My area of research comprises syntax and semantics of various formal systems (lambda calculi and related theories) of constructive mathematics and topological aspects of computational complexity.
I introduced in my papers, entitled Algebra of Constructions I, II, a certain new algebraic method of investigation of the mentioned formal systems which provides a better understanding of their mathematical (categorical) semantics and on the other hand which gives rise to some new algorithms for their decidability.
Concerning aspects of computational complexity, I discovered the interconnections between this complexity an a certain hierarchy of complexity of some finite topological presentations of the infinite graphs which are the natural representations of computable functions.
Since the year 2000 I have extended my area of research by a new field called Molecular Computing, where mathematical models of natural processes investigated in Biology and Biochemistry are applied in designing and implementation of new computing devices which realize massively parallel computations.
In my recent papers in this field I apply membrane systems and P-systems, due to Gheorghe Păun, to describe new efficient computing devices for solving computationally complex problems of Cryptography and Number Theory.