Image Gospers glider gun.gif frame right Bill Gosper Gosper s Gun cellular automaton Glider Gun creating Glider Conway s Life gliders in the cellular automaton Conway s Game of Life ref Daniel Dennett ... A cellular automaton pl. cellular automata , abbrev. CA is a discrete mathematics discrete model ... cellular automaton is with an infinite sheet of graph paper along with a set of rules for the cells ... programmable using modular arithmetic functions. For example, in a 1 dimensional cellular automaton ... Also in the 1940s, Norbert Wiener and Arturo Rosenblueth developed a cellular automaton model of excitable ... a two state, two dimensional cellular automaton named Conway s Game of Life Game of Life became .... It is possible to arrange the automaton so that the gliders interact to perform computations, and after ... computation on a giant cellular automaton. This was the first book on what today is called ... elementary cellular automaton elementary cellular automata see below . The unexpected complexity of the behavior ... different abstract systems. Elementary cellular automata Main Elementary cellular automaton ... in the history of the automaton, with t 0 being the top row. Each pixel is colored white for 0 and black for 1. div align center Image CA rule30s.png br Rule 30 cellular automaton class wikitable ... cell 0 0 0 1 1 1 1 0 Image CA rule110s.png br Rule 110 cellular automaton class wikitable style text ... main Reversible cellular automaton A cellular automaton is said to be reversible if for every current configuration of the cellular automaton there is exactly one past configuration preimage . If one thinks of a cellular automaton as a function mapping configurations to configurations, reversibility implies that this function is bijective . If a cellular automaton is reversible, its time reversed behavior can also be described as a cellular automaton this fact is a consequence of the Curtis Hedlund ... is undecidable that is, there is no algorithm that takes as input an automaton rule and is guaranteed ... more details
merge to Embedded pushdownautomaton discuss Talk Nested stack automaton Merge proposal date April 2012 In automata theory , a nested stack automaton is a finite state machine finite automaton that can make use of a Stack data structure stack containing data which can be additional stacks. ref name aho cite journal last Alfred Aho Aho first Alfred year 1969 title Nested stack automata journal Journal of the ACM volume 16 issue 3 pages 383 406 issn 0004 5411 url http portal.acm.org ft gateway.cfm?id 321529&type pdf&coll GUIDE&dl GUIDE,&CFID 21501966&CFTOKEN 95121590 doi 10.1145 321526.321529 ref A nested stack automaton may read its stack, in addition to pushing or popping it. A nested stack automaton is capable of recognizing an indexed language ref cite book last Barbara Partee Partee first Barbara coauthors Alice ter Meulen, and Robert E. Wall title Mathematical Methods in Linguistics year 1990 publisher Kluwer Academic Publishers pages 536 542 isbn 978 90 277 2245 4 ref , and in fact the class of indexed languages is exactly the class of languages accepted by one way nondeterministic nested stack automata. ref name aho See also Automata theory References references Formal languages and grammars comp sci stub Category Models of computation Category Automata theory hr Automat s ugnije enim stogom sr zh ... more details
, nondeterministic finite automaton with moves , pushdownautomaton , automaton , probabilistic automata . Informal introduction An NFA, similar to a deterministic finite automaton DFA , consumes ...In the automata theory , a nondeterministic finite automaton NFA or nondeterministic finite state machine is a finite state machine where from each state and a given input symbol the automaton may jump into several possible next states. This distinguishes it from the deterministic finite automaton DFA , where the next possible state is uniquely determined. Although the DFA and NFA have distinct definitions, a NFA can be translated to equivalent DFA using powerset construction , i.e., the constructed DFA and the NFA recognize the same formal language . Both types of automata recognize only regular languages . NFAs were introduced in 1959 by Michael O. Rabin and Dana Scott , ref cite journal doi 10.1147 rd.32.0114 last Rabin first M. O. last2 Scott first2 D. title Finite Automata and Their Decision ... . Let w a sub 1 sub a sub 2 sub ... a sub n sub be a word over the alphabet . The automaton M accepts ... states. Otherwise, it is said that the automaton rejects the string. The set of strings M accepts ... of NFA Deterministic finite automaton DFA In this automaton, for each state and alphabet, the transition relation has exactly one state. Nondeterministic finite automaton with moves NFA This automaton ... automaton with moves NFA , the above closures are proved using closure properties of NFA . The above ... alphabet . The automaton uses the state transition function to determine the next state using ... nfa Finite State Machine ref If, when the automaton has finished reading, it is in an accepting state ... NFA a deterministic finite automaton DFA can be found that accepts the same language. Therefore ... nondeterministic finite automaton Proofs here . Implementation There are many ways to implement a NFA Convert to the equivalent DFA. In some cases this may cause exponential blowup in the size of the automaton ... more details
