However, if you insist on seeing a genuine North American smile, click here

Welcome !!

Lev  Goldfarb

Diploma Math/CS  (Leningrad)


Ph.D. in Systems Design Engineering  (Waterloo)

Area: Pattern Recognition


Retired prof., Faculty of Computer Science, UNB

Short Professional Bio


Inductive  Information Systems
Fredericton,  NB,  E3B 2V1

tel:         (506) 455-4323
e-mail:   goldfarbat’ unb ‘dot’ ca






Book in progress: “Is There a Common Structuring Law in the Universe:  Integrating Mind into Scientific View of the Universe”





A general description of the fundamentally new, event-based, representational formalism  (ETS)  proposed by us :


It is the first and so far the only general formal framework for modeling evolving forms of (object and class) representations.

While all of modern science is based on the formalism that is precise elaboration of the ‘continuous’, ETS can be considered as a proposal for a precise and general elaboration of the ‘discrete’.  Moreover, and what is more, while in the conventional scientific models syntax is not related to semantics—and hence, of necessity, we have no choice but to project onto reality  their formal structures, e.g. the vector space structure—ETS is the first formalism which has been designed in such a way that syntax and semantics are congruent, so that the proposed formal structures are supposed to be the blueprints of the corresponding structures in nature.

Also, in contrast to the conventional scientific models—which do not make any explicit assumptions about the structure of objects in nature and represent objects as ‘points’—in ETS, objects are viewed and represented as irreversible structural processes,  i.e. as  (non-linear, temporal)  streams of interconnected structured events.

On the philosophical side, the opposition between the ‘mind’ and ‘matter’ has been overcome, since now both ‘rely’ on the same form of representation.


Is there a different mathematics, of generatively structured entities,

which would clarify the nature of the structural ‘measurement’ processes?


Natural numbers—think of them as  strings of •'s—which have gradually emerged over many millennia, served as the basis of the ubiquitous numeric forms for representing information about objects or events.  All our basic scientific paradigms are built on the foundation of this representation.  Measurement, as conventionally understood, is the corresponding process for (numeric) representation of objects, i.e. it is a procedure or device that realizes the mapping from the set of objects to the set of numbers.

Accordingly, in science, there has existed only one underlying (i.e. numeric) representational model, and it has served as a universal blueprint for building all known measurement devices.  Moreover, we, collectively, have had no experience with any other kind of measurement device!  Thus, when contemplating the transition from the classical measurement processes to the structural ones, we are faced with the situation absolutely unprecedented in the history of science, with the ensuing benefits far outweighing the difficulties.

When considering structural generalization of the classical measurement, or representation, theory, one has to keep in mind that any ‘measurement device’ can be conceived (and constructed) provided we have identified the underlying formal structure.  This formal structure—in contrast to the conventional mathematical, point-like, view of objects entrenched in the concept of the set—is supposed to provide a fundamentally new, structural, form of object representation, and the developments associated with such formal structure will constitute a new, structural, mathematics.

A crucial feature of the ETS representation that we have proposed is related to the observation that all objects in nature (including mental objects) have a formative history.  We have gradually realized that the concept of formative object history and the concept of object representation are very similar.  Thus, a ‘true’ representational formalism must provide a unified formal structure for capturing an object's formative ‘history’: both, complete history (as in Nature itself) or subjective (as perceived by an agent).  It is not difficult to see that the numeric representation possesses this feature but only in a very rudimentary form:  numeric representation records the process of object formation relying on the extremely limited concatenation operation for strings over a single letter alphabet  {•}  (because this is how a natural number is built).  Such trivially temporal representation intrinsically cannot capture any non-trivial structural formative history, in which the corresponding events are of more complex structure (than the concatenation operation).

Accordingly, all conventional discrete ‘representations’—such as strings over an alphabet of size > 1, trees, and graphs—cannot be viewed as true object representations, since they do not capture the formative history.  For example, the formative history of a string is not part of the string representation.  Hence a string is not a reliable form of object representation, since it has an exponential number of formative histories associated with its generation, creating a computationally insurmountable problem for inductive learning process, which is supposed to discover the (generative) class representation.

