Testing from a finite state machine: Extending invertibility to sequences

When testing a system modelled as a finite state machine it is desirable to minimize the effort required. It has been demonstrated that it is possible to utilize test sequence overlap in order to reduce the test effort and this overlap has been represented by using invertible transitions. In this paper invertibility will be extended to sequences in order to reduce the test effort further and encapsulate a more general type of test sequence overlap. It will also be shown that certain properties of invertible sequences can be used in the generation of state identification sequences

Tridiagonal substitution Hamiltonians

We consider a family of discrete Jacobi operators on the one-dimensional integer lattice with Laplacian and potential terms modulated by a primitive invertible two-letter substitution. We investigate the spectrum and the spectral type, the fractal structure and fractal dimensions of the spectrum, exact dimensionality of the integrated density of states, and the gap structure. We present a review of previous results, some applications, and open problems. Our investigation is based largely on the dynamics of trace maps. This work is an extension of similar results on Schroedinger operators, although some of the results that we obtain differ qualitatively and quantitatively from those for the Schoedinger operators. The nontrivialities of this extension lie in the dynamics of the associated trace map as one attempts to extend the trace map formalism from the Schroedinger cocycle to the Jacobi one. In fact, the Jacobi operators considered here are, in a sense, a test item, as many other models can be attacked via the same techniques, and we present an extensive discussion on this.Comment: 41 pages, 5 figures, 81 reference