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Topic: Nondeterministic finite tree automaton

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cellular automaton

finite state automaton

pushdown automaton

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Alternating automaton

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nondeterministic finite tree automaton

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non deterministic finite automaton

deterministic tree automaton

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	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)

	tree automaton (Site not responding. Last check: 2007-11-03)
		Definition: A tree automaton is an extension of a finite state machine, but operates on n-ary constructors.
		Tree automata may be top-down (starting from the root) or bottom-up (starting from the leaves), and deterministic or nondeterministic.
		Note: Words for finite state automata can be seen as composed of unary constructors, the alphabet, and a 0-ary constructor, the end of the word.
	www.darkridge.com /~jpr5/archive/dads/HTML/treeautomata.html (172 words)

	Dr. Salomaa's Projects (Site not responding. Last check: 2007-11-03)
		Tree automata are an extension of finite automata that operate on trees instead of strings.
		The goal of this project is to implement some basic operations for tree automata: (for example) the cross-product construction and the determinization of nondeterministic automata.
		The transitions of an automaton operating on the "unranked" trees are specified using regular expressions.
	www.cs.queensu.ca /home/cisc499/2005W/Projects/Salomaa.html (283 words)

	Finite Automata
		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.
		In a probabilistic finite automata (PFA), the output in state q is a random function of q, and the state following q is a deterministic function of q and the output in q.
	www.cs.brown.edu /research/ai/dynamics/tutorial/Documents/FiniteAutomata.html (1520 words)

	Finite state machine - Wikipedia
		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.
		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).
	condor.depaul.edu /~ichu/csc415/notes/notes10/fsa.htm (696 words)

	Finite State Machine Minimization (Site not responding. Last check: 2007-11-03)
		Finite state machines are best thought of as pattern recognizers, and minimum-size machines correspond to recognizers that require less time and space.
		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.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK5/NODE207.HTM (1255 words)

	Quals: Computer Theory and Algorithms - SEWiki
		For finiteness, we can build the automaton, and of there is a cycle in some path from the start state to the final state, then it is infinite.
		A nondeterministic algorithm is much like a normal algorithm, with the addition of 3 O(1) operations: choice(S), which arbitrarily chooses an element from the set S, success(), which marks successful completion of the algorithm, and failure(), which marks unsuccessful completion.
		HeapSort creates a heap (a tree with the property that the parent is greater than or equal to each of its children), and continually extracts the largest element (the root of the tree), adjusting the heap afterwards.
	www.cs.wm.edu /~coppit/wiki/index.php?title=Quals:_Computer_Theory_and_Algorithms (6730 words)

	NFALambda (dRegAut API Specification)
		Constructs a new automaton whose language is the concatenation of the language of this automaton and the language of the given automaton.
		Constructs a new automaton whose language is the Kleene star of the language of this automaton.
		Constructs a new automaton whose language is the union of the language of this automaton and the language of the given automaton.
	www.brics.dk /~amoeller/dRegAut/doc/dRegAut/NFALambda.html (258 words)

	O.Kupferman/N.Piterman/M.Vardi: (Site not responding. Last check: 2007-11-03)
		For branching properties, the framework is known and the two-way alternating automaton is a tree automaton.
		Indeed, the fact that a tree automaton can split to copies and simultaneously read all the paths of the tree has a computational price and is irrelevant for linear properties.
		The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree.
	www.wisdom.weizmann.ac.il /~/verify/publications/2002/KPV02.html (301 words)

	Computation Theory of Cellular Automata (1984)
		Sets of cellular automaton configurations may thus be considered as formal languages, with each word in the language representing a cellular automaton configuration.
		There are many problems which can be stated in finite terms, but which are ``undecidable'' in a finite time, even for a universal computer (6) An example is the ``halting problem'': to determine whether a particular computer will ``halt'' in a finite time, given particular input.
		For a cellular automaton, an analogue of the halting problem is to determine whether a particular finite initial configuration will ultimately evolve to the null configuration.
	www.stephenwolfram.com /publications/articles/computation/84-computation/2/text.html (2894 words)

	nondeterministic tree automaton (Site not responding. Last check: 2007-11-03)
		Definition: A nondeterministic 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/nondetermTreeAutom.html (116 words)

