We propose a simple and intuitive algorithm for solving md-DFA problem using algorithm concepts within extended operators, our approach shows quadratic polynomial time and hence proves the equivalence between polynomial and non-polynomial classes, we have also shown that minimal non-emptiness of automata problem can be solved in polynomial time with help of modified subset construction, rather that building a product automaton, which lead to factorial size of the memory and time, in this work we also have used many non-tractable existing (...) examples and computed them in polynomial time, which guarantees that our algorithm solves NP-complete problem in almost linear polynomial time, we have also avoided the problem of product automata by an algorithmic approach, we are also giving the starting ground for the proof of back-reference problem which was discussed before, notion to the globally local increment is also given as the main argument towards the resolution of "P versus NP" theorem, which coincides with the finitarity term in general mathematics. (shrink)

As we have proposed our conjecture or hypothesis, we give the full disproof of this fact in this work.

As we have prior result of regular grammars over set of computational problems, we are to present the universal ‘complexity automata’ which can be used in solving any problem.

We present the basic abstract of the newly obtained results on class of non-layered artificial neural networks.

As we know we have a set conjecture by Akram Louiz, here we give the full proof of the inequality of “P” and “NP” complexity classes due to the made conjecture.

As we have presented our functional hypothesis of complexity classes in previous review, we are to present the full mathematical proof of the relations between complexity classes.

As we have defined the median PQI-operator in our previous work, it’s time to give the full proof of the existence of the functional dependence between Complexity Classes which lead to the final outcome for all of Millennium Theorems proposed by Clay Mathematics Institute.

In this work we present the algorithms to produce deterministic finite automaton (DFA) for extended operators in regular expressions like intersection, subtraction and complement. The method like "overriding" of the source NFA (NFA not defined) with subset construction rules is used. The past work described only the algorithm for AND-operator(or intersection of regular languages); in this paper the construction for the MINUS-operator (and complement) is shown.