2,455 research outputs found
Avionics and controls research and technology
The workshop provided a forum for industry and universities to discuss the state-of-the-art, identify the technology needs and opportunities, and describe the role of NASA in avionics and controls research
Algorithmic Analysis of Qualitative and Quantitative Termination Problems for Affine Probabilistic Programs
In this paper, we consider termination of probabilistic programs with
real-valued variables. The questions concerned are:
1. qualitative ones that ask (i) whether the program terminates with
probability 1 (almost-sure termination) and (ii) whether the expected
termination time is finite (finite termination); 2. quantitative ones that ask
(i) to approximate the expected termination time (expectation problem) and (ii)
to compute a bound B such that the probability to terminate after B steps
decreases exponentially (concentration problem).
To solve these questions, we utilize the notion of ranking supermartingales
which is a powerful approach for proving termination of probabilistic programs.
In detail, we focus on algorithmic synthesis of linear ranking-supermartingales
over affine probabilistic programs (APP's) with both angelic and demonic
non-determinism. An important subclass of APP's is LRAPP which is defined as
the class of all APP's over which a linear ranking-supermartingale exists.
Our main contributions are as follows. Firstly, we show that the membership
problem of LRAPP (i) can be decided in polynomial time for APP's with at most
demonic non-determinism, and (ii) is NP-hard and in PSPACE for APP's with
angelic non-determinism; moreover, the NP-hardness result holds already for
APP's without probability and demonic non-determinism. Secondly, we show that
the concentration problem over LRAPP can be solved in the same complexity as
for the membership problem of LRAPP. Finally, we show that the expectation
problem over LRAPP can be solved in 2EXPTIME and is PSPACE-hard even for APP's
without probability and non-determinism (i.e., deterministic programs). Our
experimental results demonstrate the effectiveness of our approach to answer
the qualitative and quantitative questions over APP's with at most demonic
non-determinism.Comment: 24 pages, full version to the conference paper on POPL 201
Non relativistic Kapitza-Dirac scattering
We use techniques of singular perturbation theory to investigate the scattering of nonrelativistic charged particles by a standing light wave (Kapitza-Dirac scattering). Unlike previous treatments, we give explicit results for the effects of the time-dependent part of the field. For low field intensity or low particle energy, we show that the leading-order effects can be found from an averaged equation, and we compute corrections. For the strong fields that can be produced by modern lasers and/or high particle energies, we show that the time dependence of the potential leads to focusing. Our methods can be applied to other problems with time-periodic potentials
Differences in Practices of Personal Spirituality and Beliefs Concerning Salvation between Adventist Teachers in Argentina, Australia, Brazil, Korea, Philippines, the Solomon Islands, Russia, Ukraine, the United States and Zimbabwe
The differences between the survey responses from Adventist teachers in Argentina, Australia, Brazil, Korea, Philip- pines, the Solomon Islands, Russia, Ukraine, the United States and Zimbabwe regarding practices of personal spirituality and understanding of salvation are explained by underlying cultural differences
Strong, Weak and Branching Bisimulation for Transition Systems and Markov Reward Chains: A Unifying Matrix Approach
We first study labeled transition systems with explicit successful
termination. We establish the notions of strong, weak, and branching
bisimulation in terms of boolean matrix theory, introducing thus a novel and
powerful algebraic apparatus. Next we consider Markov reward chains which are
standardly presented in real matrix theory. By interpreting the obtained matrix
conditions for bisimulations in this setting, we automatically obtain the
definitions of strong, weak, and branching bisimulation for Markov reward
chains. The obtained strong and weak bisimulations are shown to coincide with
some existing notions, while the obtained branching bisimulation is new, but
its usefulness is questionable
Stochastic Invariants for Probabilistic Termination
Termination is one of the basic liveness properties, and we study the
termination problem for probabilistic programs with real-valued variables.
Previous works focused on the qualitative problem that asks whether an input
program terminates with probability~1 (almost-sure termination). A powerful
approach for this qualitative problem is the notion of ranking supermartingales
with respect to a given set of invariants. The quantitative problem
(probabilistic termination) asks for bounds on the termination probability. A
fundamental and conceptual drawback of the existing approaches to address
probabilistic termination is that even though the supermartingales consider the
probabilistic behavior of the programs, the invariants are obtained completely
ignoring the probabilistic aspect.
In this work we address the probabilistic termination problem for
linear-arithmetic probabilistic programs with nondeterminism. We define the
notion of {\em stochastic invariants}, which are constraints along with a
probability bound that the constraints hold. We introduce a concept of {\em
repulsing supermartingales}. First, we show that repulsing supermartingales can
be used to obtain bounds on the probability of the stochastic invariants.
Second, we show the effectiveness of repulsing supermartingales in the
following three ways: (1)~With a combination of ranking and repulsing
supermartingales we can compute lower bounds on the probability of termination;
(2)~repulsing supermartingales provide witnesses for refutation of almost-sure
termination; and (3)~with a combination of ranking and repulsing
supermartingales we can establish persistence properties of probabilistic
programs.
We also present results on related computational problems and an experimental
evaluation of our approach on academic examples.Comment: Full version of a paper published at POPL 2017. 20 page
Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs
Computing reachability probabilities is a fundamental problem in the analysis
of probabilistic programs. This paper aims at a comprehensive and comparative
account on various martingale-based methods for over- and under-approximating
reachability probabilities. Based on the existing works that stretch across
different communities (formal verification, control theory, etc.), we offer a
unifying account. In particular, we emphasize the role of order-theoretic fixed
points---a classic topic in computer science---in the analysis of probabilistic
programs. This leads us to two new martingale-based techniques, too. We give
rigorous proofs for their soundness and completeness. We also make an
experimental comparison using our implementation of template-based synthesis
algorithms for those martingales
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