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Topic: Deterministic tree automaton

	Finite state machine
		A finite state machine (FSM) or finite state automaton (FSA) is an abstract machine used in the study of computation and languages that has only a finite, constant amount of memory (the state).
		Finite automata may operate on languages of finite words (the standard case), infinite words (Rabin automata, Büchi automata[?]), or various types of trees (tree automata), to name the most important cases.
		Non-deterministic automata are usually implemented by converting them to deterministic automata - in the worst case, the generated deterministic automaton is exponentially bigger than the non-deterministic automaton (although it can usually be substantially optimised).
	www.ebroadcast.com.au /lookup/encyclopedia/fs/FSM.html (830 words)

	StepAutomaton
		Query, whether or not the automaton has come to a decission, that is to be regarded as final.
		If null is passed (the regular case), the automaton is to pick it's instruction (from the instructionset) itself.
		These spawns will inherit all attributes of the current automaton, including identificator (as the copies are the same mathematical object) and StepListeners (as this method is typically called to branch after a NonDeterministicException is thrown).
	www.home.unix-ag.org /patrick/software/libtcs/api/libtcs/automaton/StepAutomaton.html (449 words)

	Tree automaton - Wikipedia, the free encyclopedia
		A tree automaton is a type of state machine.
		This definition matches the intuitive idea that for an automaton to be deterministic, one and only one transition must be possible for a given node.
		The tree language L(A) recognized by a tree automaton A is the set of all ground terms accepted by A.
	en.wikipedia.org /wiki/Tree_automaton (774 words)

	Tree automaton (Site not responding. Last check: 2007-10-19)
		Consequently a deterministic top-down tree automaton will only be able to test for tree properties that are true in all branches, because the choice of the state to write into each child branch is determined at the parent node, without knowing the child branches contents.
		As said before, a deterministic tree automaton is one where no two transition rules have the same left-hand side.
		For a bottom-up automaton, a ground term t (that is, a tree) is accepted if there exists a reduction that starts from t and ends with q(t), where q is a final state.
	www.danceage.com /biography/sdmc_Tree_automaton (764 words)

	Finite Automata
		An automaton is said to be ``reduced'' if, for all q_1 != q_2 in Q, there exists a in A such that q_1 != q_2.
		A reduced automaton is used to represent the ``discernable'' structure of a dynamical system; you cannot expect a learner to discern the difference between two states if no sequence of inputs and outputs serves to distinguish them.
		In a stochastic finite automaton (SFA), f(q,a) and h(q) are random functions and Pr(f(q,a)q,a) and Pr(h(q)) define the state transition and output probabilities respectively.
	www.cs.brown.edu /research/ai/dynamics/tutorial/Documents/FiniteAutomata.html (1520 words)

	[No title]
		Deterministic finite-state machines (FSMs) are one candidate approach for describing the syntax of a user's notes because they are well understood and relatively expressive.
		Intuitively, the representation is a finite-state machine that accepts a tree rather than a sequence, and for this reason it is termed a tree automaton.
		Tables 1 and 2, tree automatons are generalized by merging states that share similar transitions.
	www.cs.washington.edu /research/jair/volume1/schlimmer93a-html/schlimmer93-3.html (2450 words)

	Pebbles
		The pebble tree automaton and the pebble tree transducer are enhanced by additionally allowing an unbounded number of `invisible' pebbles (as opposed to the usual `visible' ones).
		This result is valid for strings, ranked trees, and in general for families of graphs having a fixed automaton that can be used to traverse the nodes of each of the graphs in the family.
		The tree languages accepted by (finite state) tree-walking automata are known to form a subclass of the regular tree languages which is not known to be proper.
	www.liacs.nl /home/hoogeboo/praatjes/pebbles (669 words)

	FSA
		The automaton accepts a Word, if takes up an ending state upon reaching the end of the input.
		Deterministic: Not more than one transition rule out of the set of rules may match the current situation.
		The engine implemented by the FSA class supports both, the deterministic, as well as the nondeterministic case.
	www.home.unix-ag.org /patrick/software/libtcs/api/libtcs/automaton/FSA.html (654 words)

	[No title]
		Particular, if we view the syntax of a formula as a tree with back edges leading from fixed-point variables to their definition, the block width of this syntax graph is bounded by the number of distinct variables used in the formula.
		We show that for an appropriate definition of bottom-up deterministic automata it is possible to minimize the number of states efficiently and to obtain a unique canonical representative of the accepted tree language.
		By generalizing a corresponding proof from the theory of ranked tree automata we show that it is decidable whether a given regular language of unranked trees can be recognized by a top-down deterministic automaton.
	www.games.rwth-aachen.de /Publications/games.bib (6368 words)

	Trie Information
		In computer science, a trie, or prefix tree, is an ordered tree data structure that is used to store an associative array where the keys are strings.
		Unlike a binary search tree, no node in the tree stores the key associated with that node; instead, its position in the tree shows what key it is associated with.
		Due to this etymology it is pronounced "tree", although some encourage the use of "try" in order to distinguish it from the more general tree.
	www.bookrags.com /wiki/Trie (1316 words)

