In this paper we provide a positive answer to a question left open by Alur and and Deshmukh in 2011 by showing that equivalence of finite-valued copyless streaming string transducers is decidable

Muscholl, A.

Puppis, G.

English

arXiv

International audienceIn this paper we provide a positive answer to a question left open by Alur and and Deshmukh in 2011 by showing that equivalence of finite-valued copyless streaming string transducers is decidable. 2012 ACM Subject Classification Theory of computation → Transducers 1 Introduction Finite transducers are simple devices that allow to reason about data transformations in an effective, and even efficient way. In their most basic form they transform strings using finite control. Unlike automata, their power heavily depends on various parameters, like non-determinism, the capability of scanning the input several times, or the kind of storage they may use. The oldest transducer model, known as generalized sequential machine, extends finite automata by outputs. Inspired by an approach that applies to arbitrary relational structures [10], logic-based transformations (also called transductions) were considered by Engelfriet and Hoogeboom [13]. They showed that two-way transducers and monadic-second order (MSO) definable transductions are equivalent in the deterministic case (and even if the transduction is single-valued, which is more general than determinism). This equivalence supports thus the notion of "regular" functions, in the spirit of classical results on regular word languages from automata theory and logics due to Büchi, Elgot, Trakhtenbrot, Rabin, and others. A one-way transducer model that uses write-only registers as additional storage was proposed a few years ago by Alur and Cerný [2], and called streaming string transducer (SST). SST were shown equivalent to two-way transducers and MSO definable transductions in the deterministic setting, and again, even in the single-valued case. In the relational case the picture is less satisfactory, as expressive equivalence is only preserved for SST and non-deterministic MSO transductions [5], which extend the original MSO transductions by existentially quantified monadic parameters. On the other hand, two-way transducers and SST are incomparable in the relational case. Between functions and relations there is however one class of transductions that exhibits a better behavior, and this is the class of finite-valued transductions. Being finite-valued means that there exists some constant k such that every input belonging to the domain has at most k outputs. Finite-valued transductions were intensively studied in the setting of one-way and two-way transducers. For one-way transducers, k-valuedness can be checked in Ptime [18]. In addition, every k-valued one-way transducer can be effectively decomposed into a union of k unambiguous one-way transducers of exponential size [27, 25]. For both two-way transducers and SST, checking k-valuedness is in Pspace

Equivalence of finite-valued streaming string transducers is decidable

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