The term information scientist developed in the latter part of the twentieth century by Wm. Hovey Smith to describe an individual, usually with a relevant subject degree (such as one in Information and Computer Science - CIS) or high level of subject knowledge, providing focused information to scientific and technical research staff in industry. It is a role quite distinct from and complementary to that of a librarian. Developments in end-user searching, together with some convergence between the roles of librarian and information scientist, have led to a diminution in its use in this context, and the term information officer or information professional (information specialist) are also now used. The term was, and is, also used for an individual carrying out research in information science. Brian C. Vickery mentions that the Institute of Information Scientists (IIS) was established in London during 1958 and lists the criteria put forward by this institute "Criteria for Information Science" (appendix 1) as well as his own "Areas of study in information science" (appendix 2). The IIS merged with the Library Association in 2002 to form the Chartered Institute of Library and Information Professionals (CILIP). == Notable Information Scientists == See also Award of Merit - Association for Information Science and Technology Marcia Bates David Blair (information technologist) Samuel C. Bradford Michael Buckland John M. Carroll Blaise Cronin Emilia Currás Brenda Dervin Eugene Garfield Paul B. Kantor Frederick Wilfrid Lancaster Calvin Mooers Tefko Saracevic Linda C. Smith Robert Saxton Taylor Brian Campbell Vickery Thomas D. Wilson == Additional reading == Ellis, David and Merete Haugan. (1997) "Modelling the information seeking patterns of engineers and research scientists in an industrial environment" (Journal of Documentation, Volume 53(4): pp. 384–403) Poole, Alex H. (2024). "'There's a big difference between going through life with the wind at your back, and going through life leaning into the wind': Feminism in Post-World War II Information Science". Proceedings of the Association for Information Science and Technology. 61: 300–313. doi:10.1002/pra2.1029. Vickery, Brian Campbell (1988) "Essays presented to B. C. Vickery" (Journal of Documentation, Volume 44, pp. 199–283). Vickery, B. & Vickery, A. (1987) Information Science in theory and practice (London: Bowker-Saur, pp. 361–369)
Gallery software
Gallery software is software that helps the user publish or share photos, pictures, videos or other digital media. Most galleries are located on Web servers, where users are allowed to register and publish their pictures. Gallery software usually features automatic image resizing, allows digital media be categorized into sets, and allows comments. == Types == Early digital media publishing and sharing was done with imageboards. The boards are by topics, sometimes called "chan". Each discussion in a "chan" are started with a piece of digital media, and follow-up discussions can contain another piece too. Software works in this way: Futallaby, Danbooru. Traditionally, galleries are managed. An administrator maintains a set of or hierarchy of albums. The users can upload their digital media in one of the existing albums defined by an administrator, or create their own albums. The users with sufficient permission can re-categorise the digital media others uploaded. Often, the site's administrator can define which album the users are allowed to categorise their media into, or delete other user's content. Examples are open source galleries Coppermine, Gallery Project. There are decentralised gallery software that does not have an administrator for managing contents. Pinterest, Flickr and DeviantArt has been successful with this model. Open source gallery software MediaGoblin works in this way. Each user can create their own "collections", to categorise theirs or other users' media. However users cannot put media into other user's collections. Each user's category is separate. There is no centralised theme or hierarchy for the media.
