We extended Isabelle/HOL with a pair of definitional commands for datatypes and codatatypes. They support mutual and nested (co)recursion through well-behaved type constructors, including mixed recursion–corecursion, and are complemented by syntaxes for introducing primitive (co)recursive functions and by a general proof method for reasoning coinductively. As a case study, we ported Isabelle’s ...

We consider neural nets whose connections are defined by growth rules taking the form of recursion relations. These are called genetic neural nets. Learning in these nets is achieved by simulated annealing optimization of the net over the space of recursion relation parameters. The method is tested on a previously defined continuous coding problem. Results of control experiments are presented s...

It is known that the digital waveguide (DW) method for solving the wave equation numerically on a grid can be manipulated into the form of the standard finite-difference time-domain (FDTD) method (also known as the “leapfrog” recursion). This paper derives a simple rule for going in the other direction, that is, converting the state variables of the FDTD recursion to corresponding wave variable...

This work concerns estimation of linear autoregressive models with Markov-switching using expectation maximisation (E.M.) algorithm. Our method generalise the method introduced by Elliot for general hidden Markov models and avoid to use backward recursion.

In this paper, we show how the clausal temporal resolution technique developed for temporal logic provides an effective method for searching for invariants, and so is suitable for mechanising of the wide class of temporal problems. We demonstrate that this scheme of searching for invariants can be also applied to a class of multi-predicate induction problems represented by mutually recursive de...

Spectral densities of the response of nonlinear systems to white noise excitation are considered. By using a formal solution of the associated Fokker-Planck-Kolmogorov equation, response spectral densities are represented by formal power series expansion for large frequencies. The coe cients of the series, known as the spectral moments, are determined in terms of rst-order response statistics. ...