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DOI: 10.4230/LIPIcs.FSTTCS.2014.147
URN: urn:nbn:de:0030-drops-48393
URL: http://drops.dagstuhl.de/opus/volltexte/2014/4839/
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Filiot, Emmanuel ; Krishna, Shankara Narayanan ; Trivedi, Ashutosh

First-order Definable String Transformations

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Abstract

The connection between languages defined by computational models and logic for languages is well-studied. Monadic second-order logic and finite automata are shown to closely correspond to each-other for the languages of strings, trees, and partial-orders. Similar connections are shown for first-order logic and finite automata with certain aperiodicity restriction. Courcelle in 1994 proposed a way to use logic to define functions over structures where the output structure is defined using logical formulas interpreted over the input structure. Engelfriet and Hoogeboom discovered the corresponding "automata connection" by showing that two-way generalised sequential machines capture the class of monadic-second order definable transformations. Alur and Cerny further refined the result by proposing a one-way deterministic transducer model with string variables - called the streaming string transducers - to capture the same class of transformations. In this paper we establish a transducer-logic correspondence for Courcelle's first-order definable string transformations. We propose a new notion of transition monoid for streaming string transducers that involves structural properties of both underlying input automata and variable dependencies. By putting an aperiodicity restriction on the transition monoids, we define a class of streaming string transducers that captures exactly the class of first-order definable transformations.

BibTeX - Entry

@InProceedings{filiot_et_al:LIPIcs:2014:4839,
  author =	{Emmanuel Filiot and Shankara Narayanan Krishna and Ashutosh Trivedi},
  title =	{{First-order Definable String Transformations}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{147--159},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Venkatesh Raman and S. P. Suresh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4839},
  URN =		{urn:nbn:de:0030-drops-48393},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.147},
  annote =	{Keywords: First-order logic, streaming string transducers}
}

Keywords: First-order logic, streaming string transducers
Seminar: 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)
Issue Date: 2014
Date of publication: 11.12.2014


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