On promise problems and a great automata diversity
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2022-02-28
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Ocampo Gamboa, Juan Pablo; Nieto Chávez, Iván Gustavo (2022). On promise problems and a great automata diversity. https://hdl.handle.net/11349/28864
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Resumen
The concept of promise problems was introduced and initially explored by Even, Selman, Yacobi, Goldreich, and other scholars in the 80's. The promise problems can be seen as a generalization of the decision problems and such problems are even more fundamental than formal language and decision problems because they are used on the most basic concepts for complexity theory and some applications like cryptography.
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Along this paper, we give the basic concepts on automata theory and we introduce the way to accept or reject promise problems and decision problems, the last one through the notions of recognizability and solvability. Afterwards, we show some results concerning promise problems, oneof these is the fact that we can find an automaton recognized exactly by measure-once one-way quantum finite automata, but no deterministic automata can recognize it. Finally, we focus in some of the applications of promise problems and how these can be useful in different topics of computer science and complexity theory.