Trie
In computer science, a trie (, ), also known as a digital tree or prefix tree, is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key. Instead, each node's position within the trie determines its associated key, with the connections between nodes defined by individual characters rather than the entire key. Tries are particularly effective for tasks such as autocomplete, spell checking, and IP routing, offering advantages over hash tables due to their prefix-based organization and lack of hash collisions. Every child node shares a common prefix with its parent node, and the root node represents the empty string. While basic trie implementations can be memory-intensive, various optimization techniques such as compression and bitwise representations have been developed to improve their efficiency. A notable optimization is the radix tree, which provides more efficient prefix-based storage. While tries store character strings, they can be adapted to work with any ordered sequence of elements, such as permutations of digits or shapes. A notable variant is the bitwise trie, which uses individual bits from fixed-length binary data (such as integers or memory addresses) as keys. == History, etymology, and pronunciation == The idea of a trie for representing a set of strings was first abstractly described by Axel Thue in 1912. Tries were first described in a computer context by René de la Briandais in 1959. The idea was independently described in 1960 by Edward Fredkin, who coined the term trie, pronouncing it (as "tree"), after the middle syllable of retrieval. However, other authors pronounce it (as "try"), in an attempt to distinguish it verbally from "tree". == Overview == Tries are a form of string-indexed look-up data structure, which is used to store a dictionary list of words that can be searched on in a manner that allows for efficient generation of completion lists. A prefix trie is an ordered tree data structure used in the representation of a set of strings over a finite alphabet set, which allows efficient storage of words with common prefixes. Tries can be efficacious on string-searching algorithms such as predictive text, approximate string matching, and spell checking in comparison to binary search trees. A trie can be seen as a tree-shaped deterministic finite automaton. == Operations == Tries support various operations: insertion, deletion, and lookup of a string key. Tries are composed of nodes that contain links, which either point to other suffix child nodes or null. As for every tree, each node except the root is pointed to by only one other node, called its parent. Each node contains as many links as the number of characters in the applicable alphabet (although tries tend to have a substantial number of null links). In some cases, the alphabet used is simply that of the character encoding—resulting in, for example, a size of 128 in the case of ASCII. The null links within the children of a node emphasize the following characteristics: Characters and string keys are implicitly stored in the trie, and include a character sentinel value indicating string termination. Each node contains one possible link to a prefix of strong keys of the set. A basic structure type of nodes in the trie is as follows: Node {\displaystyle {\text{Node}}} may contain an optional Value {\displaystyle {\text{Value}}} , which is associated with the key that corresponds to the node. === Searching === Searching for a value in a trie is guided by the characters in the search string key, as each node in the trie contains a corresponding link to each possible character in the given string. Thus, following the string within the trie yields the associated value for the given string key. A null link during the search indicates the inexistence of the key. The following pseudocode implements the search procedure for a given string key in a rooted trie x. In the above pseudocode, x and key correspond to the pointer of the trie's root node and the string key, respectively. The search operation takes O ( m ) {\displaystyle O(m)} time, where m {\displaystyle m} is the size of the string parameter key. In a balanced binary search tree, on the other hand, it takes O ( m log n ) {\displaystyle O(m\log n)} time, in the worst case, since key needs to be compared with O ( log n ) {\displaystyle O(\log n)} other keys and each comparison takes O ( m ) {\displaystyle O(m)} time, in the worst case. The trie occupies less space, in comparison with a binary search tree, in the case of a large number of short strings, since nodes share common initial string subsequences and store the keys implicitly. === Insertion === Insertion into a trie is guided by using the character sets as indexes to the children array until the last character of the string key is reached. Each node in the trie corresponds to one call of the radix sorting routine, as the trie structure reflects the execution pattern of the top-down radix sort. If null links are encountered before reaching the last character of the string key, new nodes are created. The input value is assigned to the value of the last