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42
Molecular Computation Of Solutions To Combinatorial Problems
, 1994
"... The tools of molecular biology are used to solve an instance of the directed Hamiltonian path problem. A small graph is encoded in molecules of DNA and the `operations' of the computation are performed with standard protocols and enzymes. This experiment demonstrates the feasibility of carrying out ..."
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Cited by 616 (5 self)
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The tools of molecular biology are used to solve an instance of the directed Hamiltonian path problem. A small graph is encoded in molecules of DNA and the `operations' of the computation are performed with standard protocols and enzymes. This experiment demonstrates the feasibility of carrying out computations at the molecular level.
On the Feasibility of Checking Temporal Integrity Constraints
, 1995
"... We analyze the computational feasibility of checking temporal integrity constraints formulated in some sublanguages of firstorder temporal logic. Our results illustrate the impact of the quantifier pattern on the complexity of this problem. The presence of a single quantifier in the scope of a temp ..."
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Cited by 38 (6 self)
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We analyze the computational feasibility of checking temporal integrity constraints formulated in some sublanguages of firstorder temporal logic. Our results illustrate the impact of the quantifier pattern on the complexity of this problem. The presence of a single quantifier in the scope of a temporal operator makes the problem undecidable. On the other hand, if no quantifiers are in the scope of a temporal operator and all the quantifiers are universal, temporal integrity checking can be done in exponential time. 1 Introduction As temporal databases become more widely used in practice [27, 28], the need arises to address database integrity issues that are specific to such databases. In particular, it is necessary to generalize the standard notion of static integrity (involving single database states) to temporal integrity (involving sequences of database states). This work is the first attempt to date to analyze the computational feasibility of checking temporal integrity constrain...
Hypercomputation: computing more than the Turing machine
, 2002
"... In this report I provide an introduction to the burgeoning field of hypercomputation – the study of machines that can compute more than Turing machines. I take an extensive survey of many of the key concepts in the field, tying together the disparate ideas and presenting them in a structure which al ..."
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Cited by 31 (5 self)
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In this report I provide an introduction to the burgeoning field of hypercomputation – the study of machines that can compute more than Turing machines. I take an extensive survey of many of the key concepts in the field, tying together the disparate ideas and presenting them in a structure which allows comparisons of the many approaches and results. To this I add several new results and draw out some interesting consequences of hypercomputation for several different disciplines. I begin with a succinct introduction to the classical theory of computation and its place amongst some of the negative results of the 20 th Century. I then explain how the ChurchTuring Thesis is commonly misunderstood and present new theses which better describe the possible limits on computability. Following this, I introduce ten different hypermachines (including three of my own) and discuss in some depth the manners in which they attain their power and the physical plausibility of each method. I then compare the powers of the different models using a device from recursion theory. Finally, I examine the implications of hypercomputation to mathematics, physics, computer science and philosophy. Perhaps the most important of these implications is that the negative mathematical results of Gödel, Turing and Chaitin are each dependent upon the nature of physics. This both weakens these results and provides strong links between mathematics and physics. I conclude that hypercomputation is of serious academic interest within many disciplines, opening new possibilities that were previously ignored because of long held misconceptions about the limits of computation.
Heterogeneous Active Agents, III: Polynomially Implementable Agents
 Artificial Intelligence
, 2000
"... In [17], two of the authors have introduced techniques to build agents on top of arbitrary data structures, and to "agentize" new/existing programs. They provided a series of successively more sophisticated semantics for such agent systems, and showed that as these semantics become epistemically ..."
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Cited by 25 (8 self)
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In [17], two of the authors have introduced techniques to build agents on top of arbitrary data structures, and to "agentize" new/existing programs. They provided a series of successively more sophisticated semantics for such agent systems, and showed that as these semantics become epistemically more desirable, a computational price may need to be paid. In this paper, we identify a class of agents that are called weakly regularthis is done by first identifying a fragment of agent programs [17] called weakly regular agent programs (WRAPs for short).
The many forms of hypercomputation
 Applied Mathematics and Computation
, 2006
"... This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess. ..."
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Cited by 16 (0 self)
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This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess.
On the Impact of Forgetting on Learning Machines
 Journal of the ACM
, 1993
"... this paper contributes toward the goal of understanding how a computer can be programmed to learn by isolating features of incremental learning algorithms that theoretically enhance their learning potential. In particular, we examine the effects of imposing a limit on the amount of information that ..."
