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Computability and Complexity pp 394–417Cite as

Injection Structures Specified by Finite State Transducers

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10010))

Abstract

An injection structure \({\mathcal A}= (A,f)\) is a set A together with a one-place one-to-one function f. \({\mathcal A}\) is an FST injection structure if A is a regular set, that is, the set of words accepted by some finite automaton, and f is realized by a finite-state transducer. We initiate the study of FST injection structures. We show that the model checking problem for FST injection structures is undecidable which contrasts with the fact that the model checking problem for automatic relational structures is decidable. We also explore which isomorphisms types of injection structures can be realized by FST injections. For example, we completely characterize the isomorphism types that can be realized by FST injection structures over a unary alphabet. We show that any FST injection structure is isomorphic to an FST injection structure over a binary alphabet. We also prove a number of positive and negative results about the possible isomorphism types of FST injection structures over an arbitrary alphabet.

Buss was partially supported by NSF grants DMS-1101228 and CCF-1213151. Cenzer was partially supported by the NSF grant DMS-1101123. Minnes was partially supported by the NSF grant DMS-1060351.

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Authors and Affiliations

  1. Department of Mathematics, University of California-San Diego, La Jolla, California, 92093-0112, USA

    Sam Buss & Jeffrey B. Remmel

  2. Department of Mathematics, University of Florida, Gainesville, Florida, 32611, USA

    Douglas Cenzer

  3. Department of Computer Science and Engineering, University of California-San Diego, La Jolla, California, 92093-0404, USA

    Mia Minnes

Authors
  1. Sam Buss
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  2. Douglas Cenzer
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  3. Mia Minnes
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  4. Jeffrey B. Remmel
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Corresponding author

Correspondence to Douglas Cenzer .

Editor information

Editors and Affiliations

  1. Victoria University of Wellington, Wellington, New Zealand

    Adam Day

  2. University of Bergen, Bergen, Norway

    Michael Fellows

  3. Victoria University of Wellington, Wellington, New Zealand

    Noam Greenberg

  4. University of Auckland, Auckland, New Zealand

    Bakhadyr Khoussainov

  5. Massey University, Auckland, New Zealand

    Alexander Melnikov

  6. University of Bergen, Bergen, Norway

    Frances Rosamond

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Buss, S., Cenzer, D., Minnes, M., Remmel, J.B. (2017). Injection Structures Specified by Finite State Transducers. In: Day, A., Fellows, M., Greenberg, N., Khoussainov, B., Melnikov, A., Rosamond, F. (eds) Computability and Complexity. Lecture Notes in Computer Science(), vol 10010. Springer, Cham. https://doi.org/10.1007/978-3-319-50062-1_24

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  • DOI: https://doi.org/10.1007/978-3-319-50062-1_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-50061-4

  • Online ISBN: 978-3-319-50062-1

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