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# Topic: Machine that always halts

 Machine that always halts In computability theory, a machine that always halts — also called a decider (Sipser, 1996) — is any abstract machine or model of computation that, contrary to the most general Turing machines, is guaranteed to halt for any particular description and input (see halting problem). Since any description makes the machine halt at some point, it is not hard to see that the set of machine descriptions D that lead to total functions is effectively enumerable. Despite the above theorem, it is possible to construct a machine that always halts and yet computes the majority of functions of interest (the so-called primitive recursive functions), an exception being the Ackermann function. www.brainyencyclopedia.com /encyclopedia/m/ma/machine_that_always_halts.html   (593 words)

 PlanetMath: random Turing machine A random Turing machine is defined the same way as a non-deterministic Turing machine, but with different rules governing when it accepts or rejects. The definition of a positive one-sided error machine is stricter than the definition of a non-deterministic machine, since a non-deterministic machine rejects when there is no certificate and accepts when there is at least one, while a positive one-sided error machine requires that half of all possible guess inputs be certificates. It is a testament to the robustness of the definition of the Turing machine (and the Church-Turing thesis) that each of these definitions computes the same functions as a standard Turing machine. planetmath.org /encyclopedia/RandomTuringMachine.html   (426 words)

 PlanetMath: Turing machine The machine has a finite set of states, and with every move the machine can change states, change the symbol written on the current cell, and move one space left or right. When viewed as a function, the tape begins with a set of symbols which are the input, and when the machine halts, whatever is on the tape is the output. If the machine halts whenever there is any series of legal moves which leads to a situation without moves, the machine is called non-deterministic. planetmath.org /encyclopedia/TuringMachine2.html   (747 words)

 Machine gun Summary Manual machine guns are manually-powered, e.g., a crank must be turned to power reloading and firing, as opposed to simply holding down a trigger, as with automatic machine guns. The two major operation systems of modern automatic machine guns are gas operation (which uses the gas generated from the burning powder to cycle the action), or recoil operation (which uses the recoil generated from the ejecting bullet to cycle the action). Medium and heavy machine guns are either mounted on a tripod or on a vehicle; when carried on foot, the machine gun and associated equipment (tripod, ammunition, spare barrels) require additional crew members. www.bookrags.com /Machine_gun   (5080 words)

 Machine that always halts - Wikipedia, the free encyclopedia Because it always halts, the machine is able to decide whether a given string is a member of a formal language. It is important to note, however, that, due to the Halting Problem, determining whether an arbitrary Turing machine is total is an undecidable decision problem. A machine can be forced to halt for every input by restricting its flow control capabilities so that no program will ever cause the machine to enter an infinite loop. en.wikipedia.org /wiki/Machines_that_always_halt   (898 words)

 Chapter 14 Pushdown Automata This machine is fed input just as a finite automaton is. Some texts, ours included, speak of the input coming in on a read-only tape with a tape head that moves left to right until it comes to the end of the input. When the tape head reads a blank the machine halts, or begins the process of halting (which will be explained later.) The tape head may not reverse directions, nor may it be used to write to the tape. This machine is nondeterministic because from state 1, when there is an a in the input, the machine can either stay in state 1 and not pop the stack or it can go to state 2 and not pop the stack. www.mathsci.appstate.edu /~dap/classes/2490/chap14.html   (1220 words)

 COT 6315 - Intro Machines will always include a means of reading input from an input tape, one symbol at a time, and will contain some amount of finite state control. Machines with output capabilities may also be considered as generators of languages (they output exactly the strings of the language delimited in some fashion) or computers (given an input string, the machine may produce an output string and halt, or if the function is not defined for that input string, it may not halt). For the most part, we will consider machines as language recognizers, that is, given an input string, the machine will execute for some number of steps and halt in an accepting state or not (it may not halt, or it may halt in a non-accepting state). www-pub.cise.ufl.edu /~nemo/cot6315/intro.html   (2426 words)

 CMSC 451 Lecture 26, Turing Machine Model The "Halting Problem" is a very strong, provably correct, statement that no one will ever be able to write a computer program or design a Turing machine that can determine if an arbitrary program will halt (stop, exit) for a given input. This is NOT saying that some programs or some Turing machines can not be analyzed to determine that they, for example, always halt. To prove the Halting Problem is unsolvable we will construct one program and one input for which there is no computer program or Turing machine that can correctly determine if it halts or does not halt. www.csee.umbc.edu /~squire/cs451_l26.html   (678 words)

