There is no complete axiom system for shuffle expressions

A. Szepietowski

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 33, Issue: 3, page 271-277
  • ISSN: 0988-3754

Abstract

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In this paper we show that neither the set of all valid equations between shuffle expressions nor the set of schemas of valid equations is recursively enumerable. Thus, neither of the sets can be recursively generated by any axiom system.

How to cite

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Szepietowski, A.. "There is no complete axiom system for shuffle expressions." RAIRO - Theoretical Informatics and Applications 33.3 (2010): 271-277. <http://eudml.org/doc/222023>.

@article{Szepietowski2010,
abstract = { In this paper we show that neither the set of all valid equations between shuffle expressions nor the set of schemas of valid equations is recursively enumerable. Thus, neither of the sets can be recursively generated by any axiom system. },
author = {Szepietowski, A.},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {shuffle expressions},
language = {eng},
month = {3},
number = {3},
pages = {271-277},
publisher = {EDP Sciences},
title = {There is no complete axiom system for shuffle expressions},
url = {http://eudml.org/doc/222023},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Szepietowski, A.
TI - There is no complete axiom system for shuffle expressions
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 3
SP - 271
EP - 277
AB - In this paper we show that neither the set of all valid equations between shuffle expressions nor the set of schemas of valid equations is recursively enumerable. Thus, neither of the sets can be recursively generated by any axiom system.
LA - eng
KW - shuffle expressions
UR - http://eudml.org/doc/222023
ER -

References

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  1. S.L. Bloom and Z. Ésik, Axiomatizing shuffle and concatenation in languages. Inform. and Comput.139 (1997) 62-91.  Zbl0892.68055
  2. S.L. Bloom and Z. Ésik, Shuffle binoids. Theor. Informatics Appl.32 (1998) 175-198.  
  3. J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley (1979).  Zbl0426.68001
  4. K. Iwama, The universe problem for unrestricted flow languages. Acta Inform.19 (1983) 85-96.  Zbl0487.68065
  5. T. Kimura, An algebraic systems for process structuring and interprocess communication, Proc. 8 Annual Symposium on Theory of Computing (1976) 92-100.  Zbl0365.68066
  6. D. Krob, Complete systems of B-rational identities. Theoret. Comput. Sci.89 (1991) 207-343.  Zbl0737.68053
  7. A.R. Meyer and A. Rabinovich, A solution of an interleaving decision problem by a partial order techniques, Proc. Workshop on Partial-order Methods in Verification, July 1996, Princeton NJ, Ed. G. Holzmann, D. Peled, V. Pratt, AMS-DIMACS Series in Discrete Math.  
  8. A. Salomaa, Theory of Automata, Pergamon Press, Oxford (1969).  Zbl0193.32901

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