4 research outputs found
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
Infinite and bi-infinite words with decidable monadic theories
We study word structures of the form (D,<,P) where D is either the naturals or the integers with the natural linear order < and P is a predicate on D. In particular we show: The set of recursive infinite words with decidable monadic second order theories is Sigma_3-complete. We characterise those sets P of integers that yield bi-infinite words with decidable monadic second order theories. We show that such "tame" predicates P exist in every Turing degree. We determine, for a set of integers P, the number of indistinguishable biinfinite words. Through these results we demonstrate similarities and differences between logical properties of infinite and bi-infinite words
The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars
We present observations and timing analyses of 68 millisecond pulsars (MSPs)
comprising the 15-year data set of the North American Nanohertz Observatory for
Gravitational Waves (NANOGrav). NANOGrav is a pulsar timing array (PTA)
experiment that is sensitive to low-frequency gravitational waves. This is
NANOGrav's fifth public data release, including both "narrowband" and
"wideband" time-of-arrival (TOA) measurements and corresponding pulsar timing
models. We have added 21 MSPs and extended our timing baselines by three years,
now spanning nearly 16 years for some of our sources. The data were collected
using the Arecibo Observatory, the Green Bank Telescope, and the Very Large
Array between frequencies of 327 MHz and 3 GHz, with most sources observed
approximately monthly. A number of notable methodological and procedural
changes were made compared to our previous data sets. These improve the overall
quality of the TOA data set and are part of the transition to new pulsar timing
and PTA analysis software packages. For the first time, our data products are
accompanied by a full suite of software to reproduce data reduction, analysis,
and results. Our timing models include a variety of newly detected astrometric
and binary pulsar parameters, including several significant improvements to
pulsar mass constraints. We find that the time series of 23 pulsars contain
detectable levels of red noise, 10 of which are new measurements. In this data
set, we find evidence for a stochastic gravitational-wave background.Comment: 90 pages, 74 figures, 6 tables; published in Astrophysical Journal
Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational
Wave Background. For questions or comments, please email
[email protected]
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