Returning to the measurement process, one can say that all classical measurement processes ‘produce’ numbers as their outputs, while the generalized measurement process is supposed to output non-numeric entities, which we call structs.  Thus, the generalized measurement process captures the temporal, or informational, structure of objects in an inductive manner, through a more dynamic interaction with the environment.

I am convinced that gradually, as the development of various applications of the ETS formalism progresses, the new form of object representation should supersede such preliminary and incomplete ones as the string, tree, graph, etc.

ETS  group


Muhammad Al-Digeil

Sean Falconer

Dave Gay

Lev Goldfarb

Oleg Golubitsky

Alexander Gutkin

Dmitry Korkin

Reuben Peter-Paul

Ian Scrimger


Research areas of interest

Inductive informatics :


·       structural  representations  (equivalently:  evolutionary-, or  inductively-,  structured environments);

           structural  (inductive, intelligent)  measurement processes

                       connections with:  physics,  chemistry,  biochemistry,  biology,  neurobiology,  neuroscience,  cognitive science


·       fundamental limitations of the classical (numeric) representations and measurement processes

·       inductive learning processes (natural and artificial)

·       ETS  (theory and applications)

·       fundamental limitations of numeric learning models

·       pattern recognition/machine learning

·       protein representation & classification

·       inductive databases and data  (including image and web)  mining

·       bioinformatics  &  cheminformatics

·       information retrieval

·       inductive models of vision and their applications

·       speech recognition and understanding

·       cognitive models based on ETS formalism


Journal editorial boards

  ·  Pattern Recognition                   (1991 – 2008)


·  Pattern Recognition Letters       (2004 – 2007)


·  Cognitive  Neurodynamics        (2007 2010)


Selected publications, talks, and workshops


My second (updated) FQXi essay “Nature is fundamentally discrete but our basic formalism is not”  and its discussion


My first FQXi essay and its discussion  “What is possible in physics depends on the chosen representational formalism”


A simplified visual illustration of the process of spatial instantiation of the ETS representation for the Bubble Man example from Part III of our main paper  (produced by Reuben Peter-Paul)


Slightly modified talk at MPI , Tübingen, July 2007 (PowerPoint slides: if you want to see the “hidden” slides and notes, save the file first; the latter option is also faster)


IIT, Ottawa, talk, September 2006  “The first class(ification)-oriented representational formalism” (PowerPoint slides; if you want to see the “hidden” slides and notes, save the file first; the latter option is also faster)


"Pattern representation and the future of pattern recognition: a program for action"  ICPR 2004 satellite workshop, Cambridge, UK, Aug 22 , 2004See the introductory paper for this workshop "Representational formalisms: why we haven't had one"  and  the introductory talk


Cornell Biophysics  March 2003 talk  "Can a formal model unify biology?"


Topic for "Birds of a Feather" discussion at ISMB 2002 (MSWord version)


·       Four papers for the ETS book

·       Dmitry Korkin and Lev Goldfarb, "Multiple genome rearrangement: A General approach via the evolutionary genome graph" (PDF version), ISMB 2002  (also to appear in a special issue of Bioinformatics).

·       Lev Goldfarb and Oleg Golubitsky, "What is a structural measurement process?" (PDF version), Faculty of Computer Science, U.N.B., Technical Report  TR01-147, October 2001.

·       Lev Goldfarb, Oleg Golubitsky, and Dmitry Korkin, "What is a structural representation?" (PDF version), Faculty of Computer Science, U.N.B., Technical Report  TR00-137, December 2000.

·       Lev Goldfarb, Oleg Golubitsky, and Dmitry Korkin, "What is a structural representation in chemistry: Towards a unified framework for CADD?" (PDF version), Faculty of Computer Science, U.N.B., Technical Report  TR00-138, December 2000.