node traversed, which is the node that corresponds to the key. === Deletion === Deletion of a key–value pair from a trie involves finding the node corresponding to the key, setting its value to null, and recursively removing nodes that have no children. The procedure begins by examining key; an empty string indicates arrival at the node corresponding to the (original) key, in which case its value is set to null. If the node, then, has null value and no children, it is removed from the trie by returning null; otherwise, the node is kept by returning the node itself. == Replacing other data structures == === Replacement for hash tables === A trie can be used to replace a hash table, over which it has the following advantages: Searching for a node with an associated key of size m {\displaystyle m} has the complexity of O ( m ) {\displaystyle O(m)} , whereas an imperfect hash function may have numerous colliding keys, and the worst-case lookup speed of such a table would be O ( N ) {\displaystyle O(N)} , where N {\displaystyle N} denotes the total number of nodes within the table. Tries do not need a hash function for the operation, unlike a hash table; there are also no collisions of different keys in a trie. Within a trie, keys can be efficiently sorted lexicographically. However, tries are less efficient than a hash table when the data is directly accessed on a secondary storage device such as a hard disk drive that has higher random access time than the main memory. == Implementation strategies == Tries can be represented in several ways, corresponding to different trade-offs between memory use and speed of the operations. Using a vector of pointers for representing a trie consumes enormous space; however, memory space can be reduced at the expense of running time if a singly linked list is used for each node vector, as most entries of the vector contains nil {\displaystyle {\text{nil}}} . Techniques such as alphabet reduction may reduce the large space requirements by reinterpreting the original string as a longer string over a smaller alphabet. For example, a string of n bytes can alternatively be regarded as a string of 2n four-bit units. This can reduce memory usage by a factor of eight; but lookups need to visit twice as many nodes in the worst case. Another technique includes storing a vector of 256 ASCII pointers as a bitmap of 256 bits representing ASCII alphabet, which reduces the size of individual nodes dramatically. === Bitwise tries === Bitwise tries are used to address the enormous space requirement for the trie nodes in a naive simple pointer vector implementations. Each character in the string key set is represented via individual bits, which are used to traverse the trie over a string key. The implementations for these types of trie use vectorized CPU instructions to find the first set bit in a fixed-length key input (e.g. GCC's __builtin_clz() intrinsic function). Accordingly, the set bit is used to index the first item, or child node, in the 32- or 64-entry based bitwise tree. Search then proceeds by testing each subsequent bit in the key. This procedure is also cache-local and highly parallelizable due to register independency, and thus performant on out-of-order execution CPUs. === Compressed tries === Radix tree, also known as a compressed trie, is a space-optimized variant of a trie in which any node with only one child gets merged with its parent; elimination of branches of the nodes with a single child results in better metrics in both space and time. This works best when the trie remains static and set of keys stored are very sparse within their representation space. One more approach for static tries is to "pack" the trie by storing disjoint
AI Avatar Generators: Free vs Paid (2026)
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Internettolken
Internettolken (or InternetPreter) is a web-based machine translating tool. As the first Swedish online translating service, it was started in 2002 and included the English and Swedish languages. Today, there are 14 languages with more than 120 possible combinations. The service is free up to 150 words per day, and as a 2,000-word free testing account. It is available both on its website, and as a gadget on iGoogle. The interface is either English or Swedish. Being a dictionary-based tool, with its own translation software, it can sometimes offer a more accurate translation than Google Translate and others, although the grammar will be incorrect. == Languages currently available ==
Transfer function matrix
