Unreferenced date December 2009 A computationtree is a representation for the computation steps of a non deterministic Turing machine on a specified input. A computationtree graph theory tree is a rooted tree of nodes and edges. Each node in the tree represents a single computational state, while each edge represents a transition to the next possible computation. The number of nodes of the tree is the size of the tree and the length of the path from the root to a given node is the depth of the node. The largest depth of an output node is the depth of the tree. The output nodes of the tree are called leaves. In a computationtree each output node is labeled Yes or No. If a tree, T, with an input space X, if math x in X math and the path for x ends in node labeled yes, then the input x is accepted. Else it is rejected. The depth of the computationtree for a given input is the computation time for the Turing machine on that input. One of the primary methods of showing that a computational problem L is complete complexity complete for a given complexity class C is to show that the computationtree of any algorithm in C can be directly analyzed in terms of L . DEFAULTSORT ComputationTree Category Computational complexity theory ... more details
Computationtree logic CTL is a branching time Mathematical logic logic , meaning that its model of time is a tree like structure in which the future is not determined there are different paths in the future, any one of which might be an actual path that is realised. It is used in formal verification of software or hardware artifacts, typically by software applications known as model checker s which determine if a given artifact possesses safety property safety or liveness property liveness properties . For example, CTL can specify that when some initial condition is satisfied e.g., all program variables are positive or no cars on a highway straddle two lanes , then all possible executions of a program avoid some undesirable condition e.g., dividing a number by zero or two cars colliding on a highway . In this example, the safety property could be verified by a model checker that explores all possible transitions out of program states satisfying the initial condition and ensures that all such executions satisfy the property. Computationtree logic is in a class of temporal logic s that include linear temporal logic LTL . Although there are properties expressible in only one ... of CTL Computationtree logic CTL is a subset of CTL as well as of the modal mu calculus modal ... Logic ATL . CTL is complementary to LTL Computationtree logic CTL and Linear temporal logic LTL are both ... Category Temporal logic de ComputationTree Logic el ko ja ... of CTL Rules 10&ndash 15 above refer to computation paths in models and are what ultimately characterise the ComputationTree they are assertions about the nature of the infinitely deep computationtree rooted at the given state math s math . Semantic equivalences The formulae math phi math and math ..., being universal and existential computation path quantifiers respectively math neg A phi equiv E neg ... Computational tree logic Linear temporal logic References cite journal author Michael Huth and Mark ... more details
Refimprove date May 2011 Computation is any type of calculation ref http www.merriam webster.com dictionary computation ref or the use of computer technology in Information processing . ref http dictionary.reference.com browse computation ref ref http www.answers.com topic computation ref Computation is a process following a well defined Model abstract model understood and expressed in an algorithm , Protocol computing protocol , network topology , etc. Computation is also a major subject matter of computer science it investigates what can or cannot be done in a computational manner. Wiktionary computation Classes of computationComputation can be classified by at least three orthogonal criteria digital vs analog electronics analog , sequential vs parallel computation parallel vs Concurrency computer science concurrent , batch processing batch vs interactive computation interactive . In practice, digital computation is often used to simulate natural processes for example, Evolutionary computation , including those that are more naturally described by analog models of computation for example, Artificial neural network . Computations as a physical phenomenon A computation can be seen as a purely physical phenomenon occurring inside a closed physical system called a computer . Examples of such physical systems include digital computer s, mechanical computer s, quantum computer s, DNA ... adopted by the branch of theoretical physics called the physics of computation . An even more ... is a computation Pancomputationalism . Mathematical models of computation In the theory of computation ... of computation models of computers are the following State models including Turing Machine , push ... The word computation has an archaic meaning from its Latin language Latin etymological roots .... Comparison to calculation See Calculation Comparison to computation See also Portal Computer Science Computing Physical information Real computation Reversible computation Hypercomputation References ... more details
