A Short Introduction to Implicit Computational Complexity

These lecture notes are meant to serve as a short introduction to implicit computational complexity for those students who have little or no knowledge of recursion theory and proof theory. They have been obtained by enriching and polishing a set of notes the author wrote for a course (on the same subject) he gave at ESSLLI 2010. These notes are definitely not meant to be comprehensive nor exhaustive, but on the other hand much effort has been done to keep them self-contained.

[1]  Stephen A. Cook,et al.  A new recursion-theoretic characterization of the polytime functions , 1992, STOC '92.

[2]  J. Hartmanis,et al.  On the Computational Complexity of Algorithms , 1965 .

[3]  A. Turing On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[4]  Lars Kristiansen,et al.  On the computational complexity of imperative programming languages , 2004, Theor. Comput. Sci..

[5]  Jr. Hartley Rogers Theory of Recursive Functions and Effective Computability , 1969 .

[6]  Kazushige Terui Light affine lambda calculus and polynomial time strong normalization , 2007, Arch. Math. Log..

[7]  Guillaume Bonfante,et al.  Algorithms with polynomial interpretation termination proof , 2001, Journal of Functional Programming.

[8]  Jean-Yves Marion,et al.  Analysing the implicit complexity of programs , 2003, Inf. Comput..

[9]  Yehoshua Bar-Hillel,et al.  The Intrinsic Computational Difficulty of Functions , 1969 .

[10]  Yves Lafont,et al.  Soft linear logic and polynomial time , 2004, Theor. Comput. Sci..

[11]  Daniel Leivant,et al.  Ramified Recurrence and Computational Complexity II: Substitution and Poly-Space , 1994, CSL.

[12]  Peter Møller Neergaard A Functional Language for Logarithmic Space , 2004, APLAS.

[13]  Daniel Leivant,et al.  Stratified functional programs and computational complexity , 1993, POPL '93.

[14]  Tobias Nipkow,et al.  Term rewriting and all that , 1998 .

[15]  Guillaume Bonfante,et al.  Quasi-interpretations a way to control resources , 2011, Theor. Comput. Sci..

[16]  Martin Hofmann Linear types and non-size-increasing polynomial time computation , 2003, Inf. Comput..

[17]  N. Cutland Computability: An Introduction to Recursive Function Theory , 1980 .

[18]  J. Roger Hindley,et al.  Lambda-Calculus and Combinators: An Introduction , 2008 .

[19]  Sanjeev Arora,et al.  Computational Complexity: A Modern Approach , 2009 .

[20]  Jean-Yves Girard,et al.  Light Linear Logic , 1998, Inf. Comput..

[21]  Daniel Leivant,et al.  Lambda Calculus Characterizations of Poly-Time , 1993, Fundam. Informaticae.

[22]  Henk Barendregt,et al.  The Lambda Calculus: Its Syntax and Semantics , 1985 .