Linearity and nondeletion on monadic context-free tree grammars
Information Processing Letters
Restrictions on monadic context-free tree grammars
COLING '04 Proceedings of the 20th international conference on Computational Linguistics
Pseudoknot Identification through Learning TAGRNA
PRIB '08 Proceedings of the Third IAPR International Conference on Pattern Recognition in Bioinformatics
Improved Algorithms for Parsing ESLTAGs: A Grammatical Model Suitable for RNA Pseudoknots
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
Linearity and nondeletion on monadic context-free tree grammars
Information Processing Letters
GIGs: restricted context-sensitive descriptive power in bounded polynomial-time
CICLing'03 Proceedings of the 4th international conference on Computational linguistics and intelligent text processing
Improved Algorithms for Parsing ESLTAGs: A Grammatical Model Suitable for RNA Pseudoknots
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Deterministic recognition of trees accepted by a linear pushdown tree automaton
CIAA'05 Proceedings of the 10th international conference on Implementation and Application of Automata
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In this paper we present algorithms for parsing general tree-adjoining languages (TALs). Tree-adjoining grammars (TAGs) have been proposed as an elegant formalism for natural languages. It was an open question for the past ten years as to whether TAL parsing can be done in time $o(n^6)$. We settle this question affirmatively by presenting an $O(n^3 M(n))$-time algorithm, where $M(k)$ is the time needed for multiplying two Boolean matrices of size $k\times k$ each. Since $O(k^{2.376})$ is the current best-known value for $M(k)$, the time bound of our algorithm is $O(n^{5.376})$. On an exclusive read exclusive write parameter random-access machine (EREW PRAM) our algorithm runs in time $O(n\log n)$ using $\frac{n^2 M(n)}{\log n}$ processors. In comparison, the best-known previous parallel algorithm had a run time of $O(n)$ using $n^5$ processors (on a systolic array machine). We also present algorithms for parsing context-free languages (CFLs) and TALs whose worst case run times are $O(n^3)$ and $O(n^6)$, respectively, but whose average run times are better. Therefore, these algorithms may be of practical interest.