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What You Must Remember When Transforming Datawords

Author M. Praveen



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M. Praveen
  • Chennai Mathematical Institute, India
  • UMI ReLaX, Indo-French joint research unit

Acknowledgements

The author thanks C. Aiswarya, Kamal Lodaya, K. Narayan Kumar and anonymous reviewers for suggestions to improve the presentation and pointers to related works.

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M. Praveen. What You Must Remember When Transforming Datawords. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 55:1-55:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.FSTTCS.2020.55

Abstract

Streaming Data String Transducers (SDSTs) were introduced to model a class of imperative and a class of functional programs, manipulating lists of data items. These can be used to write commonly used routines such as insert, delete and reverse. SDSTs can handle data values from a potentially infinite data domain. The model of Streaming String Transducers (SSTs) is the fragment of SDSTs where the infinite data domain is dropped and only finite alphabets are considered. SSTs have been much studied from a language theoretical point of view. We introduce data back into SSTs, just like data was introduced to finite state automata to get register automata. The result is Streaming String Register Transducers (SSRTs), which is a subclass of SDSTs. We use origin semantics for SSRTs and give a machine independent characterization, along the lines of Myhill-Nerode theorem. Machine independent characterizations for similar models are the basis of learning algorithms and enable us to understand fragments of the models. Origin semantics of transducers track which positions of the output originate from which positions of the input. Although a restriction, using origin semantics is well justified and is known to simplify many problems related to transducers. We use origin semantics as a technical building block, in addition to characterizations of deterministic register automata. However, we need to build more on top of these to overcome some challenges unique to SSRTs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
  • Theory of computation → Automata over infinite objects
Keywords
  • Streaming String Transducers
  • Data words
  • Machine independent characterization

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