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Linearizing Bad Sequences: Upper Bounds for the Product and Majoring Well Quasi-orders

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7456)

Abstract

Well quasi-orders (wqo’s) are an important mathematical tool for proving termination of many algorithms. Under some assumptions upper bounds for the computational complexity of such algorithms can be extracted by analyzing the length of controlled bad sequences.

We develop a new, self-contained study of the length of bad sequences over the product ordering of ℕn, which leads to known results but with a much simpler argument.

We also give a new tight upper bound for the length of the longest controlled descending sequence of multisets of ℕn, and use it to give an upper bound for the length of controlled bad sequences in the majoring ordering of sets of tuples. We apply this upper bound to obtain complexity upper bounds for decision procedures of automata over data trees.

In both cases the idea is to linearize bad sequences, i.e. transform them into a descending one over a well-order for which upper bounds can be more easily handled.

Keywords

  • Decision Procedure
  • Recursive Function
  • Lexicographic Order
  • Termination Proof
  • Proper Norm

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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Abriola, S., Figueira, S., Senno, G. (2012). Linearizing Bad Sequences: Upper Bounds for the Product and Majoring Well Quasi-orders. In: Ong, L., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2012. Lecture Notes in Computer Science, vol 7456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32621-9_9

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  • DOI: https://doi.org/10.1007/978-3-642-32621-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32620-2

  • Online ISBN: 978-3-642-32621-9

  • eBook Packages: Computer ScienceComputer Science (R0)