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Limited Automata and Regular Languages

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Descriptional Complexity of Formal Systems (DCFS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8031))

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Abstract

Limited automata are one-tape Turing machines that are allowed to rewrite the content of any tape cell only in the first d visits, for a fixed constant d. In the case d = 1, namely, when a rewriting is possible only during the first visit to a cell, these models have the same power of finite state automata. We prove state upper and lower bounds for the conversion of 1-limited automata into finite state automata. In particular, we prove a double exponential state gap between nondeterministic 1-limited automata and one-way deterministic finite automata. The gap reduces to single exponential in the case of deterministic 1-limited automata. This also implies an exponential state gap between nondeterministic and deterministic 1-limited automata. Another consequence is that 1-limited automata can have less states than equivalent two-way nondeterministic finite automata. We show that this is true even if we restrict to the case of the one-letter input alphabet. For each d ≥ 2, d-limited automata are known to characterize the class of context-free languages. Using the Chomsky-Schützenberger representation for context-free languages, we present a new conversion from context-free languages into 2-limited automata.

Partially supported by MIUR under the project PRIN “Automi e Linguaggi Formali: Aspetti Matematici e Applicativi”.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Milano, Italy

    Giovanni Pighizzini & Andrea Pisoni

Authors
  1. Giovanni Pighizzini
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  2. Andrea Pisoni
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Editors and Affiliations

  1. Department of Computer Science, Middlesex College, Western University, N6A 5B7, London, ON, Canada

    Helmut Jurgensen

  2. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055,, 4169-007, Porto, Portugal

    Rogério Reis

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Pighizzini, G., Pisoni, A. (2013). Limited Automata and Regular Languages. In: Jurgensen, H., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2013. Lecture Notes in Computer Science, vol 8031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39310-5_24

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  • DOI: https://doi.org/10.1007/978-3-642-39310-5_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39309-9

  • Online ISBN: 978-3-642-39310-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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