arXiv subjects
Publications and source records attributed to André Luiz Barbosa.
This paper presents a little reflection about the Sleeping Beauty Problem, maybe contributing to shed light on it and perhaps helping to find a simple and elegant solution that could definitively resolve the controversies about it.
This paper presents a short and simple proof of the Four-Color Theorem that can be utterly checkable by human mathematicians, without computer assistance. The new key idea that has allowed it and the global structure of the proof are presented in the Introduction.
This paper demonstrates that P \not= NP. The way was to generalize the traditional definitions of the classes P and NP, to construct an artificial problem (a generalization to SAT: The XG-SAT, much more difficult than the former) and then to demonstrate that it is in NP but not in P (where the classes P and NP are generalized and called too simply P and NP in this paper, and then it is explained why the traditional classes P and NP should be fixed and replaced by these generalized ones into Theory of Computer Science). The demonstration consists of: 1. Definition of Restricted Type X Program; 2. Definition of the General Extended Problem of Satisfiability of a Boolean Formula - XG-SAT; 3. Generalization to classes P and NP; 4. Demonstration that the XG-SAT is in NP; 5. Demonstration that the XG-SAT is not in P; 6. Demonstration that the Baker-Gill-Solovay Theorem does not refute the proof; 7. Demonstration that the Razborov-Rudich Theorem does not refute the proof; 8. Demonstration that the Aaronson-Wigderson Theorem does not refute the proof.
This paper defines The Dead Cryptographers Society Problem - DCS (where several great cryptographers created many polynomial-time Deterministic Turing Machines (DTMs) of a specific type, ran them on their proper descriptions concatenated with some arbitrary strings, deleted them and left only the results from those running, after they died: if those DTMs only permute and sometimes invert the bits on input, is it possible to decide the language formed by such resulting strings within polynomial time?), proves some facts about its computational complexity, and discusses some possible uses on Cryptography, such as into distance keys distribution, online reverse auction and secure communication.