Image Conways game of life breeder animation.gif thumb 379px Evolution of a Puffer train cellular automaton puffer that leaves Gun cellular automaton guns in its wake type breeder Image Chart animation.gif thumb 379px Charts showing the change of cell count per generation of the four different breeder types. A polynomial trend line demonstrates the quadratic growth rate. In Conway s Game of Life , a breeder is a pattern that exhibits quadratic growth , by generating multiple copies of a secondary pattern, each of which then generates multiple copies of a tertiary pattern. ref name weisstein cite web url http www.ericweisstein.com encyclopedias life Breeder.html accessdate 2008 11 01 title Breeder from Eric Weisstein s Treasure Trove of Life C.A. ref Classification Breeders can be classed by the relative motion of the patterns. The four basic types are ref name weisstein A Gun cellular automaton gun that fires out Rake cellular automaton rakes . The primary pattern is stationary, whilst both the secondary and tertiary patterns move. A Puffer train cellular automaton puffer that leaves Gun cellular automaton guns in its wake. The secondary patterns are stationary, whilst both the primary and tertiary patterns move. A Rake cellular automaton rake that fires out Puffer train cellular automaton puffers . The tertiary patterns are stationary, whilst the primary and secondary patterns move. A Rake cellular automaton rake that fires out more Rake cellular automaton rakes . All the patterns move. A spacefiller which also undergoes quadratic growth may be thought of as a fifth class of breeder. However it differs from a true breeder in that it expands a single island of cells, rather than creating independent objects. References reflist Conway s Game of Life Category Cellular automaton patterns Comp sci stub ... more details
An aperiodic finite state automaton is a finite state automaton whose transition monoid is aperiodic monoid aperiodic . Properties A regular language is Star free language star free if and only if it is accepted by an automaton with a finite and aperiodic transition monoid . This celebrated result of algebraic automata theory is due to Marcel Paul Sch tzenberger . ref name Schutzenberger65 Sch tzenberger, Marcel Paul, On finite monoids having only trivial subgroups, Information and Control , Vol 8 No. 2, pp. 190 194, 1965. ref An aperiodic automaton satisfies the ern conjecture . ref name Trahtman07 Trahtman. The Cerny conjecture for aperiodic automata, Discrete Mathematics and Theoretical Computer Science, Vol 9 No. 2, pp. 133 138, 2007. ref References reflist Formal languages and grammars Category Automata theory Category Formal languages comp sci theory stub ... more details
Image Color coded racetrack large channel.gif thumb 348px Oscillators of varying periods that double as glider reflectors highlighted in pink. Click to view animation. In cellular automaton cellular automata such as Conway s Game of Life , a reflector is a pattern that can interact with a spaceship cellular automaton spaceship to change its direction of motion, without damage to the reflector pattern. In Life, many oscillator cellular automaton oscillators can reflect the Glider Conway s Life glider there also exist stable reflectors composed of still life cellular automaton still life patterns that, when they interact with a glider, reflect the glider and return to their stable state. External links http pentadecathlon.com lifeNews 2009 05 new stable 180degree glider re.html New stable 180 degree glider reflector , Game of Life News, May 30, 2009 Conway s Game of Life Category Cellular automaton patterns Comp sci stub ... more details
tree automaton is a state machine that deals with infinite Tree set theory Tree automata theory tree structure . It can be viewed as an extension from a tree automaton finite tree automaton , which ... automatons such as the B chi automaton and the Muller automaton . A finite automaton which runs on an infinite ... automaton and logical theories are closely connected and it allows decision problems in logic to be reduced into decision problems for automaton. Definition Infinite tree automaton runs of over ... formulations of tree automaton. Here one of the formulation is described. An infinite tree automaton ... times D rightarrow 2 Q math is a transition relation that maps an automaton state math q in Q math .... math q 0 in Q math is an initial state of automaton. math F subseteq Sigma omega math is an accepting condition. Run A run of tree automaton math A math over a math Sigma math labeled tree math T,V math is a math Q math labeled tree math T r, r math . Lets suppose that the tree automaton is at state .... math d t math is degree of node t. Then, the automaton proceeds by selecting a tuple math q 1,...,q ... F math , then the run is accepting . The interesting accepting conditions are omega automaton Acceptance conditions