Add section for Rigid Tree Automata

diff --git a/biblio.bib b/biblio.bib
index a44602e2ddd3078d70f3acd6bfe924a09c88dd7a..6d2aaf06a1d028e0ac62cfcde61a7d1ef8cacf8f 100644 (file)
--- a/biblio.bib
+++ b/biblio.bib
@@ -120,3 +120,35 @@ mechanism. We combine the above constructions adequately to provide an algorithm
        year = {2010},
        pages = {158–174},
 }
+
+@article{jacquemard:rta,
+       title = {Rigid tree automata and applications},
+       volume = {209},
+       issn = {08905401},
+       url = {http://linkinghub.elsevier.com/retrieve/pii/S0890540110002014},
+       doi = {10.1016/j.ic.2010.11.015},
+       pages = {486-512},
+       number = {3},
+       journaltitle = {Information and Computation},
+       author = {Jacquemard, Florent and Klay, Francis and Vacher, Camille},
+       urldate = {2014-03-05},
+       date = {2011-03},
+}
+
+@incollection{filiot:tagc,
+       title = {Tree Automata with Global Constraints},
+       rights = {©2008 Springer-Verlag Berlin Heidelberg},
+       isbn = {978-3-540-85779-2, 978-3-540-85780-8},
+       url = {http://link.springer.com/chapter/10.1007/978-3-540-85780-8_25},
+       series = {Lecture Notes in Computer Science},
+       abstract = {A tree automaton with global tree equality and disequality constraints, {TAGED} for short, is an automaton on trees which allows to test (dis)equalities between subtrees which may be arbitrarily faraway. In particular, it is equipped with an (dis)equality relation on states, so that whenever two subtrees t and t′ evaluate (in an accepting run) to two states which are in the (dis)equality relation, they must be (dis)equal. We study several properties of {TAGEDs}, and prove decidability of emptiness of several classes. We give two applications of {TAGEDs:} decidability of an extension of Monadic Second Order Logic with tree isomorphism tests and of unification with membership constraints. These results significantly improve the results of [10].},
+       pages = {314-326},
+       number = {5257},
+       booktitle = {Developments in Language Theory},
+       publisher = {Springer Berlin Heidelberg},
+       author = {Filiot, Emmanuel and Talbot, Jean-Marc and Tison, Sophie},
+       editor = {Ito, Masami and Toyama, Masafumi},
+       urldate = {2014-03-05},
+       date = {2008},
+       keywords = {Algorithm Analysis and Problem Complexity, Computation by Abstract Devices, Discrete Mathematics in Computer Science, Mathematical Logic and Formal Languages, Symbolic and Algebraic Manipulation}
+}

diff --git a/main.tex b/main.tex
index 16e434cfab6949ffc971336c84322d3f85b1dc6f..2d55300de7ef3cc2ab9bed6e554b22b16aa6cc04 100644 (file)
--- a/main.tex
+++ b/main.tex
@@ -244,6 +244,7 @@ or \url{http://www.gnu.org/licenses/agpl-3.0.txt}) or any later version.}}
 \maininclude{Constraints Between Brothers}{zoo-tree/awcbb}
 \maininclude{Reduction Automata}{zoo-tree/ra}
 \maininclude{Homomorphism-Equality Automata}{zoo-tree/tahom}
+\maininclude{Rigid Tree Automata}{zoo-tree/rta}
 
 %\part{Infinite Trees}
 

diff --git a/zoo-tree/rta.tex b/zoo-tree/rta.tex
new file mode 100644 (file)
index 0000000..317dcee
--- /dev/null
+++ b/zoo-tree/rta.tex
@@ -0,0 +1,34 @@
+Rigid Tree Automata (RTA) are introduced by \cite{jacquemard:rta}.
+
+An RTA has a distinguished set of configurations, $R \subseteq \config$, and
+imposes the global constraint (Def. 2) that $\forall_{p_1,p_2} . \brak{
+r(p_1) = r(p_2) \in R } \Rightarrow t\vert_{p_1} = t\vert_{p_2}$.  (That is,
+for each configuration $r \in R$, all nodes in the run labeled with $r$ must
+root equal sub-trees.)
+
+
+\subsection{Relation to other classes}
+RTA are a strict sub-class of TAGED (\autoref{sec:zoo-tree/taged}; Sec. 3.1) but are a
+super-class of TAGED+ (at possible exponential complexity; see Prop. 2 and
+\cite{filiot:tagc}).
+
+\Note{Other classes also discussed in Sec. 3: TAC, DAG automata, TA1M,
+ACRV.}
+
+Deterministic RTA are a strict sub-class of RTA (Thm. 4) but strictly
+include TA without constraints (Thm. 5).
+
+\autinfo{
+  empty={Linear time; Sec. 6.1},
+  member={NP-complete; Sec. 6.2},
+  univ={No; Sec. 6.4},
+  finite={PTIME; Sec 6.6},
+%
+  compl={No; Sec. 4.2},
+  determinize={No; Sec. 5.1},
+%
+  equiv={No; Sec. 6.5},
+%
+  union={Linear time and space; Sec. 4.1},
+  intersect={Exponential time and space; Sec. 4.1},
+}