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From Nondeterministic to Multi-Head Deterministic Finite-State Transducers (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors Martin Raszyk, David Basin, Dmitriy Traytel

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LIPIcs.ICALP.2019.127.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
Keywords
  • Formal languages
  • Nondeterminism
  • Multi-head automata
  • Finite transducers

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Abstract

Every nondeterministic finite-state automaton is equivalent to a deterministic finite-state automaton. This result does not extend to finite-state transducers - finite-state automata equipped with a one-way output tape. There is a strict hierarchy of functions accepted by one-way deterministic finite-state transducers (1DFTs), one-way nondeterministic finite-state transducers (1NFTs), and two-way nondeterministic finite-state transducers (2NFTs), whereas the two-way deterministic finite-state transducers (2DFTs) accept the same family of functions as their nondeterministic counterparts (2NFTs).
We define multi-head one-way deterministic finite-state transducers (mh-1DFTs) as a natural extension of 1DFTs. These transducers have multiple one-way reading heads that move asynchronously over the input word. Our main result is that mh-1DFTs can deterministically express any function defined by a one-way nondeterministic finite-state transducer. Of independent interest, we formulate the all-suffix regular matching problem, which is the problem of deciding for each suffix of an input word whether it belongs to a regular language. As part of our proof, we show that an mh-1DFT can solve all-suffix regular matching, which has applications, e.g., in runtime verification.

Cite As Get BibTex

Martin Raszyk, David Basin, and Dmitriy Traytel. From Nondeterministic to Multi-Head Deterministic Finite-State Transducers (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 127:1-127:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ICALP.2019.127

Author Details

Martin Raszyk
  • Department of Computer Science, ETH Zürich, Universitätstrasse 6, 8092, Switzerland
David Basin
  • Department of Computer Science, ETH Zürich, Universitätstrasse 6, 8092, Switzerland
Dmitriy Traytel
  • Department of Computer Science, ETH Zürich, Universitätstrasse 6, 8092, Switzerland

Funding

This research is supported by the Swiss National Science Foundation grant "Big Data Monitoring" (167162).

References

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