Chop Operations and Expressions: Descriptional Complexity Considerations

  • Markus Holzer
  • Sebastian Jakobi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)


The chop or fusion operation was recently introduced in [S. A. Babu, P. K. Pandya: Chop Expressions and Discrete Duration Calculus. Modern Applications of Automata Theory, World Scientific, 2010], where a characterization of regular languages in terms of chop expressions was shown. Simply speaking, the chop or fusion of two words is a concatenation were the touching letters are coalesced, if both letters are equal; otherwise the operation is undefined. We investigate the descriptional complexity of the chop operation and its iteration for deterministic and nondeterministic finite automata as well as for regular expressions. In most cases tight bounds are shown. Moreover, we also consider the conversion problem between finite automata, regular expressions, and chop expressions. Again, for most conversions we get tight bounds in order of magnitude. It is worth mentioning that regular expressions can be transformed into equivalent chop expressions of polynomial size, but chop expressions can be exponentially more succinct than regular expressions.


Regular Expression Regular Language Tight Bound Automaton Theory Polynomial Size 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Markus Holzer
    • 1
  • Sebastian Jakobi
    • 1
  1. 1.Institut für InformatikUniversität GiessenGiessenGermany

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