Decision problems of tree transducers with origin

Emmanuel Filiot, Sebastian Maneth, Pierre-Alain Reynier, Jean-Marc Talbot
2018 Information and Computation  
A tree transducer with origin translates an input tree into a pair of output tree and origin info. The origin info maps each node in the output tree to the unique input node that created it. In this way, the implementation of the transducer becomes part of its semantics. We show that the landscape of decidable properties changes drastically when origin info is added. For instance, equivalence of nondeterministic top-down and MSO transducers with origin is decidable. Both problems are
more » ... without origin. The equivalence of deterministic topdown tree-to-string transducers is decidable with origin, while without origin it is a long standing open problem. With origin, we can decide if a deterministic macro tree transducer can be realized by a deterministic top-down tree transducer; without origin this is an open problem. Tree transducers were invented in the early 1970's as a formal model for compilers and linguistics [24, 23] . They are being applied in many fields of computer science, such as syntax-directed translation [13], databases [22, 15] , linguistics [19, 4] , programming languages [27, 21] , and security analysis [16] . The most essential feature of tree transducers is their good balance between expressive power and decidability. Bojańczyk [3] introduces (string) transducers with origin. For "regular" stringto-string transducers with origin he presents a machine independent characterization which admits Angluin-style learning and the decidability of natural subclasses. These results indicate that classes of translations with origin are mathematically better behaved than their origin-less counter parts. We initiate a rigorous study of tree transducers with origin by investigating the decidability of equivalence, injectivity and query determinacy on the following models: top-down tree-to-tree transducers [24, 23] , top-down tree-to-string transducers [11] , and mso definable tree-to-string transducers (see, e.g., [10] ). The authors are grateful to Joost Engelfriet for its remarks for improvements and corrections on a preliminary of this work.
doi:10.1016/j.ic.2018.02.011 fatcat:umcrctauyzd6xgqyb2jfsse3ba