	On Computational Complexity of Basic Decision Problems of Finite Tree Automata - Veanes (ResearchIndex) (Site not responding. Last check: 2007-11-03)
		Another important decision problem is the membership problem, i.e, the problem whether a given tree automaton accepts a...
		14: nite tree automata (context) - Seidl, of - 1989
		19 Rewriting and tree automata (context) - Dauchet - 1993
	citeseer.ist.psu.edu /veanes97computational.html (995 words)

	deterministic finite tree automaton (Site not responding. Last check: 2007-11-03)
		Definition: A deterministic finite state machine that accepts finitary trees rather than just strings.
		See also nondeterministic finite tree automaton, deterministic tree automaton.
		Sandeep Kumar Shukla, "deterministic finite tree automaton", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.darkridge.com /~jpr5/archive/dads/HTML/determFinitTreeAutom.html (104 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		In an execution tree, there may be nondeterministic choices at any point in a path through the tree.
		However, each finite tree is trace equivalent to one with just a single finitely branching nondeterministic choice at the beginning.
		More specifically, in the execution tree interpretation, there are nondeterministic choices between sequential paths, with each tree trace equivalent to one with just a single nondeterministic choice at the beginning.
	theory.stanford.edu /people/jcm/cs358-96/4-15-lecture.html (3091 words)

	Uses of Package libtcs.automaton
		A Configuration is an object representing the result or intermediate result of a given automaton at a given time.
		Formally, a (nondeterministic) Finite State Automaton is a quintuple M = (Q,Σ,&delta,S,E) where Q a finite set of states, Σ an input alphabet, δ: Q ⊗ Σ → ℘(Q) the transition function, S ⊆ Q set of start states, E ⊆ Q set of end/accepting states.
		Formally, states are entities, used by automatons, to remember results from processing instructions.
	www.home.unix-ag.org /patrick/software/libtcs/api/libtcs/automaton/package-use.html (240 words)

	Automata tools
		The finite state machine is described in a high level language for modeling concrete systems.
		RX is a system that knows about regular tree grammars, finite tree automata, and rational tree expressions.
		construct a finite state automaton A(D) precisely accepting the finite state sequences satisfying D. The automaton can be used to find models and counter models, or as a synchronous observer (or monitor) for model checking.
	members.fortunecity.com /boroday/Automatatools.html (2778 words)

	Math 670 Fall 1998 MWF 10:30-12 DRL 4C4
		Finish the proof that the construction given in class of the alternating Büchi automaton associated to a given temporal formula has the desired property that the automaton accepts an infinite word iff this word when considered as a temporal model satisfies the formula.
		In each case prove in detail that the infinitary language of the alternating Büchi automaton is precisely the set of linear temporal logic models satisfying the formula.
		Prove in detail PSPACE-hardness of the satisfiablity problem for linear temporal logic by describing a logarithmic-space algorithm that given a PSPACE-bounded Turing machine M and a finite word w outputs a linear temporal logic formula such that the formula is satisfiable iff M accepts w.
	www.cis.upenn.edu /~scedrov/courses/Math670F98.html (458 words)

	HAL :: BROWSE
		The transition graph of the pushdown automaton defines the arena: the graph of the play and the partition of the vertex set needed to specify the parity winning condition.
		The idea is to simulate the pushdown system in the full W-tree, where W is a finite set of directions, and to use the expressive power of alternating two-way tree automata to answer these questions.
		Finally it is necessary to translate the 2-way tree automaton into an equivalent nondeterministic one-way tree automaton.
	hal.ccsd.cnrs.fr /ccsd-00019914/en (248 words)

	Working XML: Building a compiler for the SAX ContentHandler
		Such a table is used to implement nondeterministic finite automaton (NFA).
		Yet for increased efficiency, it is best to work with deterministic finite automaton.
		A DFA is a special case of NFA: it has no transition on the empty string, and it guarantees that the transition table has at most one edge leaving any given state for each symbol (in other words, from each state it is possible to compute the transition deterministically).
	www.ibm.com /developerworks/xml/library/x-wxxm5/index.html (1939 words)

	JFAR: Finite State Machines in Forth - J. V. Noble (Site not responding. Last check: 2007-11-03)
		This note provides methods for constructing deterministic and nondeterministic finite state automata in Forth.
		Finite state machines have been discussed previously in this journal [3, 4].
		The problem is to determine whether a piece of text is a proper identifier (that is, the name of a variable, subroutine or function) according to the rules of FORTRAN.
	dec.bournemouth.ac.uk /forth/jfar/vol7/paper1/paper.html (3396 words)

	math developments in automata theory
		Usage of separately masked both input and output states in automaton transitions, that allows to create automatons with big number of parameters.
		Forming and processing tree of alternative transitions on fly.
		One of them is including completed space of alternatives in tree.
	www.hitec.biz /pages/2/index.htm (164 words)

	nondeterministic . net : Semantics and its Applications, Day 1
		Automaton with escape on b captures correct notion
		May not be working on trees (or temporarily break a tree during an operation)
		Traces are finite sequences of actions, a "little bit" of a resumption
	www.nondeterministic.net /archive/2005/12/19_21_semantics_and_its_applications_.php (1043 words)