In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to multiple-input and multiple-output (MIMO) systems. The matrix relates the outputs of the system to its inputs. It is a particularly useful construction for linear time-invariant (LTI) systems because it can be expressed in terms of the s-plane. In some systems, especially ones consisting entirely of passive components, it can be ambiguous which variables are inputs and which are outputs. In electrical engineering, a common scheme is to gather all the voltage variables on one side and all the current variables on the other regardless of which are inputs or outputs. This results in all the elements of the transfer matrix being in units of impedance. The concept of impedance (and hence impedance matrices) has been borrowed into other energy domains by analogy, especially mechanics and acoustics. Many control systems span several different energy domains. This requires transfer matrices with elements in mixed units. This is needed both to describe transducers that make connections between domains and to describe the system as a whole. If the matrix is to properly model energy flows in the system, compatible variables must be chosen to allow this. == General == A MIMO system with m outputs and n inputs is represented by a m × n matrix. Each entry in the matrix is in the form of a transfer function relating an output to an input. For example, for a three-input, two-output system, one might write, [ y 1 y 2 ] = [ g 11 g 12 g 13 g 21 g 22 g 23 ] [ u 1 u 2 u 3 ] {\displaystyle {\begin{bmatrix}y_{1}\\y_{2}\end{bmatrix}}={\begin{bmatrix}g_{11}&g_{12}&g_{13}\\g_{21}&g_{22}&g_{23}\end{bmatrix}}{\begin{bmatrix}u_{1}\\u_{2}\\u_{3}\end{bmatrix}}} where the un are the inputs, the ym are the outputs, and the gmn are the transfer functions. This may be written more succinctly in matrix operator notation as, Y = G U {\displaystyle \mathbf {Y} =\mathbf {G} \mathbf {U} } where Y is a column vector of the outputs, G is a matrix of the transfer functions, and U is a column vector of the inputs. In many cases, the system under consideration is a linear time-invariant (LTI) system. In such cases, it is convenient to express the transfer matrix in terms of the Laplace transform (in the case of continuous time variables) or the z-transform (in the case of discrete time variables) of the variables. This may be indicated by writing, for instance, Y ( s ) = G ( s ) U ( s ) {\displaystyle \mathbf {Y} (s)=\mathbf {G} (s)\mathbf {U} (s)} which indicates that the variables and matrix are in terms of s, the complex frequency variable of the s-plane arising from Laplace transforms, rather than time. The examples in this article are all assumed to be in this form, although that is not explicitly indicated for brevity. For discrete time systems s is replaced by z from the z-transform, but this makes no difference to subsequent analysis. The matrix is particularly useful when it is a proper rational matrix, that is, all its elements are proper rational functions. In this case, the state-space representation can be applied. In systems engineering, the overall system transfer matrix G (s) is decomposed into two parts: H (s) representing the system being controlled, and C(s) representing the control system. C (s) takes as its inputs the inputs of G (s) and the outputs of H (s). The outputs of C (s) form the inputs for H (s). == Electrical systems == In electrical systems, it is often the case that the distinction between input and output variables is ambiguous. They can be either, depending on circumstance and point of view. In such cases, the concept of port (a place where energy is transferred from one system to another) can be more useful than input and output. It is customary to define two variables for each port (p): the voltage across it (Vp) and the current entering it (Ip). For instance, the transfer matrix of a two-port network can be defined as follows, [ V 1 V 2 ] = [ z 11 z 12 z 21 z 22 ] [ I 1 I 2 ] {\displaystyle {\begin{bmatrix}V_{1}\\V_{2}\end{bmatrix}}={\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\\\end{bmatrix}}{\begin{bmatrix}I_{1}\\I_{2}\end{bmatrix}}} where the zmn are called the impedance parameters, or z-parameters. They are so-called because they are in units of impedance and relate port currents to a port voltage. The z-parameters are not the only way that transfer matrices are defined for two-port networks. Six basic matrices relate voltages and currents, each with advantages for particular system network topologies. However, only two of these can be extended beyond two ports to an arbitrary number of ports. These two are the z-parameters and their inverse, the admittance parameters or y-parameters. To understand the relationship between port voltages and currents and inputs and outputs, consider the simple voltage divider circuit. If we only wish to consider the output voltage (V2) resulting from applying the input voltage (V1) then the transfer function can be expressed as, [ V 2 ] = [ R 2 R 1 + R 2 ] [ V 1 ] {\displaystyle {\begin{bmatrix}V_{2}\end{bmatrix}}={\begin{bmatrix}{\dfrac {R_{2}}{R_{1}+R_{2}}}\end{bmatrix}}{\begin{bmatrix}V_{1}\end{bmatrix}}} which can be considered the trivial case of a 1×1 transfer matrix. The expression correctly predicts the output voltage if there is no current leaving port 2, but is increasingly inaccurate as the load increases. If, however, we attempt to use the circuit in reverse, driving it with a voltage at port 2 and calculate the resulting voltage at port 1 the expression gives completely the wrong result even with no load on port 1. It predicts a greater voltage at port 1 than was applied at port 2, an impossibility