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Pure Pointer Programs and Tree Isomorphism

  • Martin Hofmann
  • Ramyaa Ramyaa
  • Ulrich Schöpp
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7794)

Abstract

In a previous work, Hofmann and Schöpp have introduced the programming language purple to formalise the common intuition of logspace-algorithms as pure pointer programs that take as input some structured data (e.g. a graph) and store in memory only a constant number of pointers to the input (e.g. to the graph nodes). It was shown that purple is strictly contained in logspace, being unable to decide st-connectivity in undirected graphs.

In this paper we study the options of strengthening purple as a manageable idealisation of computation with logarithmic space that may be used to give some evidence that ptime-problems such as Horn satisfiability cannot be solved in logarithmic space.

We show that with counting, purple captures all of logspace on locally ordered graphs. Our main result is that without a local ordering, even with counting and nondeterminism, purple cannot solve tree isomorphism. This generalises the same result for Transitive Closure Logic with counting, to a formalism that can iterate over the input structure, furnishing a new proof as a by-product.

Keywords

Boolean Variable Predicate Symbol Horn Clause Input Structure Relativised Separation 
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 2013

Authors and Affiliations

  • Martin Hofmann
    • 1
  • Ramyaa Ramyaa
    • 1
  • Ulrich Schöpp
    • 1
  1. 1.Ludwig-Maximilians Universität MünchenMunichGermany

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