Showing papers on "Turing machine published in 2002"
TL;DR: A new computational model for real-time computing on time-varying input that provides an alternative to paradigms based on Turing machines or attractor neural networks, based on principles of high-dimensional dynamical systems in combination with statistical learning theory and can be implemented on generic evolved or found recurrent circuitry.
Abstract: A key challenge for neural modeling is to explain how a continuous stream of multimodal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrate-and-fire neurons in real time. We propose a new computational model for real-time computing on time-varying input that provides an alternative to paradigms based on Turing machines or attractor neural networks. It does not require a task-dependent construction of neural circuits. Instead, it is based on principles of high-dimensional dynamical systems in combination with statistical learning theory and can be implemented on generic evolved or found recurrent circuitry. It is shown that the inherent transient dynamics of the high-dimensional dynamical system formed by a sufficiently large and heterogeneous neural circuit may serve as universal analog fading memory. Readout neurons can learn to extract in real time from the current state of such recurrent neural circuit information about current and past inputs that may be needed for diverse tasks. Stable internal states are not required for giving a stable output, since transient internal states can be transformed by readout neurons into stable target outputs due to the high dimensionality of the dynamical system. Our approach is based on a rigorous computational model, the liquid state machine, that, unlike Turing machines, does not require sequential transitions between well-defined discrete internal states. It is supported, as the Turing machine is, by rigorous mathematical results that predict universal computational power under idealized conditions, but for the biologically more realistic scenario of real-time processing of time-varying inputs. Our approach provides new perspectives for the interpretation of neural coding, the design of experiments and data analysis in neurophysiology, and the solution of problems in robotics and neurotechnology.
4,229 citations
TL;DR: This work considers a natural model analogous to Turing machines with a read-only input tape and such popular propositional proof systems as resolution, polynomial calculus, and Frege systems, and proposes two different space measures, corresponding to the maximal number of bits, and clauses/monomials that need to be kept in the memory simultaneously.
Abstract: We study space complexity in the framework of propositional proofs. We consider a natural model analogous to Turing machines with a read-only input tape and such popular propositional proof systems as resolution, polynomial calculus, and Frege systems. We propose two different space measures, corresponding to the maximal number of bits, and clauses/monomials that need to be kept in the memory simultaneously. We prove a number of lower and upper bounds in these models, as well as some structural results concerning the clause space for resolution and Frege systems.
151 citations
15 Aug 2002
TL;DR: In this article, a tissue P system is proposed, which processes symbols in a multiset rewriting sense, in a net of cells similar to a neural net, each cell has a finite state memory, processes multisets of symbol-impulses, and can send impulses ("excitations") to the neighboring cells.
Abstract: Starting from the way the inter-cellular communication takes place by means of protein channels and also from the standard knowledge about neuron functioning, we propose a computing model called a tissue P system, which processes symbols in a multiset rewriting sense, in a net of cells similar to a neural net. Each cell has a finite state memory, processes multisets of symbol-impulses, and can send impulses ("excitations") to the neighboring cells. Such cell nets are shown to be rather powerful: they can simulate a Turing machine even when using a small number of cells, each of them having a small number of states. Moreover, in the case when each cell works in the maximal manner and it can excite all the cells to which it can send impulses, then one can easily solve the Hamiltonian Path Problem in linear time. A new characterization of the Parikh images of ET0L languages are also obtained in this framework.
133 citations
TL;DR: ILAL has a polynomially costing normalization, and it is expressive enough to encode, and simulate, all PolyTime Turing machines, and the bound on the normalization cost is proved by introducing the proof-nets for ILAL.
Abstract: This article is a structured introduction to Intuitionistic Light Affine Logic (ILAL). ILAL has a polynomially costing normalization, and it is expressive enough to encode, and simulate, all PolyTime Turing machines. The bound on the normalization cost is proved by introducing the proof-nets for ILAL. The bound follows from a suitable normalization strategy that exploits structural properties of the proof-nets. This allows us to have a good understanding of the meaning of the § modality, which is a peculiarity of light logics. The expressive power of ILAL is demonstrated in full detail. Such a proof gives a hint of the nontrivial task of programming with resource limitations, using ILAL derivations as programs.
132 citations
1 Jan 2002
TL;DR: A computing model called a tissue P system is proposed, which processes symbols in a multiset rewriting sense, in a net of cells similar to a neural net, which can simulate a Turing machine even when using a small number of cells.