Buchi , Rabin automaton Acceptance conditions Rabin , Streett automaton Acceptance conditions Streett and Muller automaton Acceptance conditions Muller . If for an input math Sigma math labeled tree math T,V math there exist an accepting run then the input tree is accepted by the automaton ... L A math which is recognized by tree automaton math A math . Remarks The set D may seem unusual to some ... tree. Infinite tree automaton is deterministic if for some math q in Q math , math sigma in Sigma .... Otherwise the automaton is non deterministic . Accepting tree languages Muller, parity, Rabin, and Streett accepting conditions in a infinite tree automaton recognize the same tree languages. But, Buchi ... t be recognized by any buchi accepting condition in some infinite tree automaton. ref Rabin, M. O ... more details
unreferenced date July 2011 In automata theory , a co B chi automaton is a variant of B chi automaton . The only difference is the accepting condition a Co B chi automaton accepts an infinite word w if there exist a run, such that all the states occurring infinitely often in the run are not in the acceptance condition. In contrast, a B chi automaton accepts a word if there exists a run, such that at least one state occurring infinitely often in its acceptance condition. Co B chi automata are strictly weaker than B chi automata. Formal definition Formally, a deterministic co B chi automaton is a tuple A Q , , , q sub 0 sub , F that consists of the following components Q is a finite set . The elements of Q are called the states of A . is a finite set called the alphabet of A . Q Q is a function, called the transition function of A . q sub 0 sub is an element of Q , called the initial state. F Q is the acceptance condition . A accepts exactly those runs r , in which all of the infinitely often occurring states in r are not in F . In a non deterministic co B chi automaton , the transition function is replaced with a transition relation that returns a set of states and initial state is q sub 0 sub is replaced by a set of initial states Q sub 0 sub . Generally, co B chi automaton refers to non deterministic co B chi B chi automaton. For more comprehensive formalism see also automaton . Properties Co B chi automata are closed under union, intersection, projection and determinization. Category Automata theory ... more details
Speed of light cellular automaton speed of light including three commonly seen spaceships with four ... . See also Brian s Brain , a similar cellular automaton by the same author External links cite web author ... mcell rullex life.html title Cellular Automaton Rules Lexicon Family Life work Mirek s Cellebration Conway s Game of Life Category Cellular automaton rules ... more details
A tree walking automaton TWA is a type of finite automaton that deals with tree structure tree structures rather than strings. The concept was originally proposed in harvtxt Aho Ullman 1971 . The following article deals with tree walking automata. For a different notion of tree automaton, closely related to regular tree languages, see tree automaton branching automaton . Definition All trees are assumed to be binary, with labels from a fixed alphabet math Sigma math . Informally, a tree walking automaton A TWA is a finite state device which walks over the tree in a sequential manner. At each moment A visits node v in state q. Depending on the state q, the label of the node v, and whether the node is the root, a left child, a right child or a leaf, A changes its state from q to q and moves to the parent of v or its left or right child. A TWA accepts a tree if it enters an accepting state, and rejects if its enters a rejecting state or makes an infinite loop. As with string automata, a TWA may be deterministic or nondeterministic. More formally, a nondeterministic tree walking automaton over alphabet math Sigma math is a tuple math A Q, Sigma, I, F, R, delta math where math Q math is a finite set of states, math I, F, R subset Q math are the sets of respectively initial, accepting and rejecting states, and math delta math is the transition relation math delta subset Q times mathit root , mathit left , mathit right , mathit leaf times Sigma times mathit up , mathit left , mathit right times Q math . Example A simple example of a tree walking automaton is a TWA that performs depth first search DFS on the input tree. The automaton math A math has 3 states, math Q q 0 , q mathit left , q mathit right math . math A math begins in the root in state math q 0 math and descends to the left .... Properties Unlike tree automaton branching automata , tree walking automata are difficult to analyze ... automaton harv Bojanczyk Colcombet 2008 . See also Pebble automaton Pebble automata , an extension ... more details