and upper bounds on computational complexity of algorithms, and decision tree model s, used in proofs ... overlooked is that published lower bounds for problems are often given for a model of computation ... reading cite book first Maribel last Fern ndez authorlink Maribel Fern ndez title Models of Computation ... E. Savage title Models Of Computation Exploring the Power of Computing year 1998 url http www.cs.brown.edu jes book home.html DEFAULTSORT Model Of Computation Category Models of computation Category Theory of computation Comp sci stub bg es Modelo de computaci n hr Model ra unanja ... more details
The study of the physics of computation relates to understanding the fundamental physical limits of computer s. This field has led to the investigation of how thermodynamics limits information processing, the understanding of Chaos theory chaos and dynamical systems , and a rapidly growing effort to invent new quantum computer s. See also list of publications in physics Physics of computation important publications in physics of computation See also Digital physics Computation Theory of computation Reversible computation Hypercomputation Physical information Limits to computation Bremermann s limit References Lloyd, S., 2000, Ultimate physical limits of computation, Nature journal Nature , 406 1047 1054. Category Computational physics physics stub ... more details
Indeterminancy in computation may refer to Quantum indeterminacy in quantum computer s Nondeterministic finite automata Nondeterministic algorithm In concurrency Indeterminacy in concurrent computation Unbounded nondeterminism disambig ... more details
Morphological computation may refer to Morphological computation robotics Computational linguistics disambig Long comment to avoid being listed on short pages ... more details
In computer science , interactive computation is a mathematical model for computation that involves communication with the external world during the computation. This is in contrast to the traditional understanding of computation which assumes a simple interface between a computing agent and its environment, consisting in asking a question input and generating an answer output . The famous Church Turing thesis attempts to define computation and computability in terms of Turing machines . However the Turing machine model only provides an answer to the question of what computability of functions means and, with interactive tasks not always being reducible to functions, it fails to capture our broader intuition of computation and computability. While this fact was admitted by Alan Turing himself, it was not until recently that the theoretical computer science community realized the necessity to define adequate mathematical models of interactive computation. Among the currently studied mathematical models of computation that attempt to capture interaction are http www.csc.villanova.edu japaridz Japaridze s hard and easy play machines elaborated within the framework of computability logic , http www.cse.uconn.edu dqg Goldin s persistent Turing machines, and http research.microsoft.com gurevich Gurevich s abstract state machines. Peter Wegner has additionally done a great deal of work on this area of computer science. See also Human based computation Computability logic Game semantics Interactive programming Quasi empiricism in mathematics Quasi empiricism References and external web sources Interactive Computation The New Paradigm ISBN 354034666X. Edited by D.Goldin, S.Smolka and P.Wegner. ... dqg D.Q.Goldin , Persistent Turing Machines as a model of interactive computation . Lecture Notes ... Machines, Transition Systems, and Interaction . J. Information and Computation 194 2 2004 , pp. ... . Theoretical Computer Science 192 1998 , pp. 315 351. Category Theory of computation Category ... more details
Italic title Mathematics of Computation ref http www.ams.org mcom aboutmcom.html Mathematics of Computation Journal overview , retrieved April 2007 ref is a quarterly mathematics journal focused on computational mathematics that is published by the American Mathematical Society . It was established in 1943. The articles in all volumes older than five years are available electronically free of charge. ref http www.ams.org jourcgi jrnl toolbar nav mcom all Mathematics of Computation Archive ref References reflist Category Mathematics journals Category Quarterly journals sci journal stub ... more details