Abstract: Starting from the way the inter-cellular communication takes place by means of protein channels and also from the standard knowledge about neuron functioning, we propose a computing model called a tissue P system, which processes symbols in a multiset rewriting sense, in a net of cells similar to a neural net. Each cell has a finite state memory, processes multisets of symbol-impulses, and can send impulses (?excitations?) to the neighboring cells. Such cell nets are shown to be rather powerful: they can simulate a Turing machine even when using a small number of cells, each of them having a small number of states. Moreover, in the case when each cell works in the maximal manner and it can excite all the cells to which it can send impulses, then one can easily solve the Hamiltonian Path Problem in linear time. A new characterization of the Parikh images of ET0L languages are also obtained in this framework.
78 citations
1 Jan 2002
TL;DR: A model for the guided homologous recombinations that take place during gene rearrangement is developed and it is proved that such a model has the computational power of a Turing machine, the accepted formal model of computation.
Abstract: How do cells and nature “compute”? They read and “rewrite” DNA all the time, by processes that modify sequences at the DNA or RNA level. In 1994, Adleman’s elegant solution to a seven-city Directed Hamiltonian Path problem using DNA [1] launched the new field of DNA computing, which in a few years has grown to international scope. However, unknown to this field, ciliated protozoans of genus Oxytricha and Stylonychia had solved a potentially harder problem using DNA several million years earlier. The solution to this “problem”, which occurs during the process of gene unscrambling, represents one of nature’s ingenious solutions to the problem of the creation of genes. Here we develop a model for the guided homologous recombinations that take place during gene rearrangement and prove that such a model has the computational power of a Turing machine, the accepted formal model of computation. This indicates that, in principle, these unicellular organisms may have the capacity to perform at least any computation carried out by an electronic computer.
76 citations
TL;DR: A construction to calculate any boolean circuit with the trajectory of a single ant is given, which proves the P-hardness of the system and implies the universality of the ant and the undecidability of some problems associated to it.
67 citations
TL;DR: It is shown that the class of PTMs is isomorphic to a very general class of effective transition systems, and the extensions to the Turing-machine model embodied in PTMs are sufficient to make Turing machines expressively equivalent to transition systems.
54 citations
Journal Article•
TL;DR: In this article, it was shown that for any rational-valued function that goes nonascendingly to zero, any rec-random sequence is i.o.~truth-table-autoreducible such that the set of guessed bits has positive constant density.
Abstract: A binary sequence $A=A(0)A(1)\ldots$ is called infinitely often (i.o.)~Turing-au\-to\-re\-duc\-ible if $A$~is reducible to itself via an oracle Turing machine that never queries its oracle at the current input, outputs either $A(x)$ or a don't-know symbol on any given input~$x$, and outputs $A(x)$ for infinitely many~$x$. If in addition the oracle Turing machine terminates on all inputs and oracles, $A$~is called i.o.~truth-table-autoreducible. We obtain the somewhat counterintuitive result that every Martin-L\"of random sequence, in fact even every rec-random or p-random sequence, is i.o.~truth-table-autoreducible. Furthermore, we investigate the question of how dense the set of guessed bits can be when i.o.~autoreducing a random sequence. We show that rec-random sequences are never i.o.~truth-table-autoreducible such that the set of guessed bits has positive constant density in the limit and that a similar assertion holds for Martin-L\"of random sequences and i.o.~Turing autoreducibility. On the other hand, we show that for any rational-valued computable function~$r$ that goes nonascendingly to zero, any rec-random sequence is i.o.~truth-table-autoreducible such that on any prefix of length~$m$ at least a fraction of~$r(m)$ of the $m$~bits in the prefix are guessed. We include a self-contained account of the hat problem, a puzzle that has received some attention outside of theoretical computer science. The hat problem asks for guessing bits of a finite sequence, thus illustrating the notion of i.o.~autoreducibility in a finite setting. The solution to the hat problem is then used as a module in the proofs of the positive results on i.o.~autoreducibility.
50 citations
TL;DR: A domain-theoretic approach to recursive analysis is used to develop the basis of an effective and realistic framework for solid modelling equipped with a well defined and realistic notion of computability which reflects the observable properties of real solids.
42 citations
2 Jun 2002
TL;DR: The two studies presented here were designed to determine whether AutoTutor could pass a variation of the Turing test, the Bystander Turing Test.