A reversible cellular automaton is a cellular automaton in which every configuration has a unique predecessor ... cellular automaton can always be described by another cellular automaton rule, possibly ... these include the block cellular automaton method, in which each update partitions the cells ... cellular automaton method, in which the update rule combines states from two previous steps of the automaton ... 0 or 1 . If the update rule for a cell causes it to always remain in the same state, then the automaton ..., suppose that each state of a cellular automaton is an ordered pair r , l consisting of a right part ... cellular automaton in which the cells are offset by half a unit at each step, so the neighborhood of every ... by equation math 1 a , b c , d a , d . Then this automaton is reversible the values on the left side ... used to combine pairs of states in this automaton forms an algebraic structure known as a Band mathematics ... or by five can be performed by a one dimensional reversible cellular automaton with ten states per cell ... factors of mvar b , is an operation that forms a cellular automaton because it depends only on a bounded ..., but does not define a cellular automaton, because there is no fixed bound on the number of digits ... cellular automaton rule, because in Rule 90 every configuration has exactly four predecessors ... escape from a central random seed region in the critters block cellular automaton rule. Conway s Game of Life , one of the most famous cellular automaton rules, is not reversible for instance, it has ..., and it also has Garden of Eden cellular automaton Garden of Eden patterns with no predecessors ... rule is a block cellular automaton in which, at each step, the cells of the automaton are partitioned ... reversible, the automaton defined by these rules is a reversible cellular automaton ref ... can also support more complex Spaceship cellular automaton spaceships of varying speeds as well as Oscillator cellular automaton oscillators with infinitely many different periods. ref name critters ... more details
Image 1dCCA n4.png thumb 300px A one dimensional cyclic cellular automaton with n 4, run for 300 steps from a random initial configuration. The cyclic cellular automaton is a cellular automaton rule developed by David Griffeath and studied by several other cellular automaton researchers. In this system ... cellular automaton, the cyclic cellular automaton consists of a regular grid of cells in one or more ... this threshold. One dimension The one dimensional cyclic cellular automaton has been extensively ... other. In the three state cyclic cellular automaton, the boundary between regions with values ... 184 , a cellular automaton used to model traffic flow . ref Belitsky and Ferrari 2005 . ref In the n 4 automaton, the same two types of particles and the same annihilation reaction occur. Additionally ... of two dimensional cyclical cellular automaton growing to repeating patterns from a random beginning. Image 2dCCA n16.png thumb 300px A two dimensional cyclic cellular automaton with n 16, after 400 steps starting from a random initial configuration. All three types of patterns formed by this automaton ... or Moore neighborhood , this cellular automaton generates three general types of patterns sequentially ... to be consumed by higher ranking cells, the automaton goes to the consuming phase, where there are blocks .... Almost surely , every cell of the automaton eventually enters a repeating cycle of states, where ... the automaton stabilizes in the block of color stage without forming spirals. At intermediate values .... ref http psoup.math.wisc.edu archive recipe6.html Turbulent Equilibrium in a Cyclic Cellular Automaton ... of states and the size of the neighborhood, the spiral patterns formed by this automaton can be made ... August pages 102 105 cite journal author Fisch, R. title The one dimensional cyclic cellular automaton ..., R. title Clustering in the one dimensional three color cyclic cellular automaton journal Annals of Probability ... automaton rules ... more details
cellular automaton. The partition of the cells alternates between the set of math 2 × 2 blocks ... cellular automaton or partitioning cellular automaton is a special kind of cellular automaton in which ... to choose transition rules that obey physical constraints such as reversible cellular automaton ... Automata pages 115 116 year 2008 ref Definition A block cellular automaton consists of the following ... cellular automaton, the pattern of cell states changes over time to perform some nontrivial ... of its neighbors . With such a construction scheme, the cellular automaton is guaranteed to be reversible ... as a block cellular automaton on a finer lattice of cells, formed by the parts of each larger cell the blocks ... As long as the rule for evolving each block is reversible cellular automaton reversible , the entire automaton will also be. More strongly, in this case, the time reversed behavior of the automaton can also be described as a block cellular automaton, with the same block structure and with a transition rule that inverts the original automaton s rule within each block. The converse is also true if the blocks ... is replaced by y . That is, a cellular automaton is reversible globally if and only if it is reversible ... non block neighborhood structures, for which it is undecidable problem undecidable whether the automaton is reversible and for which the reverse dynamics may not be describable as an automaton ... 10.1016 0167 2789 90 90195 U ref Any reversible cellular automaton may be simulated by a reversible block cellular automaton with a larger number of states however, because of the undecidability of reversibility ... in the non block automaton that correspond to blocks in the simulation, and the translation from ... of the automaton will also preserve the same number. This property is useful in the applications ... name tm the block cellular automaton model does not introduce any additional power compared to a conventional cellular automaton that uses the same neighborhood structure at each time step any block ... more details
