196,274 research outputs found
SAT Solving for Argument Filterings
This paper introduces a propositional encoding for lexicographic path orders
in connection with dependency pairs. This facilitates the application of SAT
solvers for termination analysis of term rewrite systems based on the
dependency pair method. We address two main inter-related issues and encode
them as satisfiability problems of propositional formulas that can be
efficiently handled by SAT solving: (1) the combined search for a lexicographic
path order together with an \emph{argument filtering} to orient a set of
inequalities; and (2) how the choice of the argument filtering influences the
set of inequalities that have to be oriented. We have implemented our
contributions in the termination prover AProVE. Extensive experiments show that
by our encoding and the application of SAT solvers one obtains speedups in
orders of magnitude as well as increased termination proving power
On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach
In this article, we consider a receding horizon control of discrete-time
state-dependent jump linear systems, particular kind of stochastic switching
systems, subject to possibly unbounded random disturbances and probabilistic
state constraints. Due to a nature of the dynamical system and the constraints,
we consider a one-step receding horizon. Using inverse cumulative distribution
function, we convert the probabilistic state constraints to deterministic
constraints, and obtain a tractable deterministic receding horizon control
problem. We consider the receding control law to have a linear state-feedback
and an admissible offset term. We ensure mean square boundedness of the state
variable via solving linear matrix inequalities off-line, and solve the
receding horizon control problem on-line with control offset terms. We
illustrate the overall approach applied on a macroeconomic system
On subsumption and semiunification in feature algebras
AbstractWe consider a generalization of term subsumption, or matching, to a class of mathematical structures which we call feature algebras. We show how these generalize both first-order terms and the feature structures used in computational linguistics. The notion of term subsumption generalizes to a natural notion of algebra homomorphism. In the setting of feature algebras, unification, corresponds naturally to solving constraints involving equalities between strings of unary function symbols, and semiunification also allows inequalities representing subsumption constraints. Our generalization allows us to show that the semiunification problem for finite feature algebras is undecidable. This implies that the corresponding problem for rational trees (cyclic terms) is also undecidable
On the Convergence of (Stochastic) Gradient Descent with Extrapolation for Non-Convex Optimization
Extrapolation is a well-known technique for solving convex optimization and
variational inequalities and recently attracts some attention for non-convex
optimization. Several recent works have empirically shown its success in some
machine learning tasks. However, it has not been analyzed for non-convex
minimization and there still remains a gap between the theory and the practice.
In this paper, we analyze gradient descent and stochastic gradient descent with
extrapolation for finding an approximate first-order stationary point in smooth
non-convex optimization problems. Our convergence upper bounds show that the
algorithms with extrapolation can be accelerated than without extrapolation
- …