Weak MSO+U with Path Quantifiers over Infinite Trees

This paper shows that over infinite trees, satisfiability is decidable for weak monadic second-order logic extended by the unbounding quantifier U and quantification over infinite paths. The proof is by reduction to emptiness for a certain automaton model, while emptiness for the automaton model is decided using profinite trees.Comment: version of an ICALP 2014 paper with appendice

Aperiodic String Transducers

Regular string-to-string functions enjoy a nice triple characterization through deterministic two-way transducers (2DFT), streaming string transducers (SST) and MSO definable functions. This result has recently been lifted to FO definable functions, with equivalent representations by means of aperiodic 2DFT and aperiodic 1-bounded SST, extending a well-known result on regular languages. In this paper, we give three direct transformations: i) from 1-bounded SST to 2DFT, ii) from 2DFT to copyless SST, and iii) from k-bounded to 1-bounded SST. We give the complexity of each construction and also prove that they preserve the aperiodicity of transducers. As corollaries, we obtain that FO definable string-to-string functions are equivalent to SST whose transition monoid is finite and aperiodic, and to aperiodic copyless SST

Synthesis of Deterministic Top-down Tree Transducers from Automatic Tree Relations

We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of specifications that are deterministic top-down tree automatic, meaning the specification is recognizable by a deterministic top-down tree automaton that reads the two given trees synchronously in parallel. In this setting we study tree transducers that are allowed to have either bounded delay or arbitrary delay. Delay is caused whenever the transducer reads a symbol from the input tree but does not produce output. We provide decision procedures for both bounded and arbitrary delay that yield deterministic top-down tree transducers which realize the specification for valid input trees. Similar to the case of relations over words, we use two-player games to obtain our results.Comment: In Proceedings GandALF 2014, arXiv:1408.556

Decision Problems for Origin-Close Top-Down Tree Transducers

Tree transductions are binary relations of finite trees. For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable. Adding origin semantics to tree transductions, i.e., tagging each output node with the input node it originates from, is a known way to recover decidability for inclusion and equivalence. The origin semantics is rather rigid, in this work, we introduce a similarity measure for transducers with origin semantics and show that we can decide inclusion, equivalence and synthesis problems for origin-close non-deterministic top-down tree transducers