Abstract: Since the development of the first digital computer in the 1940s, the notion of computer intelligence has received considerable attention from computer scientists, philosophers, and psychologists. The question of whether it is possible to create a computer program that possesses human intelligence has spurred much debate. Turing (1950) argued that computers are not capable of thinking and provided several theological, psychological, and sociological arguments in support of his position. To determine a computer program’s intelligence, Turing proposed several benchmark methods. One such method requires humans to decide whether they are interacting with an actual computer program or another human via computer mediation. According to Turing, a computer could be described as intelligent if it could deceive a human into believing that it was human. The two studies presented here were designed to determine whether AutoTutor could pass a variation of the Turing test, the Bystander Turing Test. The subsequent sections of this paper address the following: (1) the AutoTutor system, (2) the Bystander Turing Test, (3) the two empirical studies, and (4) the conclusions of the studies.
TL;DR: This paper presents the embedding of a universal reversible Turing machine (RTM) in a two-dimensional self-timed cellular automaton (STCA), a special type of asynchronous cellular automata, of which each cell uses four bits to store its state, and a transition on a cell accesses only these four bits and one bit of each of the four neighboring cells.
Abstract: Reversible computation has attracted much attention over the years, not only for its promise for computers with radically reduced power consumption, but also for its importance for Quantum Computing. Though studied extensively in a great variety of synchronous computation models, it is virtually unexplored in an asynchronous framework. Particularly suitable asynchronous models for the study of reversibility are asynchronous cellular automata. Simple yet powerful, they update their cells at random times that are independent of each other. In this paper, we present the embedding of a universal reversible Turing machine (RTM) in a two-dimensional self-timed cellular automaton (STCA), a special type of asynchronous cellular automaton, of which each cell uses four bits to store its state, and a transition on a cell accesses only these four bits and one bit of each of the four neighboring cells. The embedding of a universal RTM on an STCA requires merely four rotation-symmetric transition rules, which are bit-conserving and locally reversible. We show that the model is globally reversible.
TL;DR: It is shown that the difficulties involved in distinguishing implementation from function make multiple realizability claims untestable and uninformative, and it is concluded that the role of Turing machines in philosophy of mind needs to be reconsidered.
Abstract: The properties of Turing's famous ‘universal machine’ has long sustained functionalist intuitions about the nature of cognition. This paper shows that there is a logical problem with standard functionalist arguments for multiple realizability. These arguments rely essentially on Turing's powerful insights regarding computation. In addressing a possible reply to this criticism, it is further argued that functionalism is not a useful approach for understanding what it is to have a mind. In particular, it is shown that the difficulties involved in distinguishing implementation from function make multiple realizability claims untestable and uninformative. As a result, it is concluded that the role of Turing machines in philosophy of mind needs to be reconsidered.
1 Jan 2002
TL;DR: The history of formalizing the notion of algorithm and of computation dates back to G.W. Leibniz (1646-1716) when it focused on trying to model the computations performed by humans, for example bank clerks as mentioned in this paper.
Abstract: The history of formalizing the notion of algorithm (and of computation) dates back to G.W. Leibniz (1646–1716) when it focused on trying to model the computations performed by humans, for example bank clerks. These efforts culminated in the first part of the 20th century with the formalization in the form of machines, in the work of Turing [238]. These formalizations were very successful, because they led to the construction of the first electronic computers in the 1940’s. These efforts already were using some ideas from biology, for example, the functioning of neurons in neural networks (Kleene [106], McCulloch and Pitts [165]).
TL;DR: The author explains how giving computers more ``initiative'' can allow them to do more than compute and says why he believes and believes that Turing believed that they will have to go beyond computation before they can become genuinely intelligent.
Abstract: According to the conventional wisdom, Turing (1950) said that computing machines can be intelligent. I don't believe it. I think that what Turing really said was that computing machines –- computers limited to computing –- can only fake intelligence. If we want computers to become genuinely intelligent, we will have to give them enough ``initiative'' (Turing, 1948, p. 21) to do more than compute. In this paper, I want to try to develop this idea. I want to explain how giving computers more ``initiative'' can allow them to do more than compute. And I want to say why I believe (and believe that Turing believed) that they will have to go beyond computation before they can become genuinely intelligent.
TL;DR: In a complexity-theoretic analysis, it is shown that the (infinite) computations of S(n)-space bounded relativistic Turing machines are equivalent to (finite) Computations of Turing machines that use a S( n)- bounded advice f, which bounds the power of polynomial-space bounded relativity Turing machines by TM/poly.
Abstract: Recent research in theoretical physics on 'Malament-Hogarth space-times' indicates that so-called relativistic computers can be conceived that can carry out certain classically undecidable queries in finite time. We observe that the relativistic Turing machines which model these computations recognize precisely the ?2-sets of the Arithmetical Hierarchy. In a complexity-theoretic analysis, we show that the (infinite) computations of S(n)-space bounded relativistic Turing machines are equivalent to (finite) computations of Turing machines that use a S(n)- bounded advice f, where f itself is computable by a S(n)-space bounded relativistic Turing machine. This bounds the power of polynomial-space bounded relativistic Turing machines by TM/poly. We also show that S(n)-space bounded relativistic Turing machines can be limited to one or two relativistic phases of computing.
