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Beyond Turing Machines
"... In this paper we describe and analyze models of problem solving and computation going beyond Turing Machines. Three principles of extending the Turing Machine's expressiveness are identified, namely, by interaction, evolution and infinity. Several models utilizing the above principles are pr ..."
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In this paper we describe and analyze models of problem solving and computation going beyond Turing Machines. Three principles of extending the Turing Machine's expressiveness are identified, namely, by interaction, evolution and infinity. Several models utilizing the above principles are presented. Other
Parallel Turing Machines
, 1984
"... A new model of parallel computation  a so called Parallel Turing Machine (PTM)  is proposed. It is shown that the PTM does not belong to the two machine classes suggested recently by van Emde Boas, i.e., the PTM belongs neither to the first machine class consisting of the machines which are polyno ..."
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A new model of parallel computation  a so called Parallel Turing Machine (PTM)  is proposed. It is shown that the PTM does not belong to the two machine classes suggested recently by van Emde Boas, i.e., the PTM belongs neither to the first machine class consisting of the machines which are polynomialtime and linearspace equivalent to the sequential Turing Machine, nor to the second machine class which consists of the machines which satisfy the parallel computation thesis. Further the notion of a pipelined PTM is introduced and the "period" is defied as a complexity measure suitable for evaluating the efficiency of pipelined computations. It is shown that to within...
N.: Comparing computational power
 Logic Journal of the IGPL
"... All models are wrong but some are useful. —George E. P. Box, “Robustness in the strategy of scientific model building ” (1979) It is common practice to compare the computational power of different models of computation. For example, the recursive functions are strictly more powerful than the primiti ..."
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Cited by 6 (4 self)
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All models are wrong but some are useful. —George E. P. Box, “Robustness in the strategy of scientific model building ” (1979) It is common practice to compare the computational power of different models of computation. For example, the recursive functions are strictly more powerful than the primitive recursive functions, because the latter are a proper subset of the former (which includes Ackermann’s function). Sidebyside with this “containment ” method of measuring power, it is standard to use an approach based on “simulation”. For example, one says that the (untyped) lambda calculus is as powerful—computationally speaking—as the partial recursive functions, because the lambda calculus can simulate all partial recursive functions by encoding the natural numbers as Church numerals. The problem is that unbridled use of these two ways of comparing power allows one to show that some computational models are strictly stronger than themselves! We argue that a better definition is that model A is strictly stronger than B if A can simulate B via some encoding, whereas B cannot simulate A under any encoding. We then show that the recursive functions are strictly stronger in this sense than the primitive recursive. We also prove that the recursive functions, partial recursive functions, and Turing machines are “complete”, in the sense that no injective encoding can make them equivalent to any “hypercomputational” model. 1
A new Gödelian argument for hypercomputing minds based on the busy beaver problem
 Applied Mathematics and Computation, in press, doi:10.1016/j.amc.2005.09.071
"... 9.9.05 1245am NY time Do human persons hypercompute? Or, as the doctrine of computationalism holds, are they information processors at or below the Turing Limit? If the former, given the essence of hypercomputation, persons must in some real way be capable of infinitary information processing. Using ..."
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Cited by 5 (1 self)
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9.9.05 1245am NY time Do human persons hypercompute? Or, as the doctrine of computationalism holds, are they information processors at or below the Turing Limit? If the former, given the essence of hypercomputation, persons must in some real way be capable of infinitary information processing. Using as a springboard Gödel’s littleknown assertion that the human mind has a power “converging to infinity, ” and as an anchoring problem Rado’s (1963) Turinguncomputable “busy beaver ” (or Σ) function, we present in this short paper a new argument that, in fact, human persons can hypercompute. The argument is intended to be formidable, not conclusive: it brings Gödel’s intuition to a greater level of precision, and places it within a sensible case against computationalism. 1
The Emergent Computational Potential of Evolving Artificial Living Systems
, 2002
"... The computational potential of artificial living systems can be studied without knowing the algorithms that govern their behavior. Modeling single organisms by means of socalled cognitive transducers, we will estimate the computational power of AL systems by viewing them as conglomerates of such org ..."