Pulse computation is a hybrid of digital computer digital and analog computer analog computation that uses aperiodic electrical spikes, as opposed to the Periodic function periodic voltages in a digital computer or the continuously varying voltages in on analog computer. Pulse streams are unlocked, so they can arrive at arbitrary times and can be generated by analog processes, although each spike is allocated a binary value, as it would be in a digital computer. ref citation first1 Jeffrey last1 Miller first2 Woodward last2 Young title Simple Pulse Asynchronous State Machines url http vlsi.eecs.harvard.edu techreports iscas96m.ps accessdate 2009 08 25 ref Pulse computation is primarily studied as part of the field of neural network s. The processing unit in such a network is called a neuron . References reflist Category Computational neuroscience comp sci stub ... more details
italictitle Infobox Journal title Neural Computation cover Image neuralcomputationlowres.jpg editor Terrence J. Sejnowski discipline Neuroscience language English abbreviation Neural Comput. publisher MIT Press country United States frequency Monthly history 1989 present openaccess impact 2.175 impact year 2009 website http www.mitpressjournals.org loi neco link1 http www.mitpressjournals.org toc neco current link1 name Online access link2 link2 name RSS atom JSTOR OCLC 39265996 LCCN CODEN ISSN 0899 7667 eISSN 1530 888X Neural Computation is a peer reviewed academic journal covering aspects of neural computation . Articles highlight problems and techniques in modeling the brain, and in the design and construction of neurally inspired information processing systems. Neural Computation was founded in 1989 and is published online and in hard copy by the MIT Press . External links http www.mitpressjournals.org loi neco Official website sci journal stub Portal Neuroscience Category Neuroscience journals Category MIT Press academic journals Category Monthly journals Category English language journals Category Publications established in 1989 Category Academic journal stubs ... more details
about accurate manipulation of mathematical expressions simultaneous exploration of the many paths computer execution can take symbolic execution Symbolic computation or algebraic computation or computer algebra relates to algorithm s and software for manipulating mathematics mathematical expression mathematics expressions and equation s in symbol symbolic form, as opposed to manipulating the approximations of specific numerical analysis numerical quantities represented by those symbols. Software applications that perform symbolic calculations are called computer algebra system s . These systems might be used for symbolic symbolic integration integration or derivative differentiation , substitution of one expression into another, simplification of an expression, etc., for most operations of calculus and, more generally, for every computation with mathematical objects for which algorithms are known. Computer algebra softwares are widely used in many scientific and engineering domains. Symbolic computation is also sometimes referred to as symbolic manipulation , symbolic processing , symbolic mathematics , or symbolic algebra , but these terms also refer to non computational manipulation. See also Automated theorem prover Computer assisted proof Proof checker Model checker Symbolic numeric computation Symbolic simulation Symbolic execution References reflist http www.risc.jku.at about editorial editorial.pdf Symbolic Computation An Editorial , Bruno Buchberger, Journal of Symbolic Computation 1985 1, pp. 1 6. http www.csd.uwo.ca watt pub reprints 2006 tc sympoly.pdf Making Computer Algebra More Symbolic Invited , Stephen M. Watt, pp. 43 49, Proc. Transgressive Computing 2006 A conference in honor or Jean Della Dora , TC 2006 , April 24 26 2006, Granada Spain. External links http www.cs.mu.oz.au schachte lpanalysis.html A Gentle Introduction to Static Analysis and Logic Programming showing an example of application of symbolic computation to perform static program anal ... more details
Citations missing date September 2007 In theoretical computer science , the theory of computation is the branch that deals with whether and how efficiently problems can be solved on a model of computation ... of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. There are several models in use, but the most commonly examined is the Turing machine ... reasonable model of computation. Citation needed date September 2010 It might seem that the potentially ... of computation The theory of computation can be considered the creation of models of all kinds in the field ... of computation were Alonzo Church , Alan Turing , Stephen Kleene , John von Neumann and Claude Shannon ... only models of computation which are reducible to the Turing model. Many mathematicians and computational ..., which are respectively how many steps does it take to perform a computation, and how much memory is required to perform that computation. In order to analyze how much time and space a given algorithm ... and NP . Models of computation This section is linked from Abstract machine main Model of computation Aside from a Turing machine , other equivalent See Church Turing thesis models of computation are in use. Lambda calculus A computation consists of an initial lambda expression or two if you want to separate ... in mathematics . mu recursive function s a computation consists of a mu recursive function, i.e. ... 