Radio Computing • Internet and Co • Programming with Stair • Theoretical Informatics (Previous | Next)

Internet and Co deals with some aspects of the future internet: How can examinations be conducted with the aid of the internet? How can a (number of) identification, the ID, assigned uniquely to each person, usefully be applied in connection with the internet? What types of content will be on the internet? How can information user profiles simplify search processes on the internet?

What tasks could a multifunction device called strap fulfil? What can modern clothes achieve (for deafblind people)? How can virtual reality be realised (in rooms and in the brain)? How can goods be transported quickly in future? What are the consequences for professions in the future? What must be in future considered for intelligent machines?

Programming with Stair presents a programming concept for development environments, with which source codes can be converted into ones of other programming languages, or rule-based into freely chosen notations. The new programming language Clare is capable of learning (by adding rules and meta-rules) and can activate (self-) optimisation algorithms that adapt themselves to the individual circumstances within a narrow time frame.

The theoretical informatics presents a \(\mathcal{O}(1)\) sorting algorithm for non-bounded hardware. The organisation of the memory locations as a binary tree makes it possible to use the \(\mathcal{O}(n)\) method bit sort for n input values read in succession. The minimum or maximum framework of a graph with n nodes is calculated in \(\mathcal{O}(log \; n)\). The halting problem newly answered with a positive respond and the P versus NP problem is solved.

Radio computing enables, by simultaneous radioing on different frequencies, parallel computing through parallel communication of each memory cell with each other one. Thus, n values can be sorted in \(\mathcal{O}(1)\), the indexing of database tables becomes widely obsolete. Networking and cloud computing solve with radio technology various problems much faster than before, what can be accessed comfortably at home.

All problems of an arbitrary (higher) world can be solved at one go by singling out those from all possible solutions with recording the solution formations by (comparative) sorting that satisfy the solution criteria. The gödelisation renders substantial comparisons broadly unnecessary. Consequently, all problems are for L in the same complexity class \(\mathcal{O}(1)\).

L does not get around the formation of all possibilities, since crucial problems are irreducible in terms of complexity. For our (finite) world, this means that crucial problems are not solvable in it. This does not mean, however, that we cannot solve the problems important for us, but only, that we cannot answer all scientific questions.

Theorem: All problems of a finite world can be solved in \(\mathcal{O}(1)\).

Proof: Conditions are checked by inserting the complete solution space into the conditions at once, possibly by parallel processing. Calculations are accelerated by summarising calculation steps. Continued summarising yields an overall calculation step. Hence the claim follows, since every finite solution space can also be constructed in one step.

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