Alan Louis Selman (April 2, 1941 – January 22, 2021)[1] was an American mathematician and theoretical computer scientist known for his research on structural complexity theory, the study of computational complexity in terms of the relation between complexity classes rather than individual algorithmic problems.

[4] His dissertation, Arithmetical Reducibilities and Sets of Formulas Valid in Finite Structures, was supervised by Paul Axt, a student of Stephen Cole Kleene.

[3] Selman's research publications included well-cited works on the classification of different types of reductions according to their computational power, the formulation of promise problems, the complexity class UP of problems solvable by unambiguous Turing machines, and their applications to the computational complexity of cryptography:[2][3] As well as being the editor of several edited volumes, Selman was the coauthor of the textbook Computability and Complexity Theory (with Steve Homer, Springer, 2001; 2nd ed., 2011).

[8] In 2002, ACM SIGACT (the Special Interest Group on Algorithms and Computation Theory of the Association for Computing Machinery) gave him their Distinguished Service Prize, noting his work in helping to found the Computational Complexity Conference and in helping to fund theoretical computer science research through his work drafting policy reports for the National Science Foundation.

[9] The journal Theory of Computing Systems is organizing a commemorative issue celebrating his memory.