Emil Leon Post（数学家与逻辑学家 1897-1954）是第一个制定了利用符号来表示逻辑的推理系统——作为一个推论，他证明了任何逻辑系统（包括数学）能够被这样的一个符号系统来表达。
标记系统是 Emil Leon Post 在1943年创立的确定性计算模型，作为一种简单形式的字符串重写系统。标记系统也可以看作抽象机，叫做 Post 标记机（不要混淆于Post-图灵机）-- 简单的说，其唯一的磁带是无限长度的 FIFO 队列的有限状态自动机，在每次状态转变中机器读在队列头部的符号，从头部删除固定数目的符号，并可以向尾部增加符号。
基本资料回目录
Emil Leon Post
Born February 11, 1897
Augustów, then Russian Empire ,
today Poland
Died April 21, 1954,
New York City, U.S.
Fields Mathematics
Alma mater Columbia University
Known for Formulation 1,
Post correspondence problem,
completeness-proof of Principia's propositional calculus
简介回目录
Emil Leon Post, Ph.D., (February 11, 1897, Augustów – April 21, 1954, New York City) was a mathematician and logician.
Early work
Post was born into a Polish-Jewish family that immigrated to America when he was a child. After completing his Ph.D. in mathematics at Columbia University, he did a post doctorate at Princeton University. While at Princeton, he came very close to discovering the incompleteness of Principia Mathematica, which Kurt Gödel proved in 1931. Post then became a high school mathematics teacher in New York City. In 1936, he was appointed to the mathematics department at the City College of the College of the City of New York, where he remained until his death.
In his Columbia University doctoral thesis, Post proved, among other things, that the propositional calculus of Principia Mathematica was complete: all tautologies are theorems, given the Principia axioms and the rules of substitution and modus ponens. Post also devised truth tables independently of Wittgenstein and C.S. Peirce and put them to good mathematical use. Jean Van Heijenoort's (1966) well-known source book on mathematical logic reprinted Post's classic article setting out these results.
Recursion theory
In 1936, Post developed, independently of Alan Turing, a mathematical model of computation that was essentially equivalent to the Turing machine model. Intending this as the first of a series of models of equivalent power but increasing complexity, he titled his paper Formulation 1. (This model is sometimes called "Post's machine" or a Post-Turing machine, but is not to be confused with Post's tag machines or other special kinds of Post canonical system, a computational model using string rewriting and developed by Post in the 1920s but first published in 1943).
The unsolvability of his Post correspondence problem turned out to be exactly what was needed to obtain unsolvability results in the theory of formal languages.
In an influential address to the American Mathematical Society in 1944, he raised the question of the existence of an uncomputable recursively enumerable set whose Turing degree is less than that of the halting problem. This question, which became known as Post's Problem, stimulated much research. It was solved in the affirmative in the 1950s by the introduction of the powerful priority method in recursion theory.
Selected papers
1936, "Finite Combinatory Processes - Formulation 1," Journal of Symbolic Logic 1: 103-105.
1943, "Formal Reductions of the General Combinatorial Decision Problem," American Journal of Mathematics 65: 197-215.
1944, "Recursively enumerable sets of positive integers and their decision problems," Bulletin of the American Mathematical Society 50: 284-316. Introduces the important concept of many-one reduction.