5 3 to appear, terms like g 5 6 and h 5,6 3 must occur above. The computation terminates only if the final ... recursive function s are a defined subclass of the recursive functions. Different models of computation ... Hopcroft, John E. , and Jeffrey D. Ullman 2006 . Introduction to Automata Theory, Languages, and Computation ... in the field. cite book author Michael Sipser year 2006 title Introduction to the Theory of Computation ... to the Theory of Computation url http www.cse.ohio state.edu gurari theory bk theory bk.html publisher Computer Science Press isbn 0 7167 8182 4 Hein, James L. 1996 Theory of Computation. Sudbury ... more details
Primary sources date January 2010 italictitle Infobox journal title Information and Computation cover File Journalcover Ic.gif editor Albert R. Meyer discipline Computer Science peer reviewed language abbreviation publisher Academic Press country United States USA frequency monthly history 1957 present formerly named Information and Control openaccess license impact 1.504 impact year 2008 website http www.elsevier.com wps find journaldescription.cws home 622844 description description link1 http www.sciencedirect.com science journal 08905401 link1 name online access link2 http projects.csail.mit.edu iandc link2 name Journal homepage at Massachusetts Institute of Technology MIT RSS http rss.sciencedirect.com publication science 6825 atom JSTOR OCLC LCCN CODEN ISSN 0890 5401 eISSN boxwidth Information and Computation is a computer science scientific journal journal published by Elsevier Academic Press . The journal was founded in 1957 under its former name Information and Control . The editor in chief is A.R. Meyer Lab. for Computer Science, Massachusetts Institute of Technology, Cambridge, USA . This particular journal publishes 12 issues a year. All articles from the Information and Computation journal can be viewed on indexing services like Scopus and Science Citation Index . The 2008 Impact Factor for this journal is 1.504 and the 5 Year Impact Factor is 1.600 Journal Citiation Reports 2009, Published by Thomson Reuters . Category Computer science journals Category Elsevier academic journals Category Publications established in 1957 sci journal stub ... more details
In computer science , a computation history is a sequence of steps taken by an abstract machine in the process of computing its result. Computation histories are frequently used in Mathematical proof proofs about the capabilities of certain machines, and particularly about the undecidable problem undecidability of various formal languages . Formally, a computation history is a normally Finite set finite sequence of configurations of a formal automaton . Each configuration fully describes the status of the machine at a particular point. To be valid, certain conditions must hold the first configuration must be a valid initial configuration of the automaton and each transition between adjacent configurations ... , a computation history must be finite and the final configuration must be a valid terminal ... has exactly one computation history for a given initial configuration, though the history may be infinite ... 642 01798 8 page 337 ref Turing Machines Computation histories are more commonly used in reference ... Blass2010 cite book author Andreas Blass title Fields of Logic and Computation Essays Dedicated to Yuri ... 468 ref Decidability results Computation histories can be used to show that certain problems for pushdown automata are undecidable problem undecidable . This is because the language of non accepting computation ... recognizable by a non deterministic pushdown automaton. We encode a Turing computation history math ... Complexity and real computation url http books.google.com books?id zxtrVqUP AwC&pg PA31 accessdate ... be used to recognize accepting computation histories with an NPDA, since non determinism could be used ... accepting computation histories. This result allows us to prove that math ALL PDA math , the language ... automaton math P math which accepts non accepting computation histories for that machine. math D P math will accept if and only if there are no accepting computation histories for math M math on math ... reflist Category Theory of computation pt Hist rico de computa o ... more details
