Symbolic computation of the Duggal transform

The Value of Symbolic Computation

Standard generative linguistic theory, which uses discrete symbolic models of cognition, has some strengths and weaknesses. It is strong on providing a network of outposts that make scientific travel in the jungles of natural language feasible. It is weak in that it currently depends on the elaborate and unformalized use of intuition to develop critical supporting assumptions about each data po...

Challenges of Symbolic Computation

The success of the symbolic mathematical computation discipline is striking. The theoretical advances have been continuous and significant: Gröbner bases, the Risch integration algorithm, integer lattice basis reduction, hypergeometric summation algorithms, etc. From the beginning in the early 1960s, it has been the tradition of our discipline to create software that makes our ideas readily ava...

Symbolic computation of reachability

Merging Sub-symbolic and Symbolic Computation

In a recent short paper and a report (see [Neto et al. 98] and [Neto and Costa 99]) it was shown that programming languages can be translated efficiently on recurrent (analog, rational weighted) neural nets, using bounded resources. This fact was achieved by creating a neural programming language called NETDEF, such that each program corresponds to a modular neural net that computes it. This fr...

Numeric versus Symbolic Computation

Twentyfive years ago when I studied Physics, only one of the students who participated in a laboratory course that I took was possessing one of the first calculators to process the data we were obtaining. Believe it or not, everybody else, including me, had to use a slide-rule for this purpose. Nowadays, the calculator is used by everybody, by far not only for academic purposes. Hence it is the...

Symbolic Computation Software Composability

We present three examples of the composition of Computer Algebra Systems to illustrate the progress on a composability infrastructure as part of the SCIEnce (Symbolic Computation Infrastructure for Europe) project. One of the major results of the project so far is an OpenMath based protocol called SCSCP (Symbolic Computation Software Composability Protocol). SCSCP enables the various software p...