37,981 research outputs found
Certified Roundoff Error Bounds Using Semidefinite Programming.
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs or custom hardware implementation. This problem becomes challenging when the program does not employ solely linear operations as non-linearities are inherent to many interesting computational problems in real-world applications. Existing solutions to reasoning are limited in the presence of nonlinear correlations between variables, leading to either imprecise bounds or high analysis time. Furthermore, while it is easy to implement a straightforward method such as interval arithmetic, sophisticated techniques are less straightforward to implement in a formal setting. Thus there is a need for methods which output certificates that can be formally validated inside a proof assistant. We present a framework to provide upper bounds on absolute roundoff errors. This framework is based on optimization techniques employing semidefinite programming and sums of squares certificates, which can be formally checked inside the Coq theorem prover. Our tool covers a wide range of nonlinear programs, including polynomials and transcendental operations as well as conditional statements. We illustrate the efficiency and precision of this tool on non-trivial programs coming from biology, optimization and space control. Our tool produces more precise error bounds for 37 percent of all programs and yields better performance in 73 percent of all programs
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
Formal Proofs for Nonlinear Optimization
We present a formally verified global optimization framework. Given a
semialgebraic or transcendental function and a compact semialgebraic domain
, we use the nonlinear maxplus template approximation algorithm to provide a
certified lower bound of over . This method allows to bound in a modular
way some of the constituents of by suprema of quadratic forms with a well
chosen curvature. Thus, we reduce the initial goal to a hierarchy of
semialgebraic optimization problems, solved by sums of squares relaxations. Our
implementation tool interleaves semialgebraic approximations with sums of
squares witnesses to form certificates. It is interfaced with Coq and thus
benefits from the trusted arithmetic available inside the proof assistant. This
feature is used to produce, from the certificates, both valid underestimators
and lower bounds for each approximated constituent. The application range for
such a tool is widespread; for instance Hales' proof of Kepler's conjecture
yields thousands of multivariate transcendental inequalities. We illustrate the
performance of our formal framework on some of these inequalities as well as on
examples from the global optimization literature.Comment: 24 pages, 2 figures, 3 table
Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models
A computation scheme for solving elliptic boundary value problems with
axially symmetric confining potentials using different sets of one-parameter
basis functions is presented. The efficiency of the proposed symbolic-numerical
algorithms implemented in Maple is shown by examples of spheroidal quantum dot
models, for which energy spectra and eigenfunctions versus the spheroid aspect
ratio were calculated within the conventional effective mass approximation.
Critical values of the aspect ratio, at which the discrete spectrum of models
with finite-wall potentials is transformed into a continuous one in strong
dimensional quantization regime, were revealed using the exact and adiabatic
classifications.Comment: 6 figures, Submitted to Proc. of The 12th International Workshop on
Computer Algebra in Scientific Computing (CASC 2010) Tsakhkadzor, Armenia,
September 5 - 12, 201
Third Conference on Artificial Intelligence for Space Applications, part 2
Topics relative to the application of artificial intelligence to space operations are discussed. New technologies for space station automation, design data capture, computer vision, neural nets, automatic programming, and real time applications are discussed
Symblicit algorithms for optimal strategy synthesis in monotonic Markov decision processes
When treating Markov decision processes (MDPs) with large state spaces, using
explicit representations quickly becomes unfeasible. Lately, Wimmer et al. have
proposed a so-called symblicit algorithm for the synthesis of optimal
strategies in MDPs, in the quantitative setting of expected mean-payoff. This
algorithm, based on the strategy iteration algorithm of Howard and Veinott,
efficiently combines symbolic and explicit data structures, and uses binary
decision diagrams as symbolic representation. The aim of this paper is to show
that the new data structure of pseudo-antichains (an extension of antichains)
provides another interesting alternative, especially for the class of monotonic
MDPs. We design efficient pseudo-antichain based symblicit algorithms (with
open source implementations) for two quantitative settings: the expected
mean-payoff and the stochastic shortest path. For two practical applications
coming from automated planning and LTL synthesis, we report promising
experimental results w.r.t. both the run time and the memory consumption.Comment: In Proceedings SYNT 2014, arXiv:1407.493
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