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On languages accepted with simultaneous complexity bounds and their ranking problem

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Mathematical Foundations of Computer Science 1994 (MFCS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 841))

Abstract

In this paper, we consider Turing machines having simultaneous bounds on working space s(n), input head inversions i(n) and ambiguity degree d(n). Besides the standard notion of space complexity (Type 1), we discuss a stronger notion (Type 2). In the deterministic case, we show an optimal Ω ∞(log n/log log n) bound on input head inversions for recognizing nonregular languages on Type 1 machines that does not hold for Type 2 machines. Subsequently, the parallel complexity of the ranking problem is studied. We prove that any language accepted on Type 2 machines within s(n), i(n), d(n) simultaneous bounds such that s(n) · i(n) · d(n)=O(log n) can be ranked in DET.

This work was supported in part by the ESPRIT Basic Research Action No. 6317: “Algebraic and Syntactic Methods in Computer Science (ASMICS 2)” and by the Ministero dell'Università e della Ricerca Scientifica e Tecnologica (MURST).

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Authors and Affiliations

  1. Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, Via Comelico, 39, 20135, Milano, Italy

    Alberto Bertoni, Carlo Mereghetti & Giovanni Pighizzini

Authors
  1. Alberto Bertoni
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  2. Carlo Mereghetti
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  3. Giovanni Pighizzini
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Igor Prívara Branislav Rovan Peter Ruzička

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© 1994 Springer-Verlag Berlin Heidelberg

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Bertoni, A., Mereghetti, C., Pighizzini, G. (1994). On languages accepted with simultaneous complexity bounds and their ranking problem. In: Prívara, I., Rovan, B., Ruzička, P. (eds) Mathematical Foundations of Computer Science 1994. MFCS 1994. Lecture Notes in Computer Science, vol 841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58338-6_71

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  • DOI: https://doi.org/10.1007/3-540-58338-6_71

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  • Print ISBN: 978-3-540-58338-7

  • Online ISBN: 978-3-540-48663-3

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