A Characterization of NCk by First Order Functional Programs

  • Jean-Yves Marion
  • Romain Péchoux
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4978)

Abstract

This paper is part of a research on static analysis in order to predict program resources and belongs to the implicit computational complexity line of research. It presents intrinsic characterizations of the classes of functions, which are computable in \(\textit{NC}^{\textit{k}}\), that is by a uniform, poly-logarithmic depth and polynomial size family of circuits, using first order functional programs. Our characterizations are new in terms of first order functional programming language and extend the characterization of \(\textit{NC}^{\textit{1}}\) in [9]. These characterizations are obtained using a complexity measure, the sup-interpretation, which gives upper bounds on the size of computed values and captures a lot of program schemas.

Keywords

Function Symbol Transitive Closure Linear Logic Recursive Call Input Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jean-Yves Marion
    • 1
  • Romain Péchoux
    • 1
  1. 1.Loria-INPLÉcole Nationale Supérieure des Mines de NancyVandœuvre-lès-Nancy CedexFrance

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