50,971 research outputs found
New Douglas-Rachford algorithmic structures and their convergence analyses
In this paper we study new algorithmic structures with Douglas- Rachford (DR)
operators to solve convex feasibility problems. We propose to embed the basic
two-set-DR algorithmic operator into the String-Averaging Projections (SAP) and
into the Block-Iterative Pro- jection (BIP) algorithmic structures, thereby
creating new DR algo- rithmic schemes that include the recently proposed cyclic
Douglas- Rachford algorithm and the averaged DR algorithm as special cases. We
further propose and investigate a new multiple-set-DR algorithmic operator.
Convergence of all these algorithmic schemes is studied by using properties of
strongly quasi-nonexpansive operators and firmly nonexpansive operators.Comment: SIAM Journal on Optimization, accepted for publicatio
Parameterized Linear Temporal Logics Meet Costs: Still not Costlier than LTL
We continue the investigation of parameterized extensions of Linear Temporal
Logic (LTL) that retain the attractive algorithmic properties of LTL: a
polynomial space model checking algorithm and a doubly-exponential time
algorithm for solving games. Alur et al. and Kupferman et al. showed that this
is the case for Parametric LTL (PLTL) and PROMPT-LTL respectively, which have
temporal operators equipped with variables that bound their scope in time.
Later, this was also shown to be true for Parametric LDL (PLDL), which extends
PLTL to be able to express all omega-regular properties.
Here, we generalize PLTL to systems with costs, i.e., we do not bound the
scope of operators in time, but bound the scope in terms of the cost
accumulated during time. Again, we show that model checking and solving games
for specifications in PLTL with costs is not harder than the corresponding
problems for LTL. Finally, we discuss PLDL with costs and extensions to
multiple cost functions.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Exact linear modeling using Ore algebras
Linear exact modeling is a problem coming from system identification: Given a
set of observed trajectories, the goal is find a model (usually, a system of
partial differential and/or difference equations) that explains the data as
precisely as possible. The case of operators with constant coefficients is well
studied and known in the systems theoretic literature, whereas the operators
with varying coefficients were addressed only recently. This question can be
tackled either using Gr\"obner bases for modules over Ore algebras or by
following the ideas from differential algebra and computing in commutative
rings. In this paper, we present algorithmic methods to compute "most powerful
unfalsified models" (MPUM) and their counterparts with variable coefficients
(VMPUM) for polynomial and polynomial-exponential signals. We also study the
structural properties of the resulting models, discuss computer algebraic
techniques behind algorithms and provide several examples
Алгебра алгоритмов, базирующаяся на данных
На основі модифікованої моделі ЕОМ Глушкова побудовано систему алгоритмічних алгебр. Дані формалізовані й специфіковані на вході й виході Д-операторів і, таким чином, побудований формальний апарат базується на даних. Доведено деякі властивості Д-операторів і операцій, що утворюють сигнатуру алгебри, а також можливість побудови похідних Д-операторів.A system of algorithmic algebras is formed based on a modified Glushkov’s computer model. Data are formalized and specified at the input and output of D-operators and thus the formal apparatus is based on data. Some properties of D-operators and of operations that form the signature of algebra are proved and setting up derived D-operators is shown to be possible
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