Unreferenced date December 2009 In automata theory , an alternating finite automaton AFA is a nondeterministic finite automaton whose transitions are divided into existential quantification existential and universal quantification universal transitions. For example, let A be an alternating automaton . For an existential transition math q, a, q 1 vee q 2 math , A nondeterministically chooses to switch the state to either math q 1 math or math q 2 math , reading a . Thus, behaving like a regular nondeterministic finite automaton . For a universal transition math q, a, q 1 wedge q 2 math , A moves to math q 1 math and math q 2 math , reading a , simulating the behavior of a parallel machine. Note that due to the universal quantification a run is represented by a run tree . A accepts a word w , if there exists a run tree on w such that every path ends in an accepting state. A basic theorem tells that any AFA is equivalent to an non deterministic finite automaton NFA by performing a similar kind of powerset construction as it is used for the transformation of an NFA to a deterministic finite automaton DFA . This construction converts an AFA with k states to an NFA with up to math 2 k math states. An alternative model which is frequently used is the one where Boolean combinations are represented as clauses . For instance, one could assume the combinations to be in Disjunctive normal form Disjunctive Normal Form so that math q 1 , q 2,q 3 math would represent math q 1 vee q 2 wedge q 3 math . The state tt true is represented by math math in this case and ff false by math varnothing math . This clause representation is usually more efficient. Formal Definition An alternating finite automaton AFA is a n tuple 6 tuple , math S exists , S forall , Sigma, delta, P 0, F math , where math S exists math is a finite set of existential states. Also commonly represented as math S vee math ... cup S forall math . DEFAULTSORT Alternating Finite Automaton Category Automata theory Compu sci ... more details
Image JdlV osc 5.56.gif thumb The fumarole, a period 5 Oscillator cellular automaton oscillator in Conway s Game of Life . The two live cells appearing at the top of the pattern every five generations form a spark. In Conway s Game of Life and Life like cellular automaton similar cellular automaton rules , a spark is a small collection of live cells that appears at the edge of some larger pattern such as a Spaceship cellular automaton spaceship or Oscillator cellular automaton oscillator , then quickly dies off. ref http www.argentum.freeserve.co.uk lex s.htm spark Life Lexicon , Stephen Silver. ref Sparks are commonly separated by some distance from the main body of the pattern the analogy is to an object throwing off sparks but the minimum requirement is a set of cells on the pattern boundary that are alive in one phase but dead in a later phase, and that are unaffected by other parts of the pattern they would die in the same way if the rest of the pattern were removed . The converse is not necessarily true for example, removing the spark in the accompanying illustration would destabilize the fumarole. Sparks are an important way for components of a larger pattern to interact with each other for instance, Niemiec ref citation first Mark D. last Niemiec contribution Synthesis of Complex Life Objects from Gliders title New Constructions in Cellular Automata editor1 first David editor1 last Griffeath editor2 first Cristopher editor2 last Moore editor2 link Cris Moore publisher Oxford University Press series Santa Fe Institute Studies in the Sciences of Complexity year 2003 pages 55 77 , section 3.2, Use of Sparks , p.69. ref describes the use of sparks formed by colliding Glider Conway s Life gliders as part of the synthesis of other life objects. Bell ref Spaceships in Conway ... they all have small sparks which may be used to perturb nearby Puffer train cellular automaton puffer ... Conway s Game of Life Category Cellular automaton patterns ... more details
