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

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 polynomial-time and linear-space 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...

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.

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 little-known assertion that the human mind has a power “converging to infinity, ” and as an anchoring problem Rado’s (1963) Turing-uncomputable “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

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.

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.

Accelerating Turing machines are abstract devices that have the same computational structure as Turing machines, but can perform super-tasks. I argue that performing super-tasks 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.