In computability theory , the theory of real computation deals with hypothetical computing machines using infinite precision real number s. They are given this name because they operate on the set of real number s. Within this theory, it is possible to prove interesting statements such as the complement of the Mandelbrot set is only partially decidable . These hypothetical computing machines can be viewed as idealised analog computer s which operate on real numbers, whereas digital computer s are limited to computable numbers. They may be further subdivided into differential mathematics differential and algebraic models digital computers, in this context, should be thought of as topology topological , at least insofar as their operation on computable real s is concerned ref cite book title A Simple Introduction to Computable Analysis author Klaus Weihrauch year 1995 url http eccc.uni trier.de static books A Simple Introduction to Computable Analysis Fragments of a Book ref . Depending on the model chosen, this may enable real computers to solve problems that are inextricable on digital computers for example, Hava Siegelmann s neural nets can have noncomputable real weights, making them able to compute nonrecursive languages , or vice versa Claude Shannon s idealized analog computer can only solve algebraic differential equations, while a digital computer can solve some transcendental ... analog computer computations are immediately done, i.e. computation is done in real time. Shannon ... 317 335 month Jun year 2007 doi 10.1016 j.jco.2006.12.005 ref A canonical model of computation over the reals is Blum Shub Smale machine BSS . If real computation were physically realizable, one could ... Lenore Blum , Felipe Cucker, Michael Shub, and Stephen Smale title Complexity and Real Computation ... and Analog Computation Beyond the Turing Limit isbn 0 8176 3949 7 authorlink Hava Siegelmann cite book ... ftp ftp.cs.cuhk.hk pub neuro papers jcss1.ps.Z Category Theory of computation Category Hypercomputation ... more details
Use mdy dates date January 2012 for the journal Evolutionary Computation journal Evolutionary biology In computer science , evolutionary computation is a subfield of artificial intelligence more particularly computational intelligence that involves combinatorial optimization problems. Evolutionary computation uses iterative progress, such as growth or development in a population. This population is then artificial selection selected in a guided random search using parallel processing to achieve the desired ... computation has largely become swarm based computation, and nature inspired algorithms are becoming ... Main Evolutionary algorithm Evolutionary algorithms form a subset of evolutionary computation in that they generally ... to become a parent or to survive. Evolutionary computation practitioners Incomplete list Kalyanmoy ... R. V. Rao Major conferences and workshops IEEE Congress on Evolutionary Computation CEC Genetic and Evolutionary Computation Conference GECCO ref name SIGEVO cite web title Special Interest Group on Genetic and Evolutionary Computation url http www.sigevo.org publisher SIGEVO ref International Conference ... robotics Fitness approximation Grammatical evolution Human based evolutionary computation Inferential programming Interactive evolutionary computation Mutation testing No free lunch in search and optimization ... computation a unified approach. MIT Press , Cambridge MA, 2006 A. E. Eiben and J.E. Smith, Introduction ... An Introduction. Morgan Kaufmann, 1998. D. B. Fogel. Evolutionary Computation. Toward a New Philosophy .... An overview of evolutionary algorithms for parameter optimization. Evolutionary Computation, 1 ... Europe http www.fmi.uni stuttgart.de fk evolalg Evolutionary Computation Repository http www.cse.dmu.ac.uk rij gafaq top.htm Hitch Hiker s Guide to Evolutionary Computation FAQ for comp.ai.genetic http userweb.eng.gla.ac.uk yun.li ga demo Interactive illustration of Evolutionary Computation http www.vita sciences.org VitaSCIENCES DEFAULTSORT Evolutionary Computation Category Evolutionary computation ... more details
There are several physical and practical limits to the amount of computation or data storage device data storage that can be performed with a given amount of mass, volume, or energy The Bekenstein bound limits the amount of information that can be stored within a spherical volume to the entropy of a black hole with the same surface area. The temperature of the cosmic microwave background radiation gives a practical lower limit to the energy consumed to perform computation of approximately 4 kT per state change, where T is the temperature of the background about 3 kelvin s , and k is the Boltzmann constant . While a device could be cooled to operate below this temperature, the energy expended by the cooling would offset the benefit of the lower operating temperature . Bremermann s limit is the maximum computational speed of a self contained system in the material universe, and is based on mass energy versus quantum uncertainty constraints. Several methods have been proposed for producing computing devices or data storage devices that approach physical and practical limits A cold degenerate star could conceivably be used as a giant data storage device, by carefully perturbing it to various excited states, in the same manner as an atom or quantum well used for these purposes. Such a star would have to be artificially constructed, as no natural degenerate stars will cool to this temperature for an extremely long time. It is also possible that nucleon s on the surface of neutron star s could form complex molecules ref cite encyclopedia year title Life on neutron stars encyclopedia ... and Computation date 20041025030505 ref creating a type of computronium based on femtotechnology ... this hypothetical computation is performed at ultra high densities and speeds, the total number ... 2000 month title Ultimate physical limits to computation journal Nature journal Nature volume 406 ... problem References Reflist Category Theory of computation pt Limites da computa o ... more details
