Theoretical Computer Science and Computing Paradigms
Classical formal Languages and automata theory are important bases of Theoretical Computer Science. The language classes of the Chomsky hierarchy are well-known, we are doing research on them and some of their refinement: on union-free, regular, fixed-linear, 2det-lin, linear, context-free, permutation, context-sensitive and recursively enumerable languages. Other fields of formal language theory, such as pattern languages, regulated rewriting, programmed grammars, contextual hypergraph grammars, primitive words and permutations, 2-head automata, automata with translucent letters, (CD-systems of) restarting automata are also addressed. Some of our results are connected to the fields of decidability and complexity.
New computing paradigms are bio-inspired and/or highly parallel models of computation. The Interval-valued computing is based on the interval-valued (fuzzy) logic, and the PSPACE-complete qSAT is solved in linear interval-valued computation. DNA and membrane computing are developed in a fast way from 1990's. They are based on the massive parallelism given by the Nature in biological (or biochemical) processes. The nature of the parallelism in computations are analysed: the 'and'-parallelism and the 'or'-parallelism are described... WK automata are 2-head automata working on double stranded DNA molecules, several variations of them are investigated...
Genetic algorithms are parallel algorithms based on the biological evolution. They are effectively used to solve computationally hard problems in a reasonable way...
For detailed research activity in this field, see Theoretical Computer Science and Computing Paradigms
Digital Geometry and its Applications
Discrete Geometry, Computer Graphics, Digital Image Processing, Combinatorics : digital (path-based) distance functions on various grids, neighborhood sequences, digital circles, digital discs, discrete tomography, distance transform, weighted distances, triangular grid, face-centered cubic grid, body-centered cubic grid, diamond grid, nD grids. The geometry of digital world (e.g., digital pictures, screens) differs from the Euclidean geometry: there are neighbor points (there are points without points between them), the number of points with a given Euclidean distance r is finite and usually not connected, there could be lines “crossing each other" without common point (such as the two diagonals of a chess board)… Therefore the digital geometry is needed. Based on the various neighborhood structures of various grids digital, i.e., path-based distance functions are defined and they can be used in various (digital) fields…
There is also a strong argument to use various (non-standard) grids in applications: With higher precision in image acquisition equipment, the amount of data that is used when processing these images is increasing. By using optimal sampling grids, in 3D, almost 30% fewer samples are needed to get the same representation/reconstruction quality; and as the images are computed, rather than captured directly, there is no special reason to use the standard cubic grid.
For detailed research activity in this field, see Digital Geometry and its Applications
I am doing research on other fields, like
Logic, Puzzles, Combinatorics, Graphs, Diagrams, Artificial Intelligence, Game theory, Soft Computing
Logic and reasoning: there are various arguments for many-valued logic instead two-valued logic. We have developed the interval-valued logic as a general fuzzy logic. This logic can also be used in visual reasoning. Based on this system a new computing paradigm is investigated...
Another way of diagrammatic reasoning goes by graphs. Various types of logical (truth-teller - liar) puzzles are represented and solved by graphs. Some related Boolean programming problems are also solved in a similar way...
Various concepts of graphs connected to formal language and automata theory are also analysed...
In Artificial Intelligence the state-space representation is a cruical point to solve the problem in an efficient way; we did some work related to this fact...
Games with chance nodes and multiplayer games were analysed...
Genetic algorithms are frequently used to obtain resonable solution for computationally hard problems... Other soft computing methods use fuzzy values. Simulated annealing is also a soft computing technique for optimization.
For detailed research activity in these fields, see my Further research activities
Contact:
- Benedek Nagy
- E-mail: nbenedek (dot) inf (at) gmail