 Chapter 23 Turing Machine Languages Note that an invalid Turing machine may not have a state 1 (the start state) or may have edges leaving state 2 (the HALT state.) Here is an example of a string in the language ALAN along with the Turing machine that the string encodes. The membership question is always something like, "Given a machine (or a grammar or expression), does that machine (or grammar or expression) accept (generate) string w?" We found that it is always possible to decide membership for the regular and context-free languages. HALT contains pairs of strings separated by # as a marker; the first string is an encoded Turing machine T, and the second string is an input string for T. Only those pairs where the machine T accepts the string w are in HALT. www.mathsci.appstate.edu /~dap/classes/2490/chap23.html   (2434 words)

 14 The algorithm ends when the machine halts either because all of the input characters have been replaced and a palindrome recognized or the candidate has been rejected. In the final transition, the machine is looking for a matching 1 on the tape, but when it finds an end marker, it recognizes that it is validating a 1-character substring and halts in an accepting state. A Turing machine for multiplying two unary positive integers can be constructed  with an input alphabet that includes the binary digits 0 and 1, an end marker, #, and an operation indicator, *, that separates the multiplicand and multiplier. www.academic.marist.edu /~jzbv/algorithms/TuringMachine.htm   (5971 words)

 [No title] The machine also has an input and output tape (all the books call this a tape but in reality it is a toilet roll). The instance of the problem, encoded into a finite sequence of 0's and 1's, appears on the tape and the read/write head is positioned on a symbol of the input. Since we are willing to accept machines whose computations may not terminate, then those machines are not algorithms (they are called partial functions), but we will see that our arguments apply even to those more general machines. www.massey.ac.nz /~mjjohnso/notes/59102/notes/l22.html   (1275 words)

 Karel J Robot as a Turing Machine One of the states is a final state and if the machine ever enters this final state it halts. Depending on what it finds there and its current state, it optionally writes something (a blank or a 1) at that position of the head, moves the head one cell left or right or not at all, and changes to some state, which could be the current state or another. With this infrastructure the states of the machine are a set of methods that might be called state1, state2, etc. The body of the method defines how the machine behaves in that state for any value on the tape. csis.pace.edu /~bergin/KarelJava2ed/turingmachine.html   (748 words)

 The xTuringMachine Applet Given this information, the Turing machine takes three actions: It writes a symbol to the cell (possibly the same one that is already there); it moves one cell to the left or one cell to the right; and it sets its internal state (possibly to the same state that it is currently in). The blue rectangle between the machine and the rule maker is a "palette" that is used in making and editing rules, changing the contents of the tape, and changing the current state of the machine. If the machine moves outside the applet as it is computing, the machine along with its tape will jerk back about 1/4 of the width of the applet. math.hws.edu /TMCM/java/xTuringMachine/index.html   (1668 words)

 Definitions of Computable Programming a Turing machine is tedious and thus much work at higher levels of abstraction make the reasonable assumption that any completely defined algorithm or computer program could be implemented by a Turing machine. The "Halting Problem" is a very strong, provably correct, statement that no one will ever be able to write a computer program or design a Turing machine that can determine if a arbitrary program will halt (stop, exit) for a given input. To prove the Halting Problem is unsolvable we will construct one program and one input for which there is no computer program or Turing machine. www.csee.umbc.edu /help/theory/computable.shtml   (2082 words)

 Good Math has moved to ScienceBlogs: Level 0, recursive and ... Machines for level 0 are turing machines (or any equivalent). A recursively enumerable function is a possibly partial function where a machine that computes it will never halt for some values; until the machine halts, you can never be sure that it won't; so you can't ever be certain that the value of the function for a given input is undefined. If we have a universal computing machine, we can treat it as a two parameter function: the first parameter is a program; and the second parameter is the input to the program. goodmath.blogspot.com /2006/05/level-0-recursive-and-recursively.html   (1001 words)

 xTuringMachine Lab The purpose of this machine is to move to the right along its tape, until it finds two x's in a row; it then halts on the leftmost of those two x's. The purpose of the machine is to multiply the length of the string by 3. The purpose of the machine is to divide the length of the string by 3. math.hws.edu /TMCM/java/labs/xTuringMachineLab.html   (4113 words)

 Turing Machine | World of Mathematics Turing machines were invented by Alan Turing, the father of computer science, in 1936. The machine begins when it is fed a tape with zeros and ones already written on it (or it could be blank). It is equivalent to the statement that there is no Turing machine that can determine whether any two given Turing machines always produce the same output when given the same input. www.bookrags.com /research/turing-machine-wom   (784 words)

