The paper entitled:**“The P versus NP Problem is Wrong, P=NP iff P=!NP”** was submitted to the *Journal of the Association for Computing Machinery* on 20th June, 2013. Its current status is:”Awaiting Referee Selection”. It can be accessed at the following link:

https://www.4shared.com/office/wEF-PqOr/JACM_Lambda.html

Any comments are welcome.

Best,

Rafee Kamouna.

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Abstract

After analysis of the “Y” paradoxical fixpoint operator that is used to define recursion over the $\lambda$-calculus, a similar paradox is discovered over Turing machines. Established belief in computation theory for decades is that the $\lambda$- calculus Kleene-Rosser paradox recognition problem is {\em undefined} over the $\lambda$-calculus and {\em undecidable} over Turing machines. It is the $\lambda$-calculus corresponding counter-part to the halting problem over Turing machines. This long-established result is {\bf\underline{refuted}} by a proof in this paper. Instead, it is shown that the recognition problem of the $\lambda$-calculus Kleene-Rosser paradox is {\em decidable if and only if it is undecidable}, over both the $\lambda$-calculus and Turing machines. Via {\bf\underline{diagonalization}}, the paradoxical recursion in $\lambda$- calculus is directly transported to a paradox over Turing machines resulting in the subtitle paradoxes.