We present an inductive characterization for an invariant to stand in a given finite-state transition system. We show how this characterization can be computed by means of BDD-based operations, without performing a fixpoint iteration over sets of states as the CTL symbolic model checking algorithm does.

We propose a novel numerical method for solving a quadratic vector equation arising in Markovian Binary Trees. The numerical method consists in a fixed point iteration, expressed by means of the Perron vectors of a sequence of nonnegative matrices. A theoretical convergence analysis is performed. The proposed method outperforms the existing methods for close-to-critical problems.

We define strong regularity of a parametric interval matrix and give conditions that characterize it. The new conditions give a better estimation for regularity of a parametric matrix than the conditions used so far. Verifiable sufficient regularity conditions are also presented for parametric matrices. The new sufficient conditions motivate a generalization of Rump’s parametric fixed-point ite...

We prove that the fixed point iteration of arbitrary positive concave mappings with nonempty set converges geometrically for any starting point. also show positivity is crucial this result to hold, and concept (nonlinear) spectral radius asymptotic provides us information about convergence factor. As a practical implication results shown here, we rigorously explain why some power control load e...

Iterative image estimation methods have been widely used in emission tomography. Accurate estimation of the uncertainty of the reconstructed images is essential for quantitative applications. While both iteration-based noise analysis and fixed-point noise analysis have been developed, current iteration-based results are limited to only a few algorithms that have an explicit multiplicative updat...

In this paper, the aim is to make the predictive control of a plant described by a Timed Event Graph which follows the specifications defined by a P-time Event Graph. We propose a compromise approach between the ideal optimality of the solution and the on-line application of the computed solution when the relevant optimal control cannot be applied for a given computer. The technique is based on...

We study a principal-agent game where the principal commits to an affine contract. We suppose that the principal has incomplete information but he can adjust the contract according to the myopically behaving agent’s reactions when the game is played repeatedly. The adjustment process can be considered as a learning model. We derive convergence conditions for fixed-point iteration as an adjustme...

Non-trivial analysis problems require posets with infinite ascending and descending chains. In order to compute reasonably precise post-fixpoints of the resulting systems of equations, Cousot and Cousot have suggested accelerated fixpoint iteration by means of widening and narrowing (Cousot and Cousot, 1976, 1977a). The strict separation into phases, however, may unnecessarily give up precision...

In the constraint proposal method a mediator locates points at which the two decision makers have joint tangent hyperplanes. We give conditions under which these points are Pareto optimal and we prove that under these conditions the mediator’s problem has a solution, when the number of issues in the negotiation is two or any odd number greater than two. In practice, the mediator adjusts a hyper...

In this paper, we study the existence and uniqueness of fractional differential equations with boundary value conditions. A new generalized singular type Gronwall inequality is given to obtain important a priori bounds. Existence and uniqueness results of solutions are established by virtue of fractional calculus and fixed point method under some weak conditions. An example is given to illustra...