Given that we want a 1-bit query data structure, the querying algorithm basically suggests itself. Consider a bipartite graph G, whose pieces L and R stand for the Universe and Memory bits, respectively (so |L| = m). Based on the input set S ⊆ L, for every vertex of R we decide whether to write either 0 or 1 on it. Then given a query x ∈ L, we pick a random neighbor y of x and output “x ∈ S” if...

In this paper, we develop a numerically efficient scheme for setmembership prediction and filtering for discrete-time nonlinear systems, that takes into explicit account the effects of nonlinearities via local second-order information. The filtering scheme is based on a classical prediction/update recursion that requires at each step the solution of a convex semidefinite optimization problem. T...

Hammerstein system identification from measurements affected by bounded noise is considered in the paper. First, we show that the computation of tight parameter bounds requires the solution to nonconvex optimization problems where the number of decision variables increases with the length of the experimental data sequence. Then, in order to reduce the computational burden of the identification ...

Qualitative thematic maps are graphic representations of the process of areal differentiation, a process recognized as one of the hallmarks of the geographer’s craft and one of geography’s grand traditions. Traditionally the process can best be described as classification based on Boolean Set Theory wherein the area bounded by the cartographic line is considered to be in that class for the targ...

Set-membership identification of a Linear Parameter Varying (LPV) model describing the vehicle lateral dynamics is addressed in the paper. The model structure, chosen as much as possible on the ground of physical insights into the vehicle lateral behavior, consists of two single-input single-output LPV models relating the steering angle to the yaw rate and to the sideslip angle. A set of experi...

An undirected graph is commonly represented as a set of vertices and a set of doubletons of vertices; but one can also represent vertices by finite sets so as to ensure that membership mimics, over those sets, the edge relation of the graph. This alternative modeling, applied to connected claw-free graphs, recently gave crucial clues for obtaining simpler proofs of some of their properties (e.g...

We consider the following problem: Given a commitment to a value σ, prove in zero-knowledge that σ belongs to some discrete set Φ. The set Φ can perhaps be a list of cities or clubs; often Φ can be a numerical range such as [1, 2]. This problem arises in e-cash systems, anonymous credential systems, and various other practical uses of zeroknowledge protocols. When using commitment schemes relyi...

In this paper, one aims at investigating the stability and convergence properties of a set membership identification methods involving ARMAX and OE model structures and optimal bounding ellipsoid based parameter adaptation. Fundamental results are obtained, they generalize some results that have been already established for FIR and ARX model structures.

| This paper presents a set-membership state estimation scheme for linear systems with unknown but bounded inputs and noise. The approach is to compute 100% conndence regions for the state vector in the form of optimal ellipsoidal sets in the state-space. The proposed algorithm entails greatly reduced computational complexity in comparison to other state estimation schemes (e.g., Schweppe's alg...

A recent perspective on model error modeling is applied to set membership identification techniques in order to highlight the separation between unmodeled dynamics and noise. Model validation issues are also easily addressed in the proposed framework. The computation of the minimum noise bound for which a nominal model is not falsified by i/o data, can be used as a rationale for selecting an ap...