Journal Article•
TL;DR: Using 2-tag systems, a new kind of computational device like Turing machine is considered, so-called circular Post machines with a circular tape and moving in one direction only, introduced recently by the second and the third authors.
Abstract: We consider a new kind of computational device like Turing machine, so-called circular Post machines with a circular tape and moving in one direction only, introduced recently by the second and the third authors Using 2-tag systems we construct new nine small universal machines of this kind
3 Jun 2002
TL;DR: It is shown that in the absence of unique identifiers even very powerful extensions of the tree-walking paradigm are not relationally complete, and that various restrictions allow to capture LOGSPACE, PTIME, PSPACE, and EXPTIME.
Abstract: XSLT is the prime example of an XML query language based on tree-walking. Indeed, stripped down, XSLT is just a tree-walking tree-transducer equipped with registers and look-ahead. Motivated by this connection, we want to pinpoint the computational power of devices based on tree-walking. We show that in the absence of unique identifiers even very powerful extensions of the tree-walking paradigm are not relationally complete. That is, these extensions do not capture all of first-order logic. In contrast, when unique identifiers are available, we show that various restrictions allow to capture LOGSPACE, PTIME, PSPACE, and EXPTIME. These complexity classes are defined w.r.t. a Turing machine model working directly on (attributed) trees. When no attributes are present, relational storage does not add power; whether look-ahead adds power is related to the open question whether tree-walking captures the regular tree languages.
Journal Article•
TL;DR: This work describes a scenario in which an AL system is engaged in a potentially unbounded, unpredictable interaction with an environment, to which it can react by learning and adjusting its behaviour.
Abstract: The information processing capabilities of artificial living (AL) systems are far more powerful than commonly believed. Modelling single organisms by means of so-called cognitive transducers, we estimate the computational power of AL systems by viewing them as conglomerates of organisms. We describe a scenario in which an AL system is engaged in a potentially unbounded, unpredictable interaction with an environment, to which it can react by learning and adjusting its behaviour. By means of lineages of cognitive transducers we also model the evolution of AL systems. Among the examples are "communities of agents", i.e., communities of mobile, interactive cognitive transducers. Most AL systems show the emergence of a computational power that is not present at the level of the individual organisms. Indeed, in all but trivial cases the resulting systems possess a super-Turing computing power. This means that the systems cannot be simulated by traditional computational models like Turing machines and may in principle solve non-computable tasks. The results derive from recent results from the theory of interactive evolutionary computing systems in terms of AL systems.
TL;DR: A new definition of resource bounded measure based on compressibility of infinite binary strings is given and it is proved that the new definition is equivalent to the one commonly used and the proofs leading to the equivalence result are shown.
Abstract: We give a new definition of resource bounded measure based on compressibility of infinite binary strings. We prove that the new definition is equivalent to the one commonly used. This new characterization offers us a different way to look at resource bounded measure, shedding more light on the meaning of measure zero results and providing one more tool to prove such results. The main contribution of the paper is the new definition and the proofs leading to the equivalence result. We then show how this new characterization can be used to prove that the class of linear autoreducible sets has p- measure 0. We also prove that the class of sets that are truth-table reducible to a p-selective set has p-measure 0 and that the class of sets that Turing reduce to a subpolynomial dense set has p-measure 0. This strengthens various results.
TL;DR: It is proved that the Julia set of a complex function f(z) = z2 + c for ∥c∥ < 1/4 can be computed locally in time O(k2M(k)) (where M(k) is a time bound for multiplication of k-bit integers).
TL;DR: The first nontrivial DCE (2-computably enumerable) Turing approximation to the class of computable enumerable degrees is obtained in this paper, which depends on the following extension of the splitting theorem for the DCE degrees.
Abstract: The first nontrivial DCE (2-computably enumerable) Turing approximation to the class of computably enumerable degrees is obtained. This depends on the following extension of the splitting theorem for the DCE degrees. For any DCE degree and any computably enumerable degree , if , then there are DCE degrees such that and . The construction is unusual in that it is incompatible with upper cone avoidance.
12 May 2002
TL;DR: It is demonstrated, that EC is not restricted to algorithmic methods, and is more expressive than Turing machines, and the general case, solutions found by evolutionary algorithms are satisfactory, given current resources and constraints, but not necessarily optimal.
