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The Isomorphism Problem for FST Injection Structures

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Book cover Logical Foundations of Computer Science (LFCS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13137))

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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 a Finite State Transducer (abbreviated 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 deterministic finite-state transducer. Automatic relational structures have been well-studied along with the isomorphism problem for automatic structures. For an FST injection structure (A, f), the graph of f is not necessarily automatic. We continue the study of the complexity of FST injection structures by showing that the isomorphism problem for unary FST injection structures is decidable in quadratic time in the size (number of states) of the FST.

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Authors and Affiliations

  1. University of Florida, Gainesville, FL, 32611, USA

    Douglas Cenzer & Richard Krogman

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  1. Douglas Cenzer
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  2. Richard Krogman
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Correspondence to Douglas Cenzer .

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Editors and Affiliations

  1. CUNY Graduate Center, New York, NY, USA

    Sergei Artemov

  2. Cornell University, Ithaca, NY, USA

    Anil Nerode

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Cenzer, D., Krogman, R. (2022). The Isomorphism Problem for FST Injection Structures. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2022. Lecture Notes in Computer Science(), vol 13137. Springer, Cham. https://doi.org/10.1007/978-3-030-93100-1_3

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  • DOI: https://doi.org/10.1007/978-3-030-93100-1_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-93099-8

  • Online ISBN: 978-3-030-93100-1

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