Copyful Streaming String Transducers

International audienceCopyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. ˇ Cern´yCern´y in 2010 as a one-way determin-istic automata model to define transductions of finite strings. Copyless SST extend deterministic finite state automata with a set of variables in which to store intermediate output strings, and those variables can be combined and updated all along the run, in a linear manner, i.e., no variable content can be copied on transitions. It is known that copyless SST capture exactly the class of MSO-definable string-to-string trans-ductions, and are as expressive as deterministic two-way transducers. They enjoy good algorithmic properties. Most notably, they have decid-able equivalence problem (in PSpace). On the other hand, HDT0L systems have been introduced for a while, the most prominent result being the decidability of the equivalence problem. In this paper, we propose a semantics of HDT0L systems in terms of transductions, and use it to study the class of deterministic copyful SST. Our contributions are as follows: (i) HDT0L systems and total deterministic copyful SST have the same expressive power, (ii) the equivalence problem for deterministic copyful SST and the equivalence problem for HDT0L systems are inter-reducible, in linear time. As a consequence, equivalence of deterministic SST is decid-able, (iii) the functionality of non-deterministic copyful SST is decidable, (iv) determining whether a deterministic copyful SST can be transformed into an equivalent deterministic copyless SST is decidable in polynomial time

Equivalence Problems for Tree Transducers: A Brief Survey

The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree transducers, (2) linear size increase, i.e., MSO definable tree transducers, and (3) monadic input and output ranked alphabets. For the full class of MTTs, decidability of equivalence remains a long-standing open problem.Comment: In Proceedings AFL 2014, arXiv:1405.527

On the decomposition of finite-valued streaming string transducers

We prove the following decomposition theorem: every 1-register streaming string transducer that associates a uniformly bounded number of outputs with each input can be effectively decomposed as a finite union of functional 1-register streaming string transducers. This theorem relies on a combinatorial result by Kortelainen concerning word equations with iterated factors. Our result implies the decidability of the equivalence problem for the considered class of transducers. This can be seen as a first step towards proving a more general decomposition theorem for streaming string transducers with multiple registers

The many facets of string transducers

Regular word transductions extend the robust notion of regular languages from a qualitative to a quantitative reasoning. They were already considered in early papers of formal language theory, but turned out to be much more challenging. The last decade brought considerable research around various transducer models, aiming to achieve similar robustness as for automata and languages. In this paper we survey some older and more recent results on string transducers. We present classical connections between automata, logic and algebra extended to transducers, some genuine definability questions, and review approaches to the equivalence problem

Reducing Transducer Equivalence to Register Automata Problems Solved by "Hilbert Method"

In the past decades, classical results from algebra, including Hilbert\u27s Basis Theorem, had various applications in formal languages, including a proof of the Ehrenfeucht Conjecture, decidability of HDT0L sequence equivalence, and decidability of the equivalence problem for functional tree-to-string transducers. In this paper, we study the scope of the algebraic methods mentioned above, particularily as applied to the functionality problem for register automata, and equivalence for functional register automata. We provide two results, one positive, one negative. The positive result is that functionality and equivalence are decidable for MSO transformations on unordered forests. The negative result comes from a try to extend this method to decide functionality and equivalence on macro tree transducers. We reduce macro tree transducers equivalence to an equivalence problem for some class of register automata naturally relevant to our method. We then prove this latter problem to be undecidable

Modular Descriptions of Regular Functions

We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one may use more human friendly descriptions based on some simple basic transformations (e.g., copy, duplicate, erase, reverse) and various combinators such as function composition or extensions of regular operations.Comment: preliminary version appeared in CAI 2019, LNCS 1154