From Monadic Second-Order Definable String Transformations to Transducers

Courcelle (1992) proposed the idea of using logic, in particular Monadic second-order logic (MSO), to define graph to graph transformations. Transducers, on the other hand, are executable machine models to define transformations, and are typically studied in the context of string-to-string transform...

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Bibliographic Details
Published in:2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 458 - 467
Main Authors: Alur, Rajeev, Durand-Gasselin, Antoine, Trivedi, Ashutosh
Format: Conference Proceeding
Language:English
Published: IEEE 01.06.2013
Subjects:
Additives
Automata
Computational modeling
Context
Cost accounting
monadic second-order logic
omega-regular transformations
Registers
Streaming string transducers
Transducers
tree transducers
ISBN:1479904139, 9781479904136
ISSN:1043-6871
Online Access:Get full text
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Summary:Courcelle (1992) proposed the idea of using logic, in particular Monadic second-order logic (MSO), to define graph to graph transformations. Transducers, on the other hand, are executable machine models to define transformations, and are typically studied in the context of string-to-string transformations. Engelfriet and Hoogeboom (2001) studied two-way finite state string-to-string transducers and showed that their expressiveness matches MSO-definable transformations (MSOT). Alur and Cerny (2011) presented streaming transducers-one-way transducers equipped with multiple registers that can store output strings, as an equi-expressive model. Natural generalizations of streaming transducers to string-to-tree (Alur and D'Antoni, 2012) and infinite-string-to-string (Alur, Filiot, and Trivedi, 2012) cases preserve MSO-expressiveness. While earlier reductions from MSOT to streaming transducers used two-way transducers as the intermediate model, we revisit the earlier reductions in a more general, and previously unexplored, setting of infinite-string-to-tree transformations, and provide a direct reduction. Proof techniques used for this new reduction exploit the conceptual tools (composition theorem and finite additive coloring theorem) presented by Shelah (1975) in his alternative proof of Bϋchi's theorem. Using such streaming string-to-tree transducers we show the decidability of functional equivalence for MSO-definable infinite-string-to-tree transducers.
ISBN:1479904139
9781479904136
ISSN:1043-6871
DOI:10.1109/LICS.2013.52