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Linear Ramified Higher Type Recursion and Parallel Complexity

Summary: Linear Ramified Higher Type Recursion and
Parallel Complexity
Klaus Aehlig 1;? , Jan Johannsen 2;?? , Helmut Schwichtenberg 1;? ? ? , and
Sebastiaan A. Terwijn 3;y
1 Mathematisches Institut, Ludwig­Maximilians­Universit¨at M¨unchen,
Theresienstraße 39, 80333 M¨unchen, Germany
2 Institut f¨ur Informatik, Ludwig­Maximilians­Universit¨at M¨unchen
Oettingenstraße 67, 80538 M¨unchen, Germany
3 Department of Mathematics and Computer Science, Vrije Universiteit Amsterdam,
De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
Abstract. A typed lambda calculus with recursion in all finite types is
defined such that the first order terms exactly characterize the parallel
complexity class NC. This is achieved by use of the appropriate forms of
recursion (concatenation recursion and logarithmic recursion), a ramified
type structure and imposing of a linearity constraint.
Keywords: higher types, recursion, parallel computation, NC, lambda
calculus, linear logic, implicit computational complexity


Source: Aehlig, Klaus T. - Institut für Informatik, Ludwig-Maximilians-Universität München


Collections: Mathematics; Computer Technologies and Information Sciences