2,357 research outputs found
Higher-Order Pushdown Systems with Data
We propose a new extension of higher-order pushdown automata, which allows to
use an infinite alphabet. The new automata recognize languages of data words
(instead of normal words), which beside each its letter from a finite alphabet
have a data value from an infinite alphabet. Those data values can be loaded to
the stack of the automaton, and later compared with some farther data values on
the input. Our main purpose for introducing these automata is that they may
help in analyzing normal automata (without data). As an example, we give a
proof that deterministic automata with collapse can recognize more languages
than deterministic automata without collapse. This proof is simpler than in the
no-data case. We also state a hypothesis how the new automaton model can be
related to the original model of higher-order pushdown automata.Comment: In Proceedings GandALF 2012, arXiv:1210.202
Introduction
Zadanie pt. Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę
Bootstrap Robust Prescriptive Analytics
We address the problem of prescribing an optimal decision in a framework
where its cost depends on uncertain problem parameters that need to be
learned from data. Earlier work by Bertsimas and Kallus (2014) transforms
classical machine learning methods that merely predict from supervised
training data into prescriptive methods
taking optimal decisions specific to a particular covariate context .
Their prescriptive methods factor in additional observed contextual information
on a potentially large number of covariates to take context specific
actions which are superior to any static decision . Any naive
use of limited training data may, however, lead to gullible decisions
over-calibrated to one particular data set. In this paper, we borrow ideas from
distributionally robust optimization and the statistical bootstrap of Efron
(1982) to propose two novel prescriptive methods based on (nw) Nadaraya-Watson
and (nn) nearest-neighbors learning which safeguard against overfitting and
lead to improved out-of-sample performance. Both resulting robust prescriptive
methods reduce to tractable convex optimization problems and enjoy a limited
disappointment on bootstrap data. We illustrate the data-driven decision-making
framework and our novel robustness notion on a small news vendor problem as
well as a small portfolio allocation problem
Efficient Intra-Household Allocation of Parental Leave
We propose a model of how parents resolve conflicts about sharing the negative short and long-term consequences from parenthood-related career interruptions on earnings. We introduce childcare sharing in a collective model of household behavior with public consumption as in Blundell, Chiappori, and Meghier (2005). Conceptually, the solution to the household problem can be thought of as a two-stage process: Parents first agree on public expenditures on professional childcare; then, conditional on the level of public consumption and the budget constraint stemming from stage one, parents determine their individual job absence durations and private consumption shares. Using relative income measures from German parental benefit data as distribution factors, we find evidence for Pareto efficiency in childcare sharing. More precisely, households with higher total incomes purchase more professional childcare, and changes in distribution factors shift the conditional parental leave allocation in favor of the partner whose relative income increased.childcare, collective model, conditional sharing rule, intra-household allocation
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
The MSO+U theory of (N, <) is undecidable
We consider the logic MSO+U, which is monadic second-order logic extended
with the unbounding quantifier. The unbounding quantifier is used to say that a
property of finite sets holds for sets of arbitrarily large size. We prove that
the logic is undecidable on infinite words, i.e. the MSO+U theory of (N,<) is
undecidable. This settles an open problem about the logic, and improves a
previous undecidability result, which used infinite trees and additional axioms
from set theory.Comment: 9 pages, with 2 figure
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