	Residual Finite State Automata - Denis, Lemay, Terlutte (ResearchIndex) (Site not responding. Last check: 2007-11-03)
		We call Residual Finite State Automata (RFSA) such automata.
		Residual Finite Tree Automata - Carme, Gilleron, Lemay, Terlutte..
		Denis, F., Lemay, A., Terlutte, A.: Residual Finite State Automata, STACS 2001.
	citeseer.ist.psu.edu /560708.html (464 words)

	DMTCS vol 4 no 2 (2001), pp. 179-192 (Site not responding. Last check: 2007-11-03)
		We examine the power of nondeterministic finite automata with acceptance of an input word defined by a leaf language, i.e., a condition on the sequence of leaves in the automaton's computation tree.
		We study leaf languages either taken from one of the classes of the Chomsky hierarchy, or taken from a time- or space-bounded complexity class.
		Timo Peichl and Heribert Vollmer (2001), Finite Automata with Generalized Acceptance Criteria, Discrete Mathematics and Theoretical Computer Science 4, pp.
	dmtcs.loria.fr /volumes/abstracts/dm040210.abs.html (256 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		A string is accepted if the machine terminates in an accept state.
		A string is rejected if the machine terminates in a non-accept state.¡>³$ ¨ÀNFA Computation on an input string is a TREE.
		A string is accepted if there is a path in the computation tree that terminates in an accept state.
	www.cs.pitt.edu /~utp/cs1502/notes/s28-NFA.ppt (241 words)

	nondeterministic - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "nondeterministic" is defined.
		nondeterministic : Dictionary of Algorithms and Data Structures [home, info]
		Phrases that include nondeterministic: nondeterministic turing machine, nondeterministic algorithm, nondeterministic finite state machine, nondeterministic finite tree automaton, nondeterministic logspace, more...
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=nondeterministic (116 words)

	N. Piterman and M.Y. Vardi (Site not responding. Last check: 2007-11-03)
		We extend the automata-theoretic framework for reasoning about infinite-state sequential systems to handle also the global model-checking problem.
		Checking that the system satisfies a temporal property can then be done by a two-way automaton that navigates through the tree.
		In order to solve the global model-checking problem we show that for both types of automata, given a regular tree, we can construct a nondeterministic word automaton that accepts all the nodes in the tree from which an accepting run of the automaton can start.
	www.wisdom.weizmann.ac.il /~verify/publications/2004/PV04.html (152 words)

	A Practical Algorithm for Reducing Nondeterministic Finite State Automata (ResearchIndex) (Site not responding. Last check: 2007-11-03)
		A Practical Algorithm for Reducing Nondeterministic Finite State Automata (2004)
		Abstract: In [3], Ilie and Yu describe a construction of a right-invariant equivalence relation on the states of a non-deterministic finite-state automaton.
		We give a more e#- cient algorithm for constructing the same equivalence, together with results from a computer implementation.
	citeseer.ist.psu.edu /albert04practical.html (261 words)

	DBLP: Ferenc Gécseg (Site not responding. Last check: 2007-11-03)
		Ferenc Gécseg, György Gyurica: On the closedness of nilpotent DR tree languages under Boolean operations.
		Ferenc Gécseg: On a representation of deterministic uniform foot-to frontier tree transformations.
		Ferenc Gécseg, Magnus Steinby: Minimal ascending tree automata.
	www.informatik.uni-trier.de /~ley/db/indices/a-tree/g/G=eacute=cseg:Ferenc.html (355 words)

	Dictionary of Algorithms and Data Structures
		deterministic finite automaton: see deterministic finite state machine
		nondeterministic finite automaton: see nondeterministic finite state machine
		Data Structures and Algorithms is a wonderful site with illustrations, explanations, analysis, and code taking the student from arrays and lists through trees, graphs, and intractable problems.
	www.itl.nist.gov /div897/sqg/dads (680 words)

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