362 research outputs found
A Characterization for Decidable Separability by Piecewise Testable Languages
The separability problem for word languages of a class by
languages of a class asks, for two given languages and
from , whether there exists a language from that
includes and excludes , that is, and . In this work, we assume some mild closure properties for
and study for which such classes separability by a piecewise
testable language (PTL) is decidable. We characterize these classes in terms of
decidability of (two variants of) an unboundedness problem. From this, we
deduce that separability by PTL is decidable for a number of language classes,
such as the context-free languages and languages of labeled vector addition
systems. Furthermore, it follows that separability by PTL is decidable if and
only if one can compute for any language of the class its downward closure wrt.
the scattered substring ordering (i.e., if the set of scattered substrings of
any language of the class is effectively regular).
The obtained decidability results contrast some undecidability results. In
fact, for all (non-regular) language classes that we present as examples with
decidable separability, it is undecidable whether a given language is a PTL
itself.
Our characterization involves a result of independent interest, which states
that for any kind of languages and , non-separability by PTL is
equivalent to the existence of common patterns in and
Determinization of One-Counter Nets
One-Counter Nets (OCNs) are finite-state automata equipped with a counter that is not allowed to become negative, but does not have zero tests. Their simplicity and close connection to various other models (e.g., VASS, Counter Machines and Pushdown Automata) make them an attractive model for studying the border of decidability for the classical decision problems.
The deterministic fragment of OCNs (DOCNs) typically admits more tractable decision problems, and while these problems and the expressive power of DOCNs have been studied, the determinization problem, namely deciding whether an OCN admits an equivalent DOCN, has not received attention.
We introduce four notions of OCN determinizability, which arise naturally due to intricacies in the model, and specifically, the interpretation of the initial counter value. We show that in general, determinizability is undecidable under most notions, but over a singleton alphabet (i.e., 1 dimensional VASS) one definition becomes decidable, and the rest become trivial, in that there is always an equivalent DOCN
Countdown games, and simulation on (succinct) one-counter nets
We answer an open complexity question by Hofman, Lasota, Mayr, Totzke (LMCS
2016) [HLMT16] for simulation preorder of succinct one-counter nets (i.e.,
one-counter automata with no zero tests where counter increments and decrements
are integers written in binary), by showing that all relations between
bisimulation equivalence and simulation preorder are EXPSPACE-hard for these
nets. We describe a reduction from reachability games whose
EXPSPACE-completeness in the case of succinct one-counter nets was shown by
Hunter [RP 2015], by using other results. We also provide a direct
self-contained EXPSPACE-completeness proof for a special case of such
reachability games, namely for a modification of countdown games that were
shown EXPTIME-complete by Jurdzinski, Sproston, Laroussinie [LMCS 2008]; in our
modification the initial counter value is not given but is freely chosen by the
first player. We also present a new simplified proof of the belt theorem that
gives a simple graphic presentation of simulation preorder on one-counter nets
and leads to a polynomial-space algorithm; it is an alternative to the proof
from [HLMT16].Comment: A part of this paper elaborates arxiv-paper 1801.01073 and the
related paper presented at Reachability Problems 201
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables
Weak Alternating Timed Automata
Alternating timed automata on infinite words are considered. The main result
is a characterization of acceptance conditions for which the emptiness problem
for these automata is decidable. This result implies new decidability results
for fragments of timed temporal logics. It is also shown that, unlike for MITL,
the characterisation remains the same even if no punctual constraints are
allowed
Bondi-Metzner-Sachs symmetry, holography on null-surfaces and area proportionality of "light-slice" entropy
It is shown that certain kinds of behavior, which hitherto were expected to
be characteristic for classical gravity and quantum field theory in curved
spacetime, as the infinite dimensional Bondi-Metzner-Sachs symmetry, holography
on event horizons and an area proportionality of entropy, have in fact an
unnoticed presence in Minkowski QFT. This casts new light on the fundamental
question whether the volume propotionality of heat bath entropy and the
(logarithmically corrected) dimensionless area law obeyed by
localization-induced thermal behavior are different geometric parametrizations
which share a common primordeal algebraic origin. Strong arguments are
presented that these two different thermal manifestations can be directly
related, this is in fact the main aim of this paper. It will be demonstrated
that QFT beyond the Lagrangian quantization setting receives crucial new
impulses from holography onto horizons. The present paper is part of a project
aimed at elucidating the enormous physical range of "modular localization". The
latter does not only extend from standard Hamitonian heat bath thermal states
to thermal aspects of causal- or event- horizons addressed in this paper. It
also includes the recent understanding of the crossing property of formfactors
whose intriguing similarity with thermal properties was, although sometimes
noticed, only sufficiently understood in the modular llocalization setting.Comment: 42 pages, changes, addition of new results and new references, in
this form the paper will appear in Foundations of Physic
- …