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The computational potential of artificial living systems can be studied without knowing the algorithms that govern their behavior. Modeling single organisms by means of socalled cognitive transducers, we will estimate the computational power of AL systems by viewing them as conglomerates of such organisms. We describe a scenario in which an artificial living (AL) system is involved in a potentially infinite, unpredictable interaction with an active or passive environment, to which it can react by learning and adjusting its behaviour. By making use of sequences of cognitive transducers one can also model the evolution of AL systems caused by `architectural' changes. Among the examples are `communities of agents', i.e. by communities of mobile, interactive cognitive transducers.
Teaching Fundamentals of Computing Theory: A Constructivist Approach
 Journal of Computer Science and Technology, special issue on Computer Science Education (submitted
"... A Fundamentals of Computing Theory course involves different topics that are core to the Computer Science curricula and whose level of abstraction makes them difficult both to teach and to learn. notions involved and the required mathematical background. Surveys conducted among our students showed t ..."
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A Fundamentals of Computing Theory course involves different topics that are core to the Computer Science curricula and whose level of abstraction makes them difficult both to teach and to learn. notions involved and the required mathematical background. Surveys conducted among our students showed that many of them were applying some theoretical concepts mechanically rather than developing significant learning. This paper shows a number of didactic strategies that we introduced in the Fundamentals of Computing Theory curricula to cope with the above problem. The proposed strategies were based on a stronger use of technology and a constructivist approach. The final goal was to promote more significant learning of the course topics.
SuperTasks, Accelerating Turing Machines and Uncomputability
"... Accelerating Turing machines are abstract devices that have the same computational structure as Turing machines, but can perform supertasks. I argue that performing supertasks alone does not buy more computational power, and that accelerating Turing machines do not solve the halting problem. To sh ..."
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Accelerating Turing machines are abstract devices that have the same computational structure as Turing machines, but can perform supertasks. I argue that performing supertasks alone does not buy more computational power, and that accelerating Turing machines do not solve the halting problem. To show this, I analyze the reasoning that leads to Thomson's paradox, point out that the paradox rests on a conflation of different perspectives of accelerating processes, and conclude that the same conflation underlies the claim that accelerating Turing machines can solve the halting problem.
Didactic Strategies for Promoting Significant Learning in Formal Languages and Automata Theory
 In SIGCSE Bulletin inroads, Proceedings of ITiCSE 2004
, 2004
"... Theory (FLAT) involves di#erent topics that are core to the CS curricula and whose level of abstraction makes them di#cult both to teach and to learn. Such di#culty stems from the complexity of the abstract notions involved and the required mathematical background. Surveys conducted among our studen ..."
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Theory (FLAT) involves di#erent topics that are core to the CS curricula and whose level of abstraction makes them di#cult both to teach and to learn. Such di#culty stems from the complexity of the abstract notions involved and the required mathematical background. Surveys conducted among our students showed that many of them were applying some theoretical concepts mechanically rather than developing a significant learning of them, leading to a lack of motivation and interest. To cope with this problem, we introduced a number of didactic strategies based on a constructivist approach. The main aim of the proposed strategies is to promote a more significant learning of several important FLAT topics.
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"... www.elsevier.com/locate/tcs Experience, generations, and limits in machine learning ..."
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www.elsevier.com/locate/tcs Experience, generations, and limits in machine learning
Preface
"... Three aspects ofsuperrecursive algorithms and hypercomputation or nding black swans Our engraved knowledge may bite into our thinking certain errors that become wellnigh ineradicable. Rogers MacVeagh and Thomas Costain “Joshua” History ofscience and technology proves that the biggest advances come ..."
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Three aspects ofsuperrecursive algorithms and hypercomputation or nding black swans Our engraved knowledge may bite into our thinking certain errors that become wellnigh ineradicable. Rogers MacVeagh and Thomas Costain “Joshua” History ofscience and technology proves that the biggest advances come not from doing more and bigger and faster of what is already being done, but from new ideas, discoveries, and starting points. Hence this special issue concerns new ideas, discoveries, and metaphors in computer science. It is not about incremental improvements, but rather it presents the opportunities opened by these related notions: superrecursive algorithms and hypercomputation. Together these new ideas, discoveries, constructions, and metaphors form a new computer science eld, the theory of superrecursive algorithms and hypercomputation. It is a part ofsuch established domain as the theory ofalgorithms, automata, and computation.