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Cited by 10 (3 self)
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this paper contributes toward the goal of understanding how a computer can be programmed to learn by isolating features of incremental learning algorithms that theoretically enhance their learning potential. In particular, we examine the effects of imposing a limit on the amount of information that learning algorithm can hold in its memory as it attempts to This work was facilitated by an international agreement under NSF Grant 9119540.
How much can analog and hybrid systems be proved (super)Turing
 Applied Mathematics and Computation
, 2006
"... Church thesis and its variants say roughly that all reasonable models of computation do not have more power than Turing Machines. In a contrapositive way, they say that any model with superTuring power must have something unreasonable. Our aim is to discuss how much theoretical computer science can ..."
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Cited by 5 (1 self)
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Church thesis and its variants say roughly that all reasonable models of computation do not have more power than Turing Machines. In a contrapositive way, they say that any model with superTuring power must have something unreasonable. Our aim is to discuss how much theoretical computer science can quantify this, by considering several classes of continuous time dynamical systems, and by studying how much they can be proved Turing or superTuring. 1
Decidability and universality in symbolic dynamical systems
 Fund. Inform
"... Abstract. Many different definitions of computational universality for various types of dynamical systems have flourished since Turing’s work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as un ..."
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Abstract. Many different definitions of computational universality for various types of dynamical systems have flourished since Turing’s work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as undecidability of a modelchecking problem. For Turing machines, counter machines and tag systems, our definition coincides with the classical one. It yields, however, a new definition for cellular automata and subshifts. Our definition is robust with respect to initial condition, which is a desirable feature for physical realizability. We derive necessary conditions for undecidability and universality. For instance, a universal system must have a sensitive point and a proper subsystem. We conjecture that universal systems have infinite number of subsystems. We also discuss the thesis according to which computation should occur at the ‘edge of chaos ’ and we exhibit a universal chaotic system. 1.
In Case of Interval (or More General) Uncertainty, No Algorithm Can Choose the Simplest Representative
, 2001
"... When we only know the interval of possible values of a certain quantity (or a more general set of possible values), it is desirable to characterize this interval by supplying the user with the "simplest" element from this interval, and by characterizing how different from this value we can get. ..."
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Cited by 4 (4 self)
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When we only know the interval of possible values of a certain quantity (or a more general set of possible values), it is desirable to characterize this interval by supplying the user with the "simplest" element from this interval, and by characterizing how different from this value we can get. For example, if, for some unknown physical quantity x, measurements result in the interval [1:95; 2:1] of possible values, then, most probably, the physicist will publish this result as y 2. Similarly, a natural representation of the measurement result x 2 [3:141592; 3:141593] is x . In this paper, we show that the problem of choosing the simplest element from a given interval (or from a given set) is, in general, not algorithmically solvable. 1 1 In Case of Interval (or More General Set) Uncertainty, a User Would Like to Have a Representative Value from This Interval (Set) The value of a physical quantity y is usually obtained either by a direct measurement, or by an indirect mea...
On the Role of Search for Learning from Examples
 Journal of Experimental and Theoretical Artificial Intelligence
"... Gold [Gol67] discovered a fundamental enumeration technique, the socalled identificationbyenumeration, a simple but powerful class of algorithms for learning from examples (inductive inference). We introduce a variety of more sophisticated (and more powerful) enumeration techniques and charac ..."
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Cited by 4 (0 self)
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Gold [Gol67] discovered a fundamental enumeration technique, the socalled identificationbyenumeration, a simple but powerful class of algorithms for learning from examples (inductive inference). We introduce a variety of more sophisticated (and more powerful) enumeration techniques and characterize their power. We conclude with the thesis that enumeration techniques are even universal in that each solvable learning problem in inductive inference can be solved by an adequate enumeration technique. This thesis is technically motivated and discussed. Keywords: Learning from examples, learning by search, identification by enumeration, enumeration techniques. Role of Search 1 1 Introduction The role of search, for learning from examples, is examined in a theoretical setting. Gold's seminal paper [Gol67] on inductive inference introduced a simple but powerful learning technique which became known as identificationby enumeration. Identificationbyenumeration begins with an infi...