	Cover Pages: SGML/XML and Forest/Hedge Automata Theory
		To locate nodes, a pointed hedge representation is first converted to triplets: (1) a deterministic hedge automaton, (2) a finite-index right-invariant equivalence of states, and (3) a string automaton over the equivalence classes.
		Informally, a hedge is a sequence of trees.
		Tree automata are proven to be closed under boolean operators; this allows us to design a XML query language in the way similar to the relational algebra, and induce precise schema for any XML query formulated in this language.
	www.oasis-open.org /cover/hedgeAutomata.html (4088 words)

	deterministic tree automaton (Site not responding. Last check: 2007-10-19)
		Definition: A deterministic finite state machine that accepts infinite trees rather than just strings.
		The tree nodes are marked with the letters of the alphabet of the automaton, and the transition function encodes the next states for each branch of the tree.
		The expressive power of such automata varies depending on the acceptance conditions of the trees.
	www.nist.gov /dads/HTML/detrmtreeaut.html (134 words)

	DTD Transformation by Patterns and Contextual Conditions
		On the basis of the tree automaton theory, this paper demonstrates DTD transformation.
		The states of this tree automaton are the states of the string automaton, namely f0 and f1.
		A match-identifying automaton performs the computation of the original tree automaton as well as the computation of the tree automaton constructed from the pattern and that constructed from the contextual condition.
	www.oasis-open.org /cover/murata-sgmlxml97.html (3065 words)

	Büchi automaton - Wikipedia, the free encyclopedia
		A Büchi automaton is the extension of a finite state automaton to infinite inputs.
		It accepts an infinite input sequence, iff there exists a run of the automaton (in case of a deterministic automaton, there is exactly one possible run) which has infinitely many states in the set of final states.
		A language defined by a Rabin automaton, Streett automaton, parity automaton, or Muller automaton is also omega-regular.
	en.wikipedia.org /wiki/B%C3%BCchi_automaton (360 words)

	FSA Reference Manual
		Deterministic density is the number of transition divided by the number of states times the number of symbols; absolute density is the number of transitions dividided by the number of states squared times the number of symbols.
		For the automaton read from In strings or string pairs accepted by In are written to Out, using a sampling procedure based on the weights in In.
		A so-called prefix tree will be written to Out, which is a weighted recognizer of all the lines read from In, where the shape of the recognizer is the corresponding trie, and the weights are derived from the counts that each transition is used in In.
	odur.let.rug.nl /vannoord/Fsa/Manual/node12.html (1392 words)

	A, D.: AI in System Theory: An Observability View,
		An arbitrary automaton is selected as an example to understand the simulation and the expert system presented to accomplish the task.
		In this paper, the assumption is that the automata representation in state space systems is expressed by the quintuple set of states, set of inputs, set of outputs, transition functions and output functions.
		An automaton is taken as a deterministic input-state-output (finite) system.
	dbpubs.stanford.edu:8090 /pub/1997-7 (382 words)

	ActiveTcl 8.4 - Online Docs : grammar fa
		This allows, for example, the transfer of automatons over arbitrary channels, persistence, etc. This method is also the basis for both the copy constructor and the assignment operator.
		This definition means that all deterministic FAs are epsilon-free as well, and epsilon-freeness is a necessary pre-condition for deterministic'ness.
		A FA is said to be deterministic if for each string of input symbols there is exactly one path in the graph of the FA beginning at the start state and whose edges are labeled with the symbols in the string.
	aspn.activestate.com /ASPN/docs/ActiveTcl/tcllib/grammar_fa/fa.html (2007 words)

	Tree-Adjoining Grammars - Joshi, Schabes (ResearchIndex) (Site not responding. Last check: 2007-10-19)
		However, a number of formal results have been established for TAGs, which we believe, would be of interest to researchers in formal languages and automata, including those interested in tree grammars and tree automata.
		16 Bidirectional parsing of lexicalized tree adjoining grammars (context) - Lavelli, Satta - 1991 ACM
		15 An Earleytype parsing algorithm for Tree Adjoining Grammars - Schabes, Joshi - 1988
	citeseer.ist.psu.edu /joshi97treeadjoining.html (856 words)

	nondeterministic finite tree automaton (Site not responding. Last check: 2007-10-19)
		Definition: A nondeterministic finite state machine that accepts finitary trees rather than just strings.
		See also deterministic finite tree automaton, nondeterministic tree automaton.
		Sandeep Kumar Shukla, "nondeterministic finite tree automaton", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.itl.nist.gov /div897/sqg/dads/HTML/nondetermFiniteTreeAutom.html (111 words)

	[No title]
		Tree pattern matching (tpm) algorithms play an important role in practical applications such as compilers and XML document validation.
		Deterministic root-to-frontier tree automata (drftas) are less powerful than nondeterministic ones, and no root-to-frontier tpm algorithm using drftas has appeared so far.
		It is an automaton built on a string p of length m that is acyclic, recognizes at least all factors of p, has m+1 states which are all final, and has m to 2m-1 transitions.
	www.fastar.org /main.php?button=pubs_p (2895 words)

