The Complexity of Transducer Synthesis from Multi-Sequential Specifications

Authors Léo Exibard, Emmanuel Filiot, Ismaël Jecker

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Léo Exibard
  • Aix-Marseille Université, Marseille, France , Université libre de Bruxelles, Brussels, Belgium
Emmanuel Filiot
  • Université libre de Bruxelles, Brussels, Belgium
Ismaël Jecker
  • Université libre de Bruxelles, Brussels, Belgium

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Léo Exibard, Emmanuel Filiot, and Ismaël Jecker. The Complexity of Transducer Synthesis from Multi-Sequential Specifications. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 46:1-46:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


The transducer synthesis problem on finite words asks, given a specification S subseteq I x O, where I and O are sets of finite words, whether there exists an implementation f: I - > O which (1) fulfils the specification, i.e., (i,f(i))in S for all i in I, and (2) can be defined by some input-deterministic (aka sequential) transducer T_f. If such an implementation f exists, the procedure should also output T_f. The realisability problem is the corresponding decision problem. For specifications given by synchronous transducers (which read and write alternately one symbol), this is the finite variant of the classical synthesis problem on omega-words, solved by Büchi and Landweber in 1969, and the realisability problem is known to be ExpTime-c in both finite and omega-word settings. For specifications given by asynchronous transducers (which can write a batch of symbols, or none, in a single step), the realisability problem is known to be undecidable. We consider here the class of multi-sequential specifications, defined as finite unions of sequential transducers over possibly incomparable domains. We provide optimal decision procedures for the realisability problem in both the synchronous and asynchronous setting, showing that it is PSpace-c. Moreover, whenever the specification is realisable, we expose the construction of a sequential transducer that realises it and has a size that is doubly exponential, which we prove to be optimal.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Transducers
  • Transducers
  • Multi-Sequentiality
  • Synthesis


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