with a purely resistive circuit like this one. To correctly predict the behaviour of the circuit, the currents entering or leaving the ports must also be taken into account, which is what the transfer matrix does. The impedance matrix for the voltage divider circuit is, [ V 1 V 2 ] = [ R 1 + R 2 R 2 R 2 R 2 ] [ I 1 I 2 ] {\displaystyle {\begin{bmatrix}V_{1}\\V_{2}\end{bmatrix}}={\begin{bmatrix}R_{1}+R_{2}&R_{2}\\R_{2}&R_{2}\end{bmatrix}}{\begin{bmatrix}I_{1}\\I_{2}\end{bmatrix}}} which fully describes its behaviour under all input and output conditions. At microwave frequencies, none of the transfer matrices based on port voltages and currents are convenient to use in practice. Voltage is difficult to measure directly, current next to impossible, and the open circuits and short circuits required by the measurement technique cannot be achieved with any accuracy. For waveguide implementations, circuit voltage and current are entirely meaningless. Transfer matrices using different sorts of variables are used instead. These are the powers transmitted into, and reflected from a port, which are readily measured in the transmission line technology used in distributed-element circuits in the microwave band. The most well-known and widely used of these sorts of parameters is the scattering parameters, or s-parameters. == Mechanical and other systems == The concept of impedance can be extended into the mechanical and other domains through a mechanical-electrical analogy, hence the impedance parameters and other forms of 2-port network parameters can also be extended to the mechanical domain. To do this, an effort variable and a flow variable are made analogues of voltage and current, respectively. For mechanical systems under translation these variables are force and velocity respectively. Expressing the behaviour of a mechanical component as a two-port or multi-port with a transfer matrix is a useful thing to do because, like electrical circuits, the component can often be operated in reverse and its behaviour is dependent on the loads at the inputs and outputs. For instance, a gear train is often characterised simply by its gear ratio, a SISO transfer function. However, the gearbox output shaft can be driven around to turn the input shaft, requiring a MIMO analysis. In this example, the effort and flow variables are torque T and angular velocity ω, respectively. The transfer matrix in terms of z-parameters will look like, [ T 1 T 2 ] = [ z 11 z 12 z 21 z 22 ] [ ω 1 ω 2 ] {\displaystyle {\begin{bmatrix}T_{1}\\T_{2}\end{bmatrix}}={\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\end{bmatrix}}{\begin{bmatrix}\omega _{1}\\\omega _{2}\end{bmatrix}}} However, the z-parameters are not necessarily the most convenient for characterising gear trains. A gear train is the analogue of an electrical transformer and the h-parameters (hybrid parameters) better describe transformers because they directly include the turns ratios (the analogue of gear ratios). The gearbox transfer matrix in h-parameter format is, [ T 1 ω 2 ] = [ h 11 h 12 h 21 h 22 ] [ ω 1 T 2 ] {\displaystyle {\begin{bmatrix}T_{1}\\\omega _{2}\end{bm
Two-way finite automaton
In computer science, in particular in automata theory, a two-way finite automaton is a finite automaton that is allowed to re-read its input. == Two-way deterministic finite automaton == A two-way deterministic finite automaton (2DFA) is an abstract machine, a generalized version of the deterministic finite automaton (DFA) which can revisit characters already processed. As in a DFA, there are a finite number of states with transitions between them based on the current character, but each transition is also labelled with a value indicating whether the machine will move its position in the input to the left, right, or stay at the same position. Equivalently, 2DFAs can be seen as read-only Turing machines with no work tape, only a read-only input tape. 2DFAs were introduced in a seminal 1959 paper by Rabin and Scott, who proved them to have equivalent power to one-way DFAs. That is, any formal language which can be recognized by a 2DFA can be recognized by a DFA which only examines and consumes each character in order. Since DFAs are obviously a special case of 2DFAs, this implies that both kinds of machines recognize precisely the class of regular languages. However, the equivalent DFA for a 2DFA may require exponentially many states, making 2DFAs a much more practical representation for algorithms for some common problems. 