In automata theory , generalized B chi automaton GBA is a variant of B chi automaton . The difference with the B chi automaton is its accepting condition, i.e., a set of sets of states. A run is accepted by the automaton if it visits at least one state of every set of the accepting condition infinitely often. Generalized b chi automata GBA is equivalent in expressive power with B chi automata a transformation is given B chi automata Transforming from other models of description to non deterministic B.C3.BCchi automata here . In formal verification , the model checking method needs to obtain an automaton from a Linear temporal logic LTL formula that specifies the program property. There are Linear temporal logic to B chi automaton algorithms that translate a Linear temporal logic LTL formula into a GBA ref name VW94 M.Y. Vardi and P. Wolper, Reasoning about infinite computations, Information and Computation, 115 1994 , 1 37. ref ref name KMMP93 Y.Kesten,Z.Manna,H.McGuire,A.Pnueli,A decision algorithm for full propositional temporal logic, CAV 93, Elounda, Greece, LNCS 697, Springer Verlag, 97 109. ref ref name GPVW93 R. Gerth, D. Peled, M.Y. Vardi and P. Wolper, Simple On The Fly Automatic Verification of Linear Temporal Logic, Proc. IFIP WG6.1 Symp. Protocol Specification, Testing, and Verification PSTV95 , pp. 3 18,Warsaw, Poland, Chapman & Hall, June 1995. ref ref name GOCAV01 P. Gastin and D. Oddoux, Fast LTL to B chi automata translation, Thirteenth Conference on Computer ..., a generalized B chi automaton is a tuple A Q , , , Q sub 0 sub , F sub 1 sub ,...,F sub ... formalism see also automaton . Labeled generalized B chi automaton Labeled generalized B chi automaton LGBA is another variation in which input is associated as labels with the states rather ... generalized B chi automaton is a tuple A Q , , L , , Q sub 0 sub , F sub 1 sub ,...,F ... the nodes to the incoming transitions. References Reflist DEFAULTSORT Generalized Buchi Automaton Category ... more details
O automaton model contains a very basic structure that enables it to model various types of Distributed ... I O automaton An I O automaton models a distributed system component that can interact with other .... The automaton uses its input and output actions to communicate with its environment, whereas the internal actions are only visible to the automaton itself. Unlike internal and output actions that are selected and carried out by the automaton, the input actions which simply arrive from the environment are not under automaton s control. ref name lynch1997 Examples I O automata can be used to be used ... in a message passing system, or a shared data structure in a shared memory systems. Process I O Automaton table border 0 width 100 tr td Figure 1 depicts an example of an I O automaton for a process ... right File ProcessIOV2.jpg thumb alt Process I O Automaton Figure 1 Process I O Automaton td tr table ... O automaton. Figure 2 illustrates a typical unidirectional FIFO channel automaton, named C sub i ... m sub i,j sub . Each message m may contain 0 or 1 m 0,1 . The state of the automaton stores a FIFO ... thumb upright 1.5 alt Channel I O Automaton Figure 2 FIFO Channel I O Automaton td tr table In a typical ... Operation composed in a way that output actions of one automaton are matched and executed ... read write register I O automaton in a shared memory system with two processes, P sub 1 sub and P sub 2 sub . The value V stored in the register is of type integer V Z . The state of the automaton ... to a read request by process P sub i sub . The automaton also includes internal actions perform Write V , which writes the value V to the register by updating the state of the automaton , and perform ... Figure 3 Atomic Read Write Register I O Automaton td tr table Formal Specification An I O automaton A, or simply an automaton, comprises five components Signature sig A States states A States start ... of an I O automaton A is the definition of its signature , sig A . A signature S describes ... more details
Image Stable puffer animation.gif thumb 400px Stable dirty puffer train. In a cellular automaton a puffer train , or simply puffer , is a finite pattern that moves itself across the universe , leaving debris behind. Thus a pattern consisting of only a puffer will grow arbitrarily large over time. Puffers differ from spaceship cellular automata spaceship s in that spaceships do not leave debris behind. Nonetheless, puffers are considered to have periods and speeds in the same way that spaceships have. The period of a puffer can be considered as the combination of two periods the first is the period of the puffer itself, while the second is the apparent period of the pattern of debris produced. This is often the same as the period of the puffer, but sometimes is a factor of the period. A puffer for which the apparent period deduced from the debris is smaller than the period of the engine is a pseudoperiod puffer . Such puffers are typically produced by artificial means. A true period puffer is one in which the period of the debris matches that of the puffer. Puffers are divided into two classes, dirty puffers and clean puffers . While there is no precise distinction, a dirty puffer is one in which there is little apparent order in the debris although the debris will still eventually be periodic . A clean puffer, conversely, has a small amount of debris that appears much more organized. A dirty puffer can sometimes be turned into a clean puffer by adding spaceships of the same velocity ... is called a Rake cellular automaton rake . In Conway s Game of Life The first known puffer, in Conway ... for this book. ref Since then, many puffers have been discovered for this cellular automaton, with many ... status page . ref Puffers are significant for Life and Life like cellular automaton related rules ... automaton breeders . Second, stabilizations of puffers that eliminate all of their output debris ..., Lifepage . ref References reflist Conway s Game of Life Category Cellular automaton patterns fr ... more details