	PXP
		The type of the class may be arbitrary (except three base methods which connect the object to the tree), and the parser has a mechanism to dynamically select the class of the object depending on the element type of the XML node.
		However, in the case that the content models are not deterministic, the parser uses a backtracking algorithm which can be much slower.
		Independent of this, it is possible to choose the encoding of the internal representation of the tree nodes; the parser automatically converts the input text to this encoding.
	www.ocaml-programming.de /programming/pxp.html (799 words)

	Mini Workshop Tree Automata
		The notion of equivalence between finite string automata is well-known and several algorithms for constructing a minimal string automaton that is equivalent to a given one exist.
		Representation of a (k,l)-contextual tree language as a finite tree automaton representation has several advantages over the representation as a set of (k,l)-forks.
		Work in progress about designing an algorithm to convert a (k,l)-contextual tree language represented as a set of (k,l)-forks into the same language represented as a finite tree automaton will be presented.
	www.cs.kuleuven.ac.be /~stefanr/MWTA.html (503 words)

	Tree-Walking Automata and Monadic Second Order Logic (Site not responding. Last check: 2007-10-19)
		At any moment in the execution of a string-walking automaton, the automaton is in one state and at one position of the string.
		A string-walking pebble automaton is able to drop its pebble at its current position in the string, pick it up at any (later) time, if it is at the same position again, and check whether or not the pebble is present at the automaton's current position.
		The definition of a deterministic string-walking pebble automaton is similar to that of a deterministic string-walking automaton.
	www.vanbest.org /janpascal/publications/inf_scriptie/scriptie.html (4854 words)

	Tree automatas
		This library provides proved algorithms on non deterministic and top down tree automatas (merge, intersection, acceptation of a term, calculus and deletion of empty states and non-coaccessible states).
		Semantics of automatas : The semantics of an automaton is its language (i.e.
		Lemma inter_correct_wrt_sign_invar : (d0, d1 : DTA ; sigma : signature) (dta_correct_wrt_sign d0 sigma) -> (dta_correct_wrt_sign d1 sigma) -> (dta_correct_wrt_sign (inter d0 d1) sigma).
	pauillac.inria.fr /coq/contribs/tree_automata.html (1206 words)

	Taxonomy of XML Schema Languages using Formal Language Theory
		There are top-down tree automata and bottom-up tree automata: the former begins with the root node and assigns states to elements after handling superior elements, while the latter begins with leaf nodes and assigns states to elements after handling subordinate elements.
		Moreover, there are deterministic tree automata and non-deterministic tree automata: the former assigns a state to each element, while the latter assigns any number of states to each element.
		However, deterministic top-down tree automata assign a state to an element without examining that element; they only examine the parent element and the state assigned to it.
	www.cobase.cs.ucla.edu /tech-docs/dongwon/mura0619.xml (6870 words)

	Finite State Machine Minimization
		Finite state machines are best thought of as edge-labeled directed graphs, where each vertex represents one of n states and each edge a transition from one state to the other on receipt of the alphabet symbol that labels the edge.
		-moves, it is straightforward to construct an automaton from a depth-first traversal of the parse tree of the regular expression.
		The deterministic construction starts with the parse tree for the regular expression, observing that each leaf represents one of the alphabet symbols in the pattern.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK5/NODE207.HTM (1255 words)

	Theory of Computation - Fall 2006 - Dr. Jody Paul (Site not responding. Last check: 2007-10-19)
		Language theory includes: regular expressions, regular languages, finite automata (deterministic and non-deterministic), context-free languages, pushdown automata, and language grammars.
		For a given finite automaton (deterministic or nondeterministic) determine if a string is accepted
		Draw a state diagram for a finite automaton (deterministic or nondeterministic) that accepts a given language
	www.jodypaul.com /cs/theory (488 words)

	Finite state machine - Wikipedia
		Apart from theory, finite state machines occur also in hardware circuits, where the input, the state and the output are bit vectors of fixed size (Moore and Mealy machines).
		For each non-deterministic FSM a deterministic FSM of equeal computational power can be constructed with an algorithm.
		In hardware a fsm may be directly implemented using a Programmable logic device.
	condor.depaul.edu /~ichu/csc415/notes/notes10/fsa.htm (696 words)

	Pattern Matching with Regular Expressions in C++ LG #27
		A regular expression implementation can always be split into a compiler, which generates a automaton from the given pattern, and an interpreter or simulator, which simulates the automaton and searches for the pattern.
		The end of the part automaton is always the last current state which index is stored in the attribute state of RegExpr.
		But it is not difficult to implement the automaton as class which administrates it in a dynamic array or a linked list.
	linuxgazette.net /issue27/mueller.html (2885 words)

	Coxeter Groups II
		The nodes of the new automaton are the saturated subsets of the nodes of
		I leave it as an exercise to verify that this is an equivalent deterministic automaton.
		The minimal finite automaton recognizing reduced words for a finite Coxeter group is always the same size as the group itself - this is essentially because all words terminate in the longest element.
	www.math.ubc.ca /~cass/coxeter/crm2.html (4798 words)

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