20 research outputs found
Methods for Structural Pattern Recognition: Complexity and Applications
Katedra kybernetik
Converting Nondeterministic Two-Way Automata into Small Deterministic Linear-Time Machines
In 1978 Sakoda and Sipser raised the question of the cost, in terms of size
of representations, of the transformation of two-way and one-way
nondeterministic automata into equivalent two-way deterministic automata.
Despite all the attempts, the question has been answered only for particular
cases (e.g., restrictions of the class of simulated automata or of the class of
simulating automata). However the problem remains open in the general case, the
best-known upper bound being exponential. We present a new approach in which
unrestricted nondeterministic finite automata are simulated by deterministic
models extending two-way deterministic finite automata, paying a polynomial
increase of size only. Indeed, we study the costs of the conversions of
nondeterministic finite automata into some variants of one-tape deterministic
Turing machines working in linear time, namely Hennie machines, weight-reducing
Turing machines, and weight-reducing Hennie machines. All these variants are
known to share the same computational power: they characterize the class of
regular languages
Mathematical Formulae Recognition
summary:We present a summary of our work in progress related to mathematical formulae recognition. Our approach is based on the structural construction paradigm and two-dimensional grammars. It is a general framework and can be successfully used in the analysis of images containing objects exhibiting rich structural relations. In contrast to most of all other known approaches, the method does not treat symbols segmentation and structural analysis as two separate processes. This allows the system to solve arising ambiguities more reliably. We have already implemented pilot studies for the off-line as well as on-line mathematical formulae recognition showing that the proposed method can be effectively implemented and practically used
Some classes of rational functions for pictures
With the aid of homogeneous morphisms, we turn the deterministic two-dimensional two-way
ordered restarting automaton and its extended variant into devices that compute
transductions of pictures, and we study the resulting classes of transductions in
detail
Two-dimensional Sgraffito automata
We present a new model of a two-dimensional computing device called Sgraffito
automaton. In general, the model is quite simple, which allows a clear design
of computations. When restricted to one-dimensional inputs, that is, strings, the
Sgraffito automaton does not exceed the power of finite-state automata. On the other hand,
for two-dimensional inputs, it yields a family of picture languages with good closure
properties that strictly includes the class REC of recognizable picture languages. The
deterministic Sgraffito automata define a class of picture languages that includes the
class of deterministic recognizable picture languages DREC, the class of picture languages
that are accepted by four-way alternating automata, those that are accepted by
deterministic one-marker automata, and the sudoku-deterministically recognizable picture
languages, but the membership problem for the accepted languages is still decidable in
polynomial time. In addition, the deterministic Sgraffito automata accept some unary
picture languages that are outside of the class REC