity of Pushdown Systems is Nonelementary
Given two pushdown systems, the bisimilarity problem asks whether they are
bisimilar. While this problem is known to be decidable our main result states
that it is nonelementary, improving EXPTIME-hardness, which was the previously
best known lower bound for this problem. Our lower bound result holds for
normed pushdown systems as well
Reachability in Higher-Order-Counters
Higher-order counter automata (\HOCS) can be either seen as a restriction of
higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an
extension of counter automata to higher levels. We distinguish two principal
kinds of \HOCS: those that can test whether the topmost counter value is zero
and those which cannot.
We show that control-state reachability for level \HOCS with -test is
complete for \mbox{}-fold exponential space; leaving out the -test
leads to completeness for \mbox{}-fold exponential time. Restricting
\HOCS (without -test) to level , we prove that global (forward or
backward) reachability analysis is \PTIME-complete. This enhances the known
result for pushdown systems which are subsumed by level \HOCS without
-test.
We transfer our results to the formal language setting. Assuming that \PTIME
\subsetneq \PSPACE \subsetneq \mathbf{EXPTIME}, we apply proof ideas of
Engelfriet and conclude that the hierarchies of languages of \HOPS and of \HOCS
form strictly interleaving hierarchies. Interestingly, Engelfriet's
constructions also allow to conclude immediately that the hierarchy of
collapsible pushdown languages is strict level-by-level due to the existing
complexity results for reachability on collapsible pushdown graphs. This
answers an open question independently asked by Parys and by Kobayashi.Comment: Version with Full Proofs of a paper that appears at MFCS 201
Effective Hamiltonians with Relativistic Corrections I: The Foldy--Wouthuysen transformation versus the direct Pauli reduction
Two different methods of obtaining ``effective Hamiltonians''
which include relativistic corrections to nonrelativistic calculations are
discussed, the standard Foldy--Wouthuysen transformation and what we call the
``direct Pauli reduction''. We wish to investigate under which circumstances
the two approaches yield the same result. Using a generic interaction with
harmonic time dependence we show that differences in the corresponding
effective S--matrices do arise beyond first--order perturbation theory. We
attribute them to the fact that the use of the direct reduction effective
Hamiltonian involves the additional approximation of neglecting contributions
from the negative--energy intermediate states, an approximation which is
unnecessary in the Foldy--Wouthuysen case as there the Hamiltonian
does not connect positive-- and negative--energy states. We conclude that at
least in the cases where the relativistic Hamiltonian is known, using the
direct Pauli reduction effective Hamiltonian introduces spurious relativistic
effects and therefore the Foldy--Wouthuysen reduction should be preferred.Comment: TRIUMF preprint TRI-PP-93-1
Consistent Treatment of Relativistic Effects in Electrodisintegration of the Deuteron
The influence of relativistic contributions to deuteron electrodisintegration
is systematically studied in various kinematic regions of energy and momentum
transfer. As theoretical framework the equation-of-motion and the unitarily
equivalent S-matrix approaches are used. In a (p/M)-expansion, all leading
order relativistic -exchange contributions consistent with the Bonn OBEPQ
model are included. In addition, static heavy meson exchange currents including
boost terms, -currents, and -isobar contributions
are considered. Sizeable effects from the various relativistic two-body
contributions, mainly from -exchange, have been found in inclusive form
factors and exclusive structure functions for a variety of kinematic regions.Comment: 41 pages revtex including 15 postscript figure
Dust detection by the wave instrument on STEREO: nanoparticles picked up by the solar wind?
The STEREO/WAVES instrument has detected a very large number of intense
voltage pulses. We suggest that these events are produced by impact ionisation
of nanoparticles striking the spacecraft at a velocity of the order of
magnitude of the solar wind speed. Nanoparticles, which are half-way between
micron-sized dust and atomic ions, have such a large charge-to-mass ratio that
the electric field induced by the solar wind magnetic field accelerates them
very efficiently. Since the voltage produced by dust impacts increases very
fast with speed, such nanoparticles produce signals as high as do much larger
grains of smaller speeds. The flux of 10-nm radius grains inferred in this way
is compatible with the interplanetary dust flux model. The present results may
represent the first detection of fast nanoparticles in interplanetary space
near Earth orbit.Comment: In press in Solar Physics, 13 pages, 5 figure
Elastic electron deuteron scattering with consistent meson exchange and relativistic contributions of leading order
The influence of relativistic contributions to elastic electron deuteron
scattering is studied systematically at low and intermediate momentum transfers
( fm). In a -expansion, all leading order
relativistic -exchange contributions consistent with the Bonn OBEPQ models
are included. In addition, static heavy meson exchange currents including boost
terms and lowest order -currents are considered. Sizeable
effects from the various relativistic two-body contributions, mainly from
-exchange, have been found in form factors, structure functions and the
tensor polarization . Furthermore, static properties, viz. magnetic
dipole and charge quadrupole moments and the mean square charge radius are
evaluated.Comment: 15 pages Latex including 5 figures, final version accepted for
publication in Phys.Rev.C Details of changes: (i) The notation of the curves
in Figs. 1 and 2 have been clarified with respect to left and right panels.
(ii) In Figs. 3 and 4 an experimental point for T_20 has been added and a
corresponding reference [48] (iii) At the end of the text we have added a
paragraph concerning the quality of the Bonn OBEPQ potential
On the complexity of resource-bounded logics
We revisit decidability results for resource-bounded logics and use decision problems for vector addition systems with states (VASS) to characterise the complexity of (decidable) model-checking problems.
We show that the model-checking problem for the logic RB+-ATL is 2EXPTIME-complete by using recent results on alternating VASS.
In addition, we establish that the model-checking problem for RBTL is decidable and has the same complexity as for RBTL* (the extension of RBTL with arbitrary path formulae), namely EXPSPACE-complete, proving a new decidability result as a by-product of the approach. Finally, we establish that the model-checking problem for RB+-ATL* is decidable by a reduction to parity games, and show how to synthesise values for resource parameters
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