cite journal last Bennett first Charles H. coauthors year 1982 title The thermodynamics of computation ... computation is somewhat simpler than reversible computing in that reverse computation is only required ... as reverse computation in software application areas such as database design, ref cite journal ... Institute National de Recherche en Informatique et en Automatique INRIA accessdate ref Reverse Computation ... computable and their costs. Based on the successful application of Reverse Computation ... 1999 title Efficient optimistic parallel simulations using reverse computation url http www.cs.uga.edu ... for Computing Machinery accessdate 2009 04 06 ref suggest the application of reverse computation ... amount of computation per event . The key property that reverse computation exploits is that a majority ... makes this operation reversible. History of Reverse Computation as applied to Parallel Discrete ... Computation has only been applied in software for optimistically synchronized, parallel discrete ... doctoral thesis focused on reverse computation at the hardware level, but included descriptions of both ... on reverse computation. ref cite journal last Vieri first C. coauthors Ammer, M.J. Frank, M. Norman ... reverse computation to 2004 and http www.eng.fsu.edu mpf pubs.htm later . ref In 1998 Carothers ..., introducing technique of Reverse Computation as an alternative rollback mechanism in optimistically ... System ROSS , which supported only reverse computation as the rollback mechanism. Carothers ... reverse computation. From 1998 to 2005 Bauer performed graduate work at RPI under Carothers, focusing solely on reverse computation. He developed the first PDES system solely based on reverse computation ... discrete event simulations of physical systems using reverse computation url http www.cs.mcgill.ca ... more details
Multiple issues notable June 2011 refimprove June 2011 italictitle Decimal Computation is a textbook by Hermann Schmid. First published in 1974 by John Wiley & Sons ISBN 047176180X and reprinted in 1983 by Robert E. Krieger Publishing Company ISBN 0898743184 , the book comprises twelve chapters providing detailed description of decimal calculations, including explanation of binary coded decimal s and algorithm s. ref cite journal title Electronic Design url http books.google.com books?id 90EAQAAIAAJ year 1974 publisher Hayden Pub. Co. volume 22 issue 19 22 oclc 1567748 page 161 ref References Reflist Category 1974 books compu book stub ... more details
in at most s text steps. 0 & text otherwise end cases math Now suppose that the computation math ... then the computation math phi X t z math converges in at most math s t math steps to math phi X z ... Theory of computation ... more details
refimprove date February 2008 Computation of a cyclic redundancy check is derived from the mathematics of Mathematics of CRC polynomial division, modulo two . In practice, it resembles long division of the Binary code binary message string, with a fixed number of zeroes appended, by the generator polynomial string except that exclusive OR operations replace subtractions. Division of this type is efficiently realised in hardware by a modified shift register , and in software by a series of equivalent algorithm s, starting with simple code close to the mathematics and becoming faster and arguably more obfuscated code obfuscated ref name williams93 cite web url http www.repairfaq.org filipg LINK F crc v3.html title A Painless Guide to CRC Error Detection Algorithms V3.00 accessdate 2008 02 07 last Williams first Ross N. date 1996 09 24 ref through byte wise parallelism and space time tradeoff s. Image CRC8 gen.gif thumb right 380 px Example of generating an 8 bit Cyclic redundancy check CRC . The generator is a Galois type LFSR shift register with xor xor gates placed according to powers white numbers of x in the generator polynomial. The message stream may be any length. After it has been shifted through the register, followed by 8 zeroes, the result in the register is the checksum. Image CRC8 rx.gif thumb 380 px Checking received data with checksum. The received message is shifted through the same register as used in the generator, but the received checksum is attached to it instead ... of the CRC in the order that matches your chosen bit ordering convention. Parallel computation ... the bit at a time code. Parallel computation without table Parallel update for a byte or a word at a time ... p p p 2 p p p 1 p p & 1 f e p 8 r c 8 f 6 f 7 f 8 Two step computation As the CRC 32 polynomial has ... input or cascaded XOR gates which increases propagation delay . To maximise computation speed, an intermediate ... name glaise cite journal last Glaise first Ren J. authorlink date 1997 01 20 title A two step computation ... more details