Abstract: Evolutionary computation (EC) has traditionally been used for the solution of hard optimization problems. In the general case, solutions found by evolutionary algorithms are satisficing, given current resources and constraints, but not necessarily optimal. Under some conditions, evolutionary algorithms are guaranteed (in infinity) to find an optimal solution. However, evolutionary techniques are not only helpful for dealing with intractable problems. In this paper, we demonstrate, that EC is not restricted to algorithmic methods, and is more expressive than Turing machines.
Journal Article•
TL;DR: Another proof of the universality of the computation model introduced by Gh.
Abstract: In [3] a variant of the computation model introduced by Gh. Paun in [1] is considered: membrane systems with external output, which were proven to be universal, in the sense that they are able to generate all Parikh images of recursively enumerable languages. Here we give another proof of the universality of this model. The proof is carried out associating to each deterministic Turing machine a P system with external output that simulates its running. Thus, although we work with symbol-objects, we get strings as a result of computations, and in this way we generate directly all recursively enumerable languages, instead of their images through Parikh mapping, as it is done in [3].
1 Jan 2002
TL;DR: A new halting protocol is proposed without augmenting the halting qubit and is shown to work without spoiling the computation.
Abstract: Foundations of the theory of quantum Turing machines are investigated. The protocol for the preparation and the measurement of quantum Turing machines is discussed. The local transition functions are characterized for fully general quantum Turing machines. A new halting protocol is proposed without augmenting the halting qubit and is shown to work without spoiling the computation.
TL;DR: In this article, modal logic and transfinite set-theory are used to define metaphysical foundations for a general theory of computation, where a possible universe is a certain kind of situation; a situation is a set of facts.
Abstract: I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds.
TL;DR: A population genetics model is introduced in which the operators of selection and inheritance are effectively computable (in polynomial time on probabilistic Turing machines) and it is shown that such systems are as powerful as the usual models of parallel computations, namely they can simulate polynomially many steps.
Abstract: We study the computational power of systems where information is stored in independent strings and each computational step consists of exchanging information between randomly chosen pairs. To this end we introduce a population genetics model in which the operators of selection and inheritance are effectively computable (in polynomial time on probabilistic Turing machines). We show that such systems are as powerful as the usual models of parallel computations, namely they can simulate polynomial space computations in polynomially many steps. We also show that the model has the same power if the recombination rules for strings are very simple (context sensitive crossing over). 2001 Elsevier Science
Journal Article•
TL;DR: In this article, a hierarchy of properly included real-time languages between deterministic languages and the log-bounded non-deterministic languages is presented, and the properness of the inclusions is proved.
Abstract: Multitape Turing machines with a restricted number of nondeterministic steps are investigated. Fischer and Kintala showed an infinite nondeterministic hierarchy of properly included real-time languages between the deterministic languages and the logbounded nondeterministic languages. This result is extended to time complexities in the range between real time and linear time, and is generalized to arbitrary dimensions.For fixed amounts of nondeterminism infinite proper dimension hierarchies are presented. The hierarchy results are established by counting arguments. For an equivalence relation and a family of witness languages the number of induced equivalence classes is compared to the number of equivalence classes distinguishable by the model in question. By contradiction the properness of the inclusions is proved.
TL;DR: This paper establishes new bounds on time(n) by num(n+o(n), improving on the previously known bound num(3n+6) and improves on the trivial relation space (n) ≤ time( n) , using a technique of counting crossing sequences.
Abstract: Consider Turing machines that use a tape infinite in both directions, with the tape alphabet {0,1} . Rado's busy beaver function, ones(n), is the maximum number of 1's such a machine, with n states, started on a blank (all-zero) tape, may leave on its tape when it halts. The function ones(n) is non-computable; in fact, it grows faster than any computable function. Other functions with a similar nature can be defined also. All involve machines of n states, started on a blank tape. The function time(n) is the maximum number of moves such a machine may make before halting. The function num(n) is the largest number of 1's such a machine may leave on its tape in the form of a single run; and the function space(n) is the maximum number of tape squares such a machine may scan before it halts. This paper establishes new bounds on these functions in terms of each other. Specifically, we bound time(n) by num(n+o(n)), improving on the previously known bound num(3n+6) . This result is obtained using a kind of ``self-interpreting'' Turing machine. We also improve on the trivial relation space(n) ≤ time(n) , using a technique of counting crossing sequences.
TL;DR: In this paper, the authors considered deterministic k-tape and multitape Turing machines with one-way, two-way and without a separated input tape and investigated the classes of languages acceptable by such devices with time bounds of the form n + r(n), where r ∈ o(n) is a sublinear function.