Image Codd CA RepeaterEmitter.gif right frame 250px A simple configuration in Codd s cellular automaton. Signals pass along wire made of cells in state 1 blue sheathed by cells in state 2 red . Two signal trains circulate around a loop and are duplicated at a T junction onto an open ended section of wire. The first 7 0 causes the sheathed end of the wire to become exposed. The second 6 0 re sheathes the exposed end, leaving the wire one cell longer than before. Codd s cellular automaton is a cellular automaton CA devised by the United Kingdom British computer science computer scientist Edgar F. Codd in 1968. It was designed to recreate the computation and construction universality of von Neumann cellular automaton von Neumann s CA but with fewer states 8 instead of 29. Codd showed that it was possible to make a self reproducing machine in his CA, in a similar way to von Neumann s von Neumann Universal Constructor universal constructor but never gave a complete implementation. History In the 1940s and 50 s, John von Neumann posed the following problem ref name vonNeumann66 cite web url http www.walenz.org vonNeumann index.html title Theory of Self Reproducing Automata. last von Neumann first John last2 Burks first2 Arthur W. year 1966 publisher www.walenz.org accessdate 2012 01 28 ... 2008 01 05 ref What kind of logical organization is sufficient for an automaton to be able to reproduce itself? He was able to construct a von Neumann cellular automaton cellular automaton with 29 ... Neumann s question What kind of logical organization is necessary for an automaton to be able to reproduce ... Langton made another tweak to Codd s cellular automaton in 1984 to create Langton s loops ... computer in the cellular automaton, based on Wang B machine Wang s W machine . However, the design ... Cellular automaton Conway s game of life Langton s loops von Neumann cellular automaton Wireworld ... life Category Cellular automaton rules fr Automate cellulaire de Codd ja ... more details
In the theory of computation , a generalized nondeterministic finite automaton GNFA , also known as expression automaton or generalized nondeterministic finite state machine is a variation of nondeterministic finite automaton NFA where each transition is labeled with any regular expression . The GNFA reads blocks of symbols from the input which constitute a string as defined by the regular expression on the transition. There are several differences between a standard finite state machine and a generalized nondeterministic finite state machine. A gNFA must have only one start state and one accept state, and these cannot be the same state, whereas a NFA or DFA both may have several accept states, and the start state can be an accept state. A gNFA must have only one transition between any two states, whereas a NFA or DFA both allow for numerous transitions between states. In a gNFA, a state has a single transition to every state in the machine, although often it is a convention to ignore the transitions that are labelled with the empty set when drawing generalized nondeterministic finite state machines. Formal definition A GNFA can be defined as a n tuple 5 tuple , S , , T , s , a , consisting of a finite set of states S a finite set called the alphabet a transition function mathematics function T S & x2216 a × S & x2216 s R a start state s S an accept state a S where R is the collection of all regular expressions over the alphabet . The transition function takes as its argument a pair of two states and outputs a regular expression the label of the transition . This differs from other finite state machines, which take as input a single state and an input from the alphabet or the empty string in the case of nondeterministic finite state machines and outputs the next state or the set of possible states in the case of nondeterministic finite state machines . A deterministic finite automaton DFA or nondeterministic finite automaton NFA can easily be converted into a GNFA ... more details
In Conway s Game of Life and related Cellular automaton cellular automata , the speed of light is a propagation rate across the grid of exactly one step either horizontally, vertically or diagonally per generation. In a single generation, a cell can only Moore neighborhood influence its nearest neighbours , and so the speed of light by analogy with the speed of light in physics is the maximum rate at which information can propagate. It is therefore an upper bound to the speed at which any pattern can move. ref name sciam Cite journal title Mathematical Games The fantastic combinations of John Conway s new solitaire game Life authorlink Martin Gardner first Martin last Gardner journal Scientific American volume 223 date October 1970 pages 120 123 postscript None ref Notation As in physics, the speed of light is represented with the letter math c math . This in turn is used as a reference for describing