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  • 4 - Monoidal Multi-Tape Automata and Finite-State Transducers

  • from Part I - Formal Background
  • Stoyan Mihov, Klaus U. Schulz, Ludwig-Maximilians-Universität Munchen
  • Book:
    Finite-State Techniques
    Published online:
    29 July 2019
    Print publication:
    01 August 2019, pp 72-93

  • Summary

    An important generalization of classical finite-state automata are multi-tape automata, which are used for recognizing relations of a particular type. The so-called regular relations (also refered to as ‘rational relations’) offer a natural way to formalize all kinds of translations and transformations, which makes multi-tape automata interesting for many practical applications and explains the general interest in this kind of device. A natural subclass are monoidal finite-state transducers, which can be defined as two-tape automata where the first tape reads strings. In this chapter we present the most important properties of monoidal multi-tape automata in general and monoidal finite-state transducers in particular. We show that the class of relations recognized by n-tape automata is closed under a number of useful relational operations like composition, Cartesian product, projection, inverse etc. We further present a procedure for deciding the functionality of classical finite-state transducers.