several tables have been given due to a − minimal sets. our main aim in this paper is tocomplete these tables by employing several examples.

A notion of entropy of a normal state on a finite von Neumann algebra in Segal’s sense is considered, and its superadditivity is proven together with a necessary and sufficient condition for its additivity. Bounds on the entropy of the state after measurement are obtained, and it is shown that a weakly repeatable measurement gives minimal entropy and that a minimal state entropy measurement sat...

Several algorithms have been proposed for generating satisfactory state assignments for normal fundamental mode asynchronous sequential circuits. Programmed versions of minimal and near-minimal techniques have been incorporated in automated synthesis systems, but are known to require computational efforts which increase exponentially with flow table size. Other methods, requiring much less effo...

We present a method to store additional information in a minimal automaton so that it is possible to compute a corresponding tree node number for a state. The number can then be used to retrieve additional information. The method works for minimal (and any other) deterministic acyclic finite state automata (DFAs). We also show how to compute the inverse mapping.

We illustrate an algorithm that starting from the image representation of a strictly bounded-real system computes a minimal balanced state variable, from which a minimal balanced state realization is readily obtained. The algorithm stems from an iterative procedure to compute a storage function, based on a technique to solve a generalization of the Nevanlinna interpolation problem.

We construct a general state which is an eigenvector of the annihilation operator of the Generalized Heisenberg Algebra. We show for several systems, which are characterized by different energy spectra, that this general state satisfies the minimal set of conditions required to obtain Klauder’s minimal coherent states.

A formula, which relates the state dimensions of a minimal trellis of a Reed-Muller code to those of another Reed-Muller code with lower order and shorter length, is derived in this correspondence. State dimension at every position of a minimal trellis of any Reed-Muller code can be obtained by a recursive application of this formula.

The problem of state-space modelling of 2D-trajectories from exponential data can be solved using a duality approach. Finding a minimal complexity model, i.e. one having the minimal number of state variables among those unfalsified by the data, can be transformed to a rank-minimization problem involving constant matrices computed from the data. We illustrate a Gröbner basis approach to solve su...

Here, the method proposed in [13] for constructing minimal-length checking sequences based on distinguishing sequences is improved. The improvement is based on optimizations of the state recognition sequences and their use in constructing test segments. It is shown that the proposed improvement further reduces the length of checking sequences produced from minimal, completely specified, and det...

We prove a tight uniform continuity bound for a family of entropies which includes the von Neumann entropy, the Tsallis entropy and the α-Rényi entropy, Sα, for α ∈ (0, 1). We establish necessary and sufficient conditions for equality in the continuity bound and prove that these conditions are the same for every member of the family. Our result builds on recent work in which we constructed a st...