"Call a Turing machine $A$ a *d-machine* if, for some polynomial $p(\cdot)$, when $A$ starts with any input string, say of length $n$, in its alphabet on its (otherwise blank) tape, it will halt in a number of steps bounded by $p(n)$ with its tape either blank or bearing just a string of length $n$. Then each d-machine $A$ corresponds to a d-machine $B$ which, when started with any input string in its alphabet, will halt with a blank tape, if $A$ halts with a blank tape for every input the length of $B$'s input, and otherwise will halt with an output tape that, input to $A$, will lead to $A$ halting with a non-blank tape."


**Interpretation:** Input for $A$ codes candidate "solutions" while blank/non-blank output indicates just refutation/verification. For $B$, input marks only length while output codes an $A$-verifiable solution.



Is the following statement a correct formulation of the (much doubted) P = NP conjecture?
This is a correct formulation of P=NP, with two caveats:


* The blank character cannot be considered part of the alphabet. Otherwise a length n+1 string with a blank at the end is indistinguishable to a length n string.
* P=NP is usually defined as "If it possible to recognize a solution it is possible to find out if there is a solution". You define it as "If it is possible to recognize a solution it is possible to find a solution". However, these to formulations are equivalent.


