
Quantified X3SAT: P = NP = PSPACE
This paper shows that P = NP via oneinthree (or exactly1) 3SAT, and t...
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Overarching Computation Model (OCM)
Existing models of computation, such as a Turing machine (hereafter, TM)...
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A class of examples demonstrating that P is different from NP in the "P vs NP" problem
The CMI Millennium "P vs NP Problem" can be resolved e.g. if one shows a...
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A GameSemantic Model of Computation, Revisited: An AutomataTheoretic Perspective
In the previous work, we have given a novel, gamesemantic model of comp...
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Postulatebased proof of the P != NP hypothesis
The paper contains a proof for the P != NP hypothesis with the help of t...
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Separation of P and NP
There have been many attempts to solve the P versus NP problem. However,...
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On randomized generation of slowly synchronizing automata
Motivated by the randomized generation of slowly synchronizing automata,...
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Philosophical Solution to P=?NP: P is Equal to NP
The P=?NP problem is philosophically solved by showing P is equal to NP in the random access with unit multiply (MRAM) model. It is shown that the MRAM model empirically best models computation hardness. The P=?NP problem is shown to be a scientific rather than a mathematical problem. The assumptions involved in the current definition of the P?=NP problem as a problem involving non deterministic Turing Machines (NDTMs) from axiomatic automata theory are criticized. The problem is also shown to be neither a problem in pure nor applied mathematics. The details of The MRAM model and the well known Hartmanis and Simon construction that shows how to code and simulate NDTMs on MRAM machines is described. Since the computation power of MRAMs is the same as NDTMs, P is equal to NP. The paper shows that the justification for the NDTM P?=NP problem using a letter from Kurt Godel to John Von Neumann is incorrect by showing Von Neumann explicitly rejected automata models of computation hardness and used his computer architecture for modeling computation that is exactly the MRAM model. The paper argues that Deolalikar's scientific solution showing P not equal to NP if assumptions from statistical physics are used, needs to be revisited.
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