 Definitions of Computable Programming a Turing machine is tedious and thus much work at higher levels of abstraction make the reasonable assumption that any completely defined algorithm or computer program could be implemented by a Turing machine. The "Halting Problem" is a very strong, provably correct, statement that no one will ever be able to write a computer program or design a Turing machine that can determine if a arbitrary program will halt (stop, exit) for a given input. To prove the Halting Problem is unsolvable we will construct one program and one input for which there is no computer program or Turing machine. www.cs.umbc.edu /~squire/reference/computable.shtml   (2142 words)

 Peter Suber, "Turing Machines I" If a Turing machine halts but not on the leftmost digit in a string of "1's", then its halt is "non-canonical". If a command instructs the machine to write a "1" to a cell that already contains a "1", or to write a "0" to a cell that is already blank, it does not matter whether we imagine that the machine makes the redundant operation or skips the command. If a Turing machine starts with a non-blank tape, we may consider that the marks already on the tape are the "input" to the program that will then execute. www.earlham.edu /~peters/courses/logsys/turing.htm   (2638 words)

 SQLite Virtual Machine Opcodes   (Site not responding. Last check: 2007-10-22) P2 is always the jump destination in any operation that might cause a jump. Execution continues until (1) a Halt instruction is seen, or (2) the program counter becomes one greater than the address of last instruction, or (3) there is an execution error. When the virtual machine halts, all memory that it allocated is released and all database cursors it may have had open are closed. www.sqlite.org /opcode.html   (8849 words)

 A Random Walk in Arithmetic To show that the so-called halting problem can never be solved, we set the program running on a Turing machine, which is a mathematical idealisation of a digital computer with no time limit. Although the halting problem is unsolvable, we can look at the probability of whether a randomly chosen program will halt. If the Nth bit of the halting probability V is a 1, then this equation for that value of the parameter N has an infinite number of solutions. www.fortunecity.com /emachines/e11/86/randwalk.html   (2221 words)

 The Googol Room The evaluator halts if the machine it is evaluating does not halt. Assume a new machine, that when fed the index of a Turing machine returns a True or False, telling whether that Turing machine halts or not. In order to evaluate this machine (assume it is fully Resolved) another machine must evaluate an infinite series of truth-states sequentially. www.googolroom.org /GrailMachineOne.htm   (4655 words)

 Juergen Schmidhuber's home page - Universal Artificial Intelligence - New AI - Recurrent neural networks - Goedel ... This optimism is driving his research on mathematically sound, general purpose universal learning machines and Artificial Intelligence, in particular, the New AI which is relevant not only for robotics but also for physics and music. The Gödel machine can be implemented on a traditional computer and solves any given computational problem in an optimal fashion inspired by Kurt Gödel's celebrated self-referential formulas (1931). Chaitin's Omega is the halting probability of a Turing machine with random input (Omega is known as the "number of wisdom" because it compactly encodes all mathematical truth). www.idsia.ch /~juergen   (1594 words)

 Large Numbers -- Notes at MROB Such a machine is identical to a machine in which states 1 and N are switched, except that it takes one extra step. If the HALT writes a 0, the same machine with a HALT that writes a 1 will be at least as good or better; thus the 0-writing version can be ignored. Since the one-to-one mapping always leads to a contradiction, the only conclusion is that there cannot in fact be a one-to-one mapping: there is no way to assign a one-to-one correspondance between the integers and the w-polynomials — thus their cardinalities are different. home.earthlink.net /~mrob/pub/math/ln-notes1.html   (8488 words)

 Computing Theory Essay The power of the rotor machine is depends on the use of multiple cylinders, in which the output pins of one cylinder are connected to the input pins of the next. Enigma Rotor machine, one of a very important class of cipher machines, heavily used during 2nd world war, comprised a series of rotor wheels with internal cross-connections, providing a substitution using a continuously changing alphabet. Turing Machine, TM More powerful machines called Turing Machine were invented by Alan Turing in 1936 which are the machines which have multiple stacks and infinite memory. www.geocities.com /indikae123   (4878 words)

 TrueVoteMD - Campaign for Verifiable Voting Wertheimer testified on behalf of voters convinced that the state's new touch-screen voting machines can't be trusted to correctly tally results in the Nov. 2 election. At issue are 16,000 voting machines that the state purchased last year for use in most precincts. California will require by 2006 that Diebold's machines provide voters with paper showing how they voted, and provide officials with an audit trail in case a recount is needed. www.truevotemd.org /facts_2004_08_26_bsun.asp   (984 words)

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