Abstract. The n-pebble tree transducer was recently proposed as a model for XML query languages. The four main results on deterministic transducers are: First, (1) the translation τ of an n-pebble tree transducer can be realized by a composition of n + 1 0-pebble tree transducers. Next, the pebble tree transducer is compared with the macro tree transducer, a well-known model for syntax-directed semantics, with decidable type checking. The 0-pebble tree transducer can be simulated by the macro tree transducer, which, by the first result, implies that (2) τ can be realized by an (n+1)-fold composition of macro tree transducers. Conversely, every macro tree transducer can be simulated by a composition of 0-pebble tree transducers. Together these simulations prove that (3) the composition closure of n-pebble tree transducers equals that of macro tree transducers (and that of 0-pebble tree transducers). Similar results hold in the nondeterministic case. Finally, (4) the output languages of deterministic n-pebble tree transducers form a hierarchy with respect to the number n of pebbles. 1

Macro tree transducers (mtts) are a useful formal model for XML query and transformation languages. In this paper one of the fundamental decision problems on translations, namely the “translation membership problem ” is studied for mtts. For a fixed translation, the translation membership problem asks whether a given input/output pair is element of the translation. For call-by-name mtts this problem is shown to be NP-complete. The main result is that translation membership for call-by-value mtts is in polynomial time. For several extensions, such as addition of regular look-ahead or the generalization to multi-return mtts, it is shown that translation membership still remains in PTIME. 1.

The present document contains notes on a course held in Tarragona/Spain at the

The hierarchy of arbitrary compositions of two-way nondeterministic finite-state transductions collapses when restricted to finitary transductions, i.e., transductions that produce a finite set of outputs for each input. The hierarchy collapses to the class of nondeterministic MSO definable transductions, which is inside the second level of that hierarchy. It is decidable whether a composition of two-way nondeterministic finite-state transducers realizes a finitary transduction (i.e., is MSO definable).

Inverse computation has many applications such as serialization/deserialization, providing support for undo, and test-case generation for software testing. In this paper, we propose an inverse computation method that always terminates for a class of functions known as parameter-linear macro tree transducers, which involve multiple data traversals and the use of accumulations. The key to our method is the observation that a function in the class can be regarded as a non-accumulative context-generating transformation without multiple data traversals. Accordingly, we demonstrate that it is easy to achieve terminating inverse computation for the class by context-wise memoization of the inverse computation results. We also show that when we use a tree automaton to express the inverse computation results, the inverse computation runs in time polynomial to the size of the original output and the textual program size.

Abstract. Visibly pushdown transducers (VPTs) form a strict subclass of pushdown transducers (PTs) that extends finite state transducers with a stack. Like visibly pushdown automata, the input symbols determine the stack operations. It has been shown that visibly pushdown languages form a robust subclass of context-free languages. Along the same line, we show that word transductions defined by VPTs enjoy strong properties, in contrast to PTs. In particular, functionality is decidable in PTIME, k-valuedness is in NPTIME and equivalence of (non-deterministic) functional VPTs is EXPTIME-C. Those problems are undecidable for PTs. Output words of VPTs are not necessarily well-nested. We identify a general subclass of VPTs that produce well-nested words, which is closed by composition, and for which the type checking problem is decidable. 1