Affiliation:
1. Technical University of Munich, Garching, Germany
2. Universität of Bremen, Bremen, Germany
Abstract
We prove that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long-standing open problem in formal language theory. We also present efficient algorithms for subclasses: for linear transducers or total transducers with unary output alphabet (over a given top-down regular domain language), as well as for transducers with the single-use restriction. These results are obtained using techniques from multi-linear algebra. For our main result, we introduce polynomial transducers and prove that for these, validity of a polynomial invariant can be certified by means of an inductive invariant of polynomial ideals. This allows us to construct two semi-algorithms, one searching for a certificate of the invariant and one searching for a witness of its violation. Via a translation into polynomial transducers, we thus obtain that equivalence of general
y
dt
transducers is decidable. In fact, our translation also shows that equivalence is decidable when the output is not in a free monoid but in a free group.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
10 articles.
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