The Tree may refer to The Tree book The Tree book , an autobiographical book by John Fowles The Tree short story The Tree short story , a short story by American horror fiction writer H. P. Lovecraft The Tree 1969 film The Tree 1969 film , an American film The Tree 1993 film The Tree 1993 film , a short film The Tree 2010 film The Tree 2010 film , an Australian French film disambig ... more details
Image with unknown copyright status removed Image Ttreenonde.png thumb right 251px An example of a T tree node structure. Image T tree 1.png thumb right 251px An example T tree. In computer science a T tree is a type of binary tree data structure that is used by main memory database main memory databases .... A T tree is a Height balanced tree balanced index tree data structure optimized for cases where both the index and the actual data are fully kept in memory, just as a B tree is an index structure ... to gain the performance benefits of in memory tree structures such as AVL trees while avoiding the large ... fields within the index tree nodes themselves. Instead, they take advantage of the fact that the actual ... data fields. The T in T tree refers to the shape of the node data structures in the original ... speed gap between cache access and main memory access. explain please Node structures A T tree ... minimum and maximum value, inclusively. Image T tree 2.png thumb right 251px Bound values. For each ... then the tree might need to be rebalanced, as described below. Deletion Search for bounding node of the value ... element in the data array then delete the node. Rebalance the tree if needed. Half leaf node ... the leaf node. Rebalance the tree if needed. Rotation and balancing Expand section date June 2008 A T tree is implemented on top of an underlying self balancing binary search tree . Specifically, Lehman and Carey s article describes a T tree balanced like an AVL tree it becomes out of balance ... or deletion of a node. After an insertion or deletion, the tree is scanned from the leaf to the root. If an imbalance is found, one tree rotation or pair of rotations is performed, which is guaranteed to balance the whole tree. When the rotation results in an internal node having fewer than the minimum ... section date June 2008 See also Tree graph theory Tree set theory Tree structure Exponential tree Other trees B tree 2 3 tree , 2 3 4 tree , B tree , B tree , UB tree DSW algorithm Dancing tree Fusion ... more details
An and or tree is a graphical representation of the reduction of problem s or goals to Logical conjunction conjunctions and disjunction s of subproblems or subgoals . Example The and or tree Image And or tree.JPG represents the search space for solving the problem P, using the goal reduction methods P if Q and R P if S Q if T Q if U Definitions Given an initial problem P0 and set of problem solving methods of the form P if P1 and and Pn the associated and or tree is a set of labelled nodes such that The root of the tree is a node labelled by P0. For every node N labelled by a problem or sub problem P and for every method of the form P if P1 and and Pn, there exists a set of children nodes N1, , Nn of the node N, such that each node Ni is labelled by Pi. The nodes are conjoined by an arc, to distinguish them from children of N that might be associated with other methods. A node N, labelled by a problem P, is a success node if there is a method of the form P if nothing i.e., P is a fact . The node is a failure node if there is no method for solving P. If all of the children of a node N, conjoined by the same arc, are success nodes, then the node N is also a success node. Otherwise the node is a failure node. Search strategies An and or tree specifies only the search space for solving a problem. Different Tree traversal search strategies for searching the space are possible. These include searching the tree depth first, breadth first, or best first using some measure of desirability of solutions. The search strategy can be sequential, searching or generating one node at a time, or parallel, searching or generating several nodes in parallel. Relationship with logic programming The methods used for generating and or trees are propositional Logic programming logic programs without variables . In the case of logic programs containing variables, the solutions of conjoint sub problems ... node of such a tree represents the problem of one of the players winning the game, starting from ... more details
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