Many probabilistic models for natural language are now written in terms of hierarchical tree structure. Tree-based modeling still lacks many of the standard tools taken for granted in (finite-state) string-based modeling. The theory of tree transducer automata provides a possible framework to draw on, as it has been worked out in an extensive literature. We motivate the use of tree transducers for natural language and address the training problem for probabilistic tree-to-tree and tree-to-string transducers.

https://faculty.washington.edu/fxia/courses/LING580MT/graehl_NAACL2004.pdf

Training tree transducers

The existence of polynomial time algorithms for the solution of parity games is a major open problem. The fastest known algorithms for the problem are randomized algorithms that run in subexponential time. These algorithms are all ultimately based on the randomized subexponential simplex algorithms of Kalai and of Matousek, Sharir and Welzl. Randomness seems to play an essential role in these algorithms. We use a completely different, and elementary, approach to obtain a deterministic subexponential algorithm for the solution of parity games. Our deterministic algorithm is almost as fast as the randomized algorithms mentioned above.

/pdf/a-deterministic-subexponential-algorithm-for-solving-parity-epoprka9m0.pdf

A deterministic subexponential algorithm for solving parity games

In syntax-directed translation, the source-language input is first parsed into a parse-tree, which is then recursively converted into a string in the target-language. We model this conversion by an extended tree-to-string transducer that has multi-level trees on the source-side, which gives our system more expressive power and flexibility. We also define a direct probability model and use a linear-time dynamic programming algorithm to search for the best derivation. The model is then extended to the general log-linear frame-work in order to incorporate other features like n-gram language models. We devise a simple-yet-effective algorithm to generate non-duplicate k-best translations for n-gram rescoring. Preliminary experiments on English-to-Chinese translation show a significant improvement in terms of translation quality compared to a state-of-the- art phrase-based system.

Statistical syntax-directed translation with extended domain of locality

We propose a new verification method for temporal properties of higher-order functional programs, which takes advantage of Ong's recent result on the decidability of the model-checking problem for higher-order recursion schemes (HORS's). A program is transformed to an HORS that generates a tree representing all the possible event sequences of the program, and then the HORS is model-checked. Unlike most of the previous methods for verification of higher-order programs, our verification method is sound and complete. Moreover, this new verification framework allows a smooth integration of abstract model checking techniques into verification of higher-order programs. We also present a type-based verification algorithm for HORS's. The algorithm can deal with only a fragment of the properties expressed by modal mu-calculus, but the algorithm and its correctness proof are (arguably) much simpler than those of Ong's game-semantics-based algorithm. Moreover, while the HORS model checking problem is n-EXPTIME in general, our algorithm is linear in the size of HORS, under the assumption that the sizes of types and specification formulas are bounded by a constant.

/pdf/types-and-higher-order-recursion-schemes-for-verification-of-nirhzze1pe.pdf

Types and higher-order recursion schemes for verification of higher-order programs

We introduce Recursive Markov Decision Processes (RMDPs) and Recursive Simple Stochastic Games (RSSGs), and study the decidability and complexity of algorithms for their analysis and verification. These models extend Recursive Markov Chains (RMCs), introduced in [EY05a, EY05b] as a natural model for verification of probabilistic procedural programs and related systems involving both recursion and probabilistic behavior. RMCs define a class of denumerable Markov chains with a rich theory generalizing that of stochastic context-free grammars and multi-type branching processes, and they are also intimately related to probabilistic pushdown systems. RMDPs & RSSGs extend RMCs with one controller or two adversarial players, respectively. Such extensions are useful for modeling nondeterministic and concurrent behavior, as well as modeling a system’s interactions with an environment.

We provide upper and lower bounds for deciding, given an RMDP (or RSSG) A and probability p, whether player 1 has a strategy to force termination at a desired exit with probability at least p. We also address “qualitative” termination, where p=1, and model checking questions.

/pdf/recursive-markov-decision-processes-and-recursive-stochastic-2ecmcrjabm.pdf

Recursive markov decision processes and recursive stochastic games

Information extraction from semi-structured documents requires to find
n-ary queries in trees that define appropriate sets of n-tuples of
nodes. We propose new representation formalisms for 
n-ary queries by tree automata that we prove to capture MSO. We then 
investigate n-ary queries by unambiguous tree automata which are
relevant for query induction in multi-slot information extraction.
We show that this representation formalism captures the 
class of n-ary queries that are finite unions of Cartesian closed 
queries, a property we prove decidable.

N-ary Queries by Tree Automata.

We investigate n-ary node selection queries in trees by successful runs of tree automata. We show that run-based n-ary queries capture MSO, contribute algorithms for enumerating answers of n-ary queries, and study the complexity of the problem. We investigate the subclass of run-based n-ary queries by unambiguous tree automata.

/pdf/n-ary-queries-by-tree-automata-1lp48m9ean.pdf

N-ary queries by tree automata

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N-ary Queries by Tree Automata.

N-ary queries by tree automata