the average propagation speed of Spaceship cellular automaton spaceships . For example, a Glider Conway s Life glider is said to have a speed of math c 4 math , as it takes four generations for a given state to be translated by one cell. Similarly, the lightweight spaceship is said to have a speed of math c 2 math , as it takes four generations for a given state to be translated by two cells. Lightspeed propagation While math c math is an absolute upper bound to propagation speed, the maximum speed of a spaceship in Conway s Game of Life is in fact math c 2 math . This is because it is impossible to build a spaceship that can move every generation. This is not true, though, for cellular automata in general for instance many light speed spaceships exist in Seeds cellular automaton Seeds . It is, however, possible for objects to travel at the speed of light if they move through a medium other than empty space. Such media include trails of Still life cellular automaton Hives ... DEFAULTSORT Speed Of Light Cellular Automaton Category Cellular automata ja ... more details
Infobox title Movable cellular automaton method titlestyle datastyle headerstyle background ccf labelstyle ... caption Movable cellular automaton actively changed self neighbors by means switching neighbors ... header4 Characteristics label4 data4 header5 label5 Influenced by data5 cellular automaton , discrete ... solid mechanics The Movable cellular automaton MCA method is a method in Computational mechanics computational ... cellular automaton and discrete element method discrete element methods. Important advantage of the ... provides simulating solids behavior. If size of automaton will be close to zero then MCA behavior becomes like classical continuum mechanics methods. Keystone of the movable cellular automaton method .... The mutual forces and rules for inter elements relationships are defined by the function of the automaton response. This function has to be specified for each automaton. Due to mobility of automata ... i sup &ndash radius vector of automaton V sup i sup &ndash velocity of automaton sup i sup &ndash rotation velocity of automaton sup i sup &ndash rotation vector of automaton m sup i sup &ndash mass of automaton J sup i sup &ndash moment of inertia of automaton. New concept neighbours File MCA neighbors.gif thumb center Each automaton has some neighbors center The new concept of the MCA method ... in addition to the conventional one &ndash the state of a separate automaton. Note that the introduction ... as an automaton overlapping parameters h sup ij sup . So the relationship of the cellular automata ... cellular automaton method in the MCA method not only a single automaton but also a relationship ... unlinked each automaton of the pair belongs to different bodies or parts of damaged body. So the changing ... Forces between automata ij coming from their neighbors. center Here m sup i sup is the mass of automaton ... of automaton i to contact point of automaton j moment arm , sup ij sup is the pair tangential ... Deformation.gif thumb center Deformation is determine by value of distance from the center of automaton ... more details
Image Gospers glider gun.gif thumb Gosper Glider Gun shooting gliders In a cellular automaton , a gun is a pattern with a main part that repeats periodically, like an oscillator CA oscillator , and that also periodically emits spaceship cellular automaton spaceship s. There are then two periods that may be considered the period of the spaceship output, and the period of the gun itself, which is necessarily a multiple of the spaceship output s period. A gun whose period is larger than the period of the output is a pseudoperiod gun . Image Day and night.gif thumb left A gun and an antigun in the Life variation Day & Night Image game of life glider gun.svg thumb The smallest gun found so far in Conway s Game of Life is the Gosper Glider Gun In the Conway s Game of Life Game of Life , for every p greater than or equal to 14, it is possible to construct a glider Conway s Life glider gun in which the gliders are emitted with period p . ref cite web url http entropymine.com jason life status.html title Game of Life Status page work Entropymine.com first Jason last Summers accessdate February 5, 2011 ref Since guns continually emit spaceships, the existence of guns in Life means that initial patterns with finite numbers of cells can eventually lead to configurations with limitless numbers of cells, something that John Horton Conway John Conway himself originally did not believe was possible. Bill Gosper discovered the first glider gun and, so far, the smallest one found in 1970, earning 50 from Conway. The discovery of the glider gun eventually led to the proof that Conway s Game of Life could function as a Turing machine . ref cite book title The Colossal Book of Mathematics publisher W. W. Norton location New York first Martin last Gardner year 2001 isbn 0 393 02023 1 ref References reflist Conway s Game of Life Category Cellular automaton patterns comp sci theory stub fr Canon automate cellulaire ja pl Dzia a automaty kom rkowe ... more details
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