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International Symposium on Mathematical Foundations of Computer Science

MFCS 1980: Mathematical Foundations of Computer Science 1980 pp 426–438Cite as

Decidability of reachability in persistent vector replacement systems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 88))

Abstract

The reachability problem for persistent vector replacement systems is shown to be decidable by giving an algorithm for constructing a semilinear representation of the reachability set.

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References

  1. Hack, M.: The equality problem for vector addition systems is undecidable. Theor. Computer Sci. 2 (1976), 77–96

    Google Scholar 

  2. Hopcroft, J. and Pansiot, J.-J.: On the reachability problem for 5-dimensional vector addition systems. Theor. Computer Sci. 8 (1979), 135–159

    Google Scholar 

  3. Jones, N.D.; Landweber, L.H. and Lien, Y.E.: Complexity of some problems in Petri nets. Theor. Computer Sci. 4 (1977), 277–299

    Google Scholar 

  4. Karp, R.M. and Miller, R.E.: Parallel program schemata. J. Comput. System Sci. 3 (1969), 147–195

    Google Scholar 

  5. Landweber, L.H. and Robertson, E.L.: Properties of conflict-free and persistent Petri nets. J. Ass. Computing Machinery 25 (1978), 352–364

    Google Scholar 

  6. Van Leeuwen, J.: A partial solution to the reachability problem for vector addition systems. Sixth Ann. ACM Symp. on the Theory of Computing (1974), 303–309

    Google Scholar 

  7. Machtey, M. and Young, P.: An introduction to the general theory of algorithms. North Holland, New York (1978)

    Google Scholar 

  8. Müller, H.: On the reachability problem for persistent vector replacement systems (to appear)

    Google Scholar 

  9. Rackoff, C.: The covering and boundedness problems for vector addition systems. Theor. Comp. Sci. 6 (1978), 223–231

    Google Scholar 

  10. Sacerdote, G.S. and Tenney, R.L.: The decidability of the reachability problem for vector addition systems. 9th Ann. ACM Symp. on theory of computing (1977), 61–77

    Google Scholar 

  11. Starke, H.P.: Semilinearity and Petri nets. Fundamentals of computation theory 79 (Ed. L. Budach), Akademie-Verlag Berlin (1979), 423–429

    Google Scholar 

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Authors and Affiliations

  1. Institut für Mathematische Maschinen und Datenverarbeitung (III), Universität Erlangen-Nürnberg, Martensstraße 3, 8520, Erlangen, Federal Republic of Germany

    Horst Müller

Authors
  1. Horst Müller
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P. Dembiński

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© 1980 Springer-Verlag Berlin Heidelberg

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Müller, H. (1980). Decidability of reachability in persistent vector replacement systems. In: Dembiński, P. (eds) Mathematical Foundations of Computer Science 1980. MFCS 1980. Lecture Notes in Computer Science, vol 88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022522

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  • DOI: https://doi.org/10.1007/BFb0022522

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10027-0

  • Online ISBN: 978-3-540-38194-5

  • eBook Packages: Springer Book Archive

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