1,833 research outputs found
Isomorphisms of scattered automatic linear orders
We prove that the isomorphism of scattered tree automatic linear orders as
well as the existence of automorphisms of scattered word automatic linear
orders are undecidable. For the existence of automatic automorphisms of word
automatic linear orders, we determine the exact level of undecidability in the
arithmetical hierarchy
An optimal construction of Hanf sentences
We give the first elementary construction of equivalent formulas in Hanf
normal form. The triply exponential upper bound is complemented by a matching
lower bound
Infinite and Bi-infinite Words with Decidable Monadic Theories
We study word structures of the form where is either
or , is the natural linear ordering on and
is a predicate on . In particular we show:
(a) The set of recursive -words with decidable monadic second order
theories is -complete.
(b) Known characterisations of the -words with decidable monadic
second order theories are transfered to the corresponding question for
bi-infinite words.
(c) We show that such "tame" predicates exist in every Turing degree.
(d) We determine, for , the number of predicates
such that and
are indistinguishable.
Through these results we demonstrate similarities and differences between
logical properties of infinite and bi-infinite words
Tipping points near a delayed saddle node bifurcation with periodic forcing
We consider the effect on tipping from an additive periodic forcing in a
canonical model with a saddle node bifurcation and a slowly varying bifurcation
parameter. Here tipping refers to the dramatic change in dynamical behavior
characterized by a rapid transition away from a previously attracting state. In
the absence of the periodic forcing, it is well-known that a slowly varying
bifurcation parameter produces a delay in this transition, beyond the
bifurcation point for the static case. Using a multiple scales analysis, we
consider the effect of amplitude and frequency of the periodic forcing relative
to the drifting rate of the slowly varying bifurcation parameter.
We show that a high frequency oscillation drives an earlier tipping when the
bifurcation parameter varies more slowly, with the advance of the tipping point
proportional to the square of the ratio of amplitude to frequency. In the low
frequency case the position of the tipping point is affected by the frequency,
amplitude and phase of the oscillation. The results are based on an analysis of
the local concavity of the trajectory, used for low frequencies both of the
same order as the drifting rate of the bifurcation parameter and for low
frequencies larger than the drifting rate. The tipping point location is
advanced with increased amplitude of the periodic forcing, with critical
amplitudes where there are jumps in the location, yielding significant advances
in the tipping point. We demonstrate the analysis for two applications with
saddle node-type bifurcations
Propositional Dynamic Logic for Message-Passing Systems
We examine a bidirectional propositional dynamic logic (PDL) for finite and
infinite message sequence charts (MSCs) extending LTL and TLC-. By this kind of
multi-modal logic we can express properties both in the entire future and in
the past of an event. Path expressions strengthen the classical until operator
of temporal logic. For every formula defining an MSC language, we construct a
communicating finite-state machine (CFM) accepting the same language. The CFM
obtained has size exponential in the size of the formula. This synthesis
problem is solved in full generality, i.e., also for MSCs with unbounded
channels. The model checking problem for CFMs and HMSCs turns out to be in
PSPACE for existentially bounded MSCs. Finally, we show that, for PDL with
intersection, the semantics of a formula cannot be captured by a CFM anymore
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