The central concept of the Evolving Transformation System (ETS) model is struc-tural object representation constructed by the process of inductive inference. The model was proposed in 1990 by Lev Goldfarb to be applied to any pattern learning or classification problem. A formal exposition of the model is presented in this the-sis. It defines the concepts that encapsulate the idea of structural representation and includes lemmas and theorems that link these concepts together into a single model. The chosen form of definitions is related to several general postulates about structural representation. The main feature of this formalization of the ETS model is the presence of an infinite hierarchy of representational levels. At each level, object representations are constructed from primitive constructive transformations (building blocks). Primitive transformations of the next level correspond to complex context-dependent additive transformations of the previous one. This hierarchy allows to reduce the complexity of representation of an object by constructing its higher-level representation through

Speech recognition has been a very active area of research over the past twenty years. Despite an evident progress, it is generally agreed by the practitioners of the field that performance of the current speech recognition systems is rather suboptimal and new ap-proaches are needed. The motivation behind the undertaken research is an observation that the notion of representation of objects and concepts that once was considered to be central in the early days of pattern recognition, has been largely marginalised by the ad-vent of statistical approaches. As a consequence of a predominantly statistical approach to speech recognition problem, due to the numeric, feature vector-based, nature of rep-resentation, the classes inductively discovered from real data using decision-theoretic techniques have little meaning outside the statistical framework. This is because deci-sion surfaces or probability distributions are difficult to analyse linguistically. Because of the later limitation it is doubtful that the gap between speech recognition and lin-guistic research can be bridged by the numeric representations. This thesis investigates an alternative, structural, approach to spoken language representation and categorisa-

We outline a formalism for "structural", or "symbolic", representation, the necessity of which is acutely felt in all sciences. One can develop an initial intuitive understanding of the proposed representation by simply generalizing the process of construction of natural numbers: replace the identical structureless units out of which numbers are built by several structural ones, attached consecutively. Now, however, the resulting constructions embody the corresponding formative/generative histories, since we can see what was attached and when.

[W]e may again recall what Einstein stressed: that given a sufficiently powerful formal assumption, a fertile and comprehensive theory may... be constructed without prior attention to the detailed facts, or even before they are known. L. L. Whyte, Internal Factors in Evolution, 1965 We outline a formalism for structural, or symbolic, representation, the necessity of which has been acutely felt in all sciences, particularly biology, for quite some time now. At the same time, biology has been gradually edging to the forefront of sciences, although the reasons obviously have nothing to do with its state of formalization or maturity—which is quite primitive as compared, for example, to that of physics. Rather, the reasons have to do with the growing realization that the objects of biology are not only more important and interesting, but that they also more explicitly exhibit the evolving nature of all objects in the Universe. It is this view of objects as evolving structural processes that we aim to address here, in contrast to the ubiquitous mathematical view of objects as points in some abstract space. One can gain an initial intuitive understanding of the proposed representation by generalizing the (Peano) process of construction of natural numbers: replace the single structureless unit out of which a number is built by multiple structural ones. An immediate but critical consequence of the distinguishability/multiplicity of units in the construction process is that we can now see which unit was attached and when. Hence, the resulting representation for the first time embodies temporal structural information in the form of a formative, or generative, history.

What is a structural representation?