Emil Post

Emil Leon Post (born the February 11th 1897, dead the April 21st 1954) was a American Mathématicien born on the territory of current the Poland in an Jewish family. It is at the origin of the problem of correspondence of Post .

It also published in 1921 an exhaustive study of the clones of the algebras with two elements.

The problem of correspondence of Post

One starts from two finished continuations U and V containing the same number of words finished on an unspecified alphabet. For example $u\_1\; =\; aba,\; u\_2\; =\; B,\; u\_3\; =\; has,\; u\_4\; =\; ab,\; v\_1\; =\; has,\; v\_2\; =\; B,\; v\_3\; =\; ababa,\; v\_4\; =\; b$.

One seeks a succession of indices $i\_1,\; i\_2,\dots \; i\_n$ such as the concatenation of the $u\_\; \{i\_k\}$ corresponds to that of the $v\_\; \{i\_k\}$. Here the continuation (1,2,3,2,1) is a solution since $u\_1\; u\_2\; u\_3\; u\_2\; u\_1\; =\; v\_1\; v\_2\; v\_3\; v\_2\; v\_1\; =\; ababababa$.

The problem of correspondence of Post (in summary PCP) consists in determining the existence of such a continuation. It is Indécidable in general: it cannot exist of algorithm able to provide an answer for U and V arbitrary.

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