·       Lev Goldfarb and Jaroslav Hook, "Why classical models for pattern recognition are not pattern recognition models", in International Conference on Advances in Pattern Recognition, ed. Sameer Singh, Springer, pp.405-414, 1998.

·       Lev Goldfarb, Sanjay S. Deshpande and Virendra C. Bhavsar, " Inductive theory of vision", Faculty of Computer Science", U.N.B., Technical Report TR96-108, April 1996.

·       Sanjay S. Deshpande, Lev Goldfarb, and Virendra C. Bhavsar, "Cooperative cellular transformation systems"

·       Lev Goldfarb, John Abela, Virendra C. Bhavsar and Vithal N. Kamat, "Can a vector space based learning model discover inductive class generalization in a symbolic environment?", Pattern Recognition Letters 16, pp. 719-726, 1995.

·       Lev Goldfarb and Sandeep Nigam, "The unified learning paradigm: A foundation for AI", in V. Honavar and L. Uhr, eds., Artificial Intelligence and Neural Networks: Steps towards Principled Integration, Academic Press, Boston, MA, 1994.

·       Lev Goldfarb, "What is distance and why do we need the metric model for pattern learning?", Pattern Recognition 25, pp. 431-438, 1992.

·       Tony Y. T. Chan and Lev Goldfarb, "Primitive pattern learning", Pattern Recognition 25, pp. 883-889, 1992.

·       Lev Goldfarb, "On the foundations of intelligent processes - I: An evolving model for pattern learning", Pattern Recognition 23, pp. 595-616, 1990. (Received an annual Pattern Recognition Society Award)



Graduate thesis supervised since 1990


·       B. Reuben Peter-Paul (2008) On the Role of Temporal and Spatial Representations in Light of ETS Formalism,  Master's Thesis

·       Ian Scrimger (2007) Structural Representation of the Game of Go,  Master's Thesis

·       Mohammad S. Al-Digeil (2005) Towards an ETS Representation of Proteins,  Master's Thesis

·       Sean Falconer (2005) On the Evolving Transformation System Model Representation of Fairy Tales,  Master's Thesis

·       Oleg Golubitsky (2004) On the Formalization of the Evolving Transformation System Model,  Ph.D. Thesis

·       Dmitry Korkin (2003) A New Model for Molecular Representation and Classification: Formal Approach Based on the ETS Framework, Ph.D. Thesis

·       David Clement (2003) Information Retrieval via the ETS Model,  Master's Thesis

·       John M. Abela (2002) ETS Learning of Kernel Languages,  Ph.D. Thesis

·       Jaroslav Hook (1998) Are Artificial Neural Networks Learning Machines?,  Master's Thesis

·       Sanjay S. Deshpande (1996) On the Foundations of Vision,  Master's Thesis

·       Vithal N. Kamat (1995) Inductive Learning with the Evolving Tree Transformation System,  Ph.D. Thesis

·       John M. Abela (1994) Topics in Evolving Transformation Systems,  Master's Thesis

·       Sandeep Nigam (1993) Metric Model Based Generalization and Generalization Capabilities of Connectionist Models,  Master's Thesis

·       Wiranto B. Santoso (1992) Learning Algorithm for the Reconfigurable Learning Machine,  Master's Thesis

·       Tony Y. T. Chan (1992) Learning as Optimization,  Ph.D. Thesis

·       Sonya Dewi (1991) Dynamic Selection of Primitives in the Metric Model for Pattern Learning,  Master's Thesis

·       Ahmady Satriawan (1990) A Tree Transformation System for Pattern Learning,  Master's Thesis



Advising external graduate students


·       Alexander Gutkin (2005) Towards Formal Structural Representation of Spoken Language:  An Evolving Transformation System (ETS) Approach,  Ph.D. Thesis,  University of Edinburgh, UK

·       Raj Verma (1991) A Metric Approach to Isolated Word Recognition,  Master's Thesis,  University of Toronto, Canada





Romanian translation of this web page:       (by  Web Geek Science: )