2DFAs are also equivalent to read-only Turing machines that use only a constant amount of space on their work tape, since any constant amount of information can be incorporated into the finite control state via a product construction (a state for each combination of work tape state and control state). == Formal description == Formally, a two-way deterministic finite automaton can be described by the following 8-tuple: M = ( Q , Σ , L , R , δ , s , t , r ) {\displaystyle M=(Q,\Sigma ,L,R,\delta ,s,t,r)} where Q {\displaystyle Q} is the finite, non-empty set of states Σ {\displaystyle \Sigma } is the finite, non-empty set of input symbols L {\displaystyle L} is the left endmarker R {\displaystyle R} is the right endmarker δ : Q × ( Σ ∪ { L , R } ) → Q × { l e f t , r i g h t } {\displaystyle \delta :Q\times (\Sigma \cup \{L,R\})\rightarrow Q\times \{\mathrm {left,right} \}} s {\displaystyle s} is the start state t {\displaystyle t} is the end state r {\displaystyle r} is the reject state In addition, the following two conditions must also be satisfied: For all q ∈ Q {\displaystyle q\in Q} δ ( q , L ) = ( q ′ , r i g h t ) {\displaystyle \delta (q,L)=(q^{\prime },\mathrm {right} )} for some q ′ ∈ Q {\displaystyle q^{\prime }\in Q} δ ( q , R ) = ( q ′ , l e f t ) {\displaystyle \delta (q,R)=(q^{\prime },\mathrm {left} )} for some q ′ ∈ Q {\displaystyle q^{\prime }\in Q} It says that there must be some transition possible when the pointer reaches either end of the input word. For all symbols σ ∈ Σ ∪ { L } {\displaystyle \sigma \in \Sigma \cup \{L\}} δ ( t , σ ) = ( t , R ) {\displaystyle \delta (t,\sigma )=(t,R)} δ ( r , σ ) = ( r , R ) {\displaystyle \delta (r,\sigma )=(r,R)} δ ( t , R ) = ( t , L ) {\displaystyle \delta (t,R)=(t,L)} δ ( r , R ) = ( r , L ) {\displaystyle \delta (r,R)=(r,L)} It says that once the automaton reaches the accept or reject state, it stays in there forever and the pointer goes to the right most symbol and cycles there infinitely. == Two-way nondeterministic finite automaton == A two-way nondeterministic finite automaton (2NFA) may have multiple transitions defined in the same configuration. Its transition function is δ : Q × ( Σ ∪ { L , R } ) → 2 Q × { l e f t , r i g h t } {\displaystyle \delta :Q\times (\Sigma \cup \{L,R\})\rightarrow 2^{Q\times \{\mathrm {left,right} \}}} . Like a standard one-way NFA, a 2NFA accepts a string if at least one of the possible computations is accepting. Like the 2DFAs, the 2NFAs also accept only regular languages. == Two-way alternating finite automaton == A two-way alternating finite automaton (2AFA) is a two-way extension of an alternating finite automaton (AFA). Its state set is Q = Q ∃ ∪ Q ∀ {\displaystyle Q=Q_{\exists }\cup Q_{\forall }} where Q ∃ ∩ Q ∀ = ∅ {\displaystyle Q_{\exists }\cap Q_{\forall }=\emptyset } . States in Q ∃ {\displaystyle Q_{\exists }} and Q ∀ {\displaystyle Q_{\forall }} are called existential resp. universal. In an existential state a 2AFA nondeterministically chooses the next state like an NFA, and accepts if at least one of the resulting computations accepts. In a universal state 2AFA moves to all next states, and accepts if all the resulting computations accept. == State complexity tradeoffs == Two-way and one-way finite automata, deterministic and nondeterministic and alternating, accept the same class of regular languages. However, transforming an automaton of one type to an equivalent automaton of another type incurs a blow-up in the number of states. Christos Kapoutsis determined that transforming an n {\displaystyle n} -state 2DFA to an equivalent DFA requires n ( n n − ( n − 1 ) n ) {\displaystyle n(n^{n}-(n-1)^{n})} states in the worst case. If an n {\displaystyle n} -state 2DFA or a 2NFA is transformed to an NFA, the worst-case number of states required is ( 2 n n + 1 ) = O ( 4 n n ) {\displaystyle {\binom {2n}{n+1}}=O\left({\frac {4^{n}}{\sqrt {n}}}\right)} . Ladner, Lipton and Stockmeyer. proved that an n {\displaystyle n} -state 2AFA can be converted to a DFA with 2 n 2 n {\displaystyle 2^{n2^{n}}} states. The 2AFA to NFA conversion requires 2 Θ ( n log n ) {\displaystyle 2^{\Theta (n\log n)}} states in the worst case, see Geffert and Okhotin. It is an open problem whether every 2NFA can be converted to a 2DFA with only a polynomial increase in the number of states. The problem was raised by Sakoda and Sipser, who compared it to the P vs. NP problem in the computational complexity theory. Berman and Lingas discovered a formal relation between this problem and the L vs. NL open problem, see Kapoutsis for a precise relation. == Sweeping automata == Sweeping automata are 2DFAs of a special kind that process the input string by making alternating left-to-right and right-to-left sweeps, turning only at the endmarkers. Sipser constructed a sequence of languages, each accepted by an n-state NFA, yet which is not accepted by any sweeping automata with fewer than 2 n {\displaystyle 2^{n}} states. == Two-way quantum finite automaton == The concept of 2DFAs was in 1997 generalized to quantum computing by John Watrous's "On the Power of 2-Way Quantum Finite State Automata", in which he demonstrates that these machines can recognize nonregular languages and so are more powerful than DFAs. == Two-way pushdown automaton == A pushdown automaton that is allowed to move either way on its input tape is called two-way pushdown automaton (2PDA); it has been studied by Hartmanis, Lewis, and Stearns (1965). Aho, Hopcroft, Ullman (1968) and Cook (1971) characterized the class of languages recognizable by deterministic (2DPDA) and non-deterministic (2NPDA) two-way pushdown automata; Gray, Harrison, and Ibarra (1967) investigated the closure properties of these languages.