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The Computational Contents of Ramified Corecurrence

  • Daniel LeivantEmail author
  • Ramyaa Ramyaa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9034)

Abstract

The vast power of iterated recurrence is tamed by data ramification: if a function over words is definable by ramified recurrence and composition, then it is feasible, i.e. computable in polynomial time, i.e. any computation using the first n input symbols can have at most p(n) distinct configurations, for some polynomial p. Here we prove a dual result for coinductive data: if a function over streams is definable by ramified corecurrence, then any computation to obtain the first n symbols of the output can have at most p(n) distinct configurations, for some polynomial p. The latter computation is by multi-cursor finite state transducer on streams.

A consequence is that a function over finite streams is definable by ramified corecurrence iff it is Turing-computable in logarithmic space. Such corecursive definitions over finite streams are of practical interest, because large finite data is normally used as a knowledge base to be consumed, rather than as recurrence template. Thus, we relate a syntactically restricted computation model, amenable to static analysis, to a major complexity class for streaming algorithms.

Keywords

Input Symbol Output Stream Tree Automaton Output Symbol Inductive Data 
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 2015

Authors and Affiliations

  1. 1.Indiana University BloomingtonBloomingtonGermany
  2. 2.Wesleyan UniversityMiddletownUSA

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