The calculus of an unnormalized relational model of data
The category of Pawlak machines
The chromatic sum of a graph: history and recent developments.
The Chu construction: history of an idea.
The closure under division and a characterization of the recognizable -subsets
The communication hierarchy of time and space bounded parallel machines
We describe the communicating alternating machines and their simulation. We show that, in the case of communicating alternating machines which are bounded, simultaneously, by polynomial time and logarithmic space, the use of three communication levels instead of two does not increase computational power of communicating alternating machines. This resolves an open problem [2] concerning the exact position of machines with three communication levels in the hierarchy.
The Communication Hierarchy of Time and Space Bounded Parallel Machines
We describe the communicating alternating machines and their simulation. We show that, in the case of communicating alternating machines which are bounded, simultaneously, by polynomial time and logarithmic space, the use of three communication levels instead of two does not increase computational power of communicating alternating machines. This resolves an open problem [2] concerning the exact position of machines with three communication levels in the hierarchy.
The completely distributive lattice of machine invariant sets of infinite words
We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. The length and width of it is c. We show the subword complexity and the growth function create machine invariant classes.
The Complexity and Construction of Many Faces in Arrangements of Lines and of Segments.
The complexity of classification problems
The complexity of constructing gerechte designs.
The Complexity of Cutting Complexes.
The Complexity of Many Cells in Arrangements of Planes and Related Problems.
The complexity of retina operators.
The complexity of systolic dissemination of information in interconnection networks
The complexity of the travelling repairman problem
The compositional construction of Markov processes II
We add sequential operations to the categorical algebra of weighted and Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones with evolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput. 37 (2007) 977–1013].
The compositional construction of Markov processes II
We add sequential operations to the categorical algebra of weighted and Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones with evolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput.37 (2007) 977–1013].
The computation of characteristic vectors of logical-probabilistic expressions
The connection between a (3,2)-semigroup automaton and a semigroup automaton