Abstract: We show that a deterministic Turing machine with one d-dimensional work tape and random access to the input cannot solve satisfiability in time na for a < √(d + 2)/(d + 1). For conondeterministic machines, we obtain a similar lower bound for any a such that a3 < 1 + a/(d + 1). The same bounds apply to almost all natural NP-complete problems known.

Abstract: According to Kolmogorov complexity, a string is considered patternless if the shortest Turing machine that can encode it is at least as long as the string itself. Conversely, a non-random string with patterns can be described by some Turing machine that is shorter than the string. Hence, special forms of Turing machines - such as functions, N-grams, finite automata and stochastic automata - can all be regarded as representations of some approximations of patterns. Based on these observations, system profiles are defined for anomaly-based intrusion detection systems. The results are encouraging.

Abstract: We present a small time-efficient universal Turing machine with 5 states and 6 symbols. This Turing machine simulates our new variant of tag system. It is the smallest known universal Turing machine that simulates Turing machine computations in polynomial time.

Abstract: As was well known, in classical computation, Turing machines, circuits, multi-stack machines, and multi-counter machines are equivalent, that is, they can simulate each other in polynomial time In quantum computation, Yao [11] first proved that for any quantum Turing machines $M$, there exists quantum Boolean circuit $(n,t)$-simulating $M$, where $n$ denotes the length of input strings, and $t$ is the number of move steps before machine stopping However, the simulations of quantum Turing machines by quantum multi-stack machines and quantum multi-counter machines have not been considered, and quantum multi-stack machines have not been established, either Though quantum counter machines were dealt with by Kravtsev [6] and Yamasaki {\it et al} [10], in which the machines count with $0,\pm 1$ only, we sense that it is difficult to simulate quantum Turing machines in terms of this fashion of quantum computing devices, and we therefore prove that the quantum multi-counter machines allowed to count with $0,\pm 1,\pm 2,,\pm n$ for some $n>1$ can efficiently simulate quantum Turing machines Therefore, our mail goals are to establish quantum multi-stack machines and quantum multi-counter machines with counts $0,\pm 1,\pm 2,,\pm n$ and $n>1$, and particularly to simulate quantum Turing machines by these quantum computing devices

Abstract: The purpose of this paper is to investigate the connection between the theory of computation and Temporal Concept Analysis, the temporal branch of Formal Concept Analysis The main idea is to represent for each possible input of a given algorithm the uniquely determined sequence of computation steps as a life track of an object in some conceptually described state space For that purpose we introduce for a given Turing machine a Conceptual Time System with Actual Objects and a Time Relation (CTSOT) which yields the state automaton of a Turing machine as well as its configuration automaton The conceptual role of the instructions of a Turing machine is understood as a set of background implications of the derived context of a Turing CTSOT

Abstract: The Turing Test(TT) was proposed by Alan Turing in his famous article ”Computing Machinery and Intelligence” in 1950 in order to give an operational definition of intelligence. TT is one of the most disputed topics in artificial intelligence, philosophy of mind, and cognitive science. In this report I will discuss Turings ideas in detail and present the important comments that have been made on them. Within this context, behaviorism, consciousness, and similar topics in philosophy of mind will be discussed. I will also cover the sociological and psychological aspects of the Turing Test. At the same time I will focus on the current situation and analyze programs that have been developed with the aim of passing the Turing Test. I conclude that the Turing Test has been, and will continue to be, an influential as well as controversial topic of Artificial Intelligence. Chapter

Abstract: An abstract rule driven system is described. We prove that it is calculated by a restricted Turing Machine.

Abstract: Present day classical computers, developed during the last sixty years are essentially logic machines, based on binary logic and arithmetic, acting on discrete valued (binary coded) data. Its unique property is algorithmic (stored) programmability, invented by John von Neumann. The mathematical concept is based on a Universal Machine on integers (Turing Machine). Cellular automata, introduced also by J. von Neumann, are fully parallel array processors with all discrete space, time and state values. Their beautiful properties have been recently rediscovered showing the deeper qualitative properties. If we allow the states and time to be continuous values like in CNN, a broader class of dynamics will be generated. Even more, the fundamental condition to generate complex features at the edge of chaos have been established: the need of local activity. Taking one step further, and using the CNN-UM architecture, a new world of algorithms is opening.

Abstract: As a result of our research in the learning of fundamental concepts and problem solving strategies in informatics, we have created a learning environment whose central part is the interaction with a physical and a virtual model of Turing's machine. This environment is different from the traditional ones: its interaction with the models is natural and gradual, there is a physical interaction as well as a sensorial perception, and the concepts and strategies in its essence are visualized without caring to learn a technical language. As a consequence, the student can conjecture and deepen in his results in an easier way, and reach a more natural conceptualization. Additionally, with this project, new didactic possibilities are open to the Turing machine, which is the simplest model of algorithm.

Abstract: The Turing Machine was designed by Alan Turing to serve as a general computational model. The machine has a tape to which data can be written by a head. A tape consists of cells where each cell has a value (similar to a cell on a hard-drive, albeit the cells of a Turing Machine’s tape can have more than two states) and that value can be changed by the head. The head can also be in multiple states and it may move. What the head writes to the tape for a given iteration is determined by the value (color) of the cell and the state of the head. For a given case, the cell’s color, the head’s state, as well as the head’s position may change. Of particular note, however, is that the head may only move by one cell in either direction [1]. A Turing Machine can be made to exhibit complex behavior for simple initial conditions by adding states, colors, or both. In [2] Wolfram shows that the simplest Turing Machine with complex behavior with an empty tape as input has four states and two colors. What we consider is whether one can create a Turing Machine which exhibits complex behavior by letting the head move by more than one cell in either direction (we assume a one-dimensional tape). We define such a machine to be a n-Skip Turing Machine, where the n refers to the maximum number of cells a head can skip for a given iteration. Notice that we do not impose the limitation that the head must move n cells. We define the rule of a n-Skip Turing Machine as follows (with two states and two colors):

Abstract: In this paper we show that the probability that a program p of n bits halts at discrete time t (with t > 2n+1 − 2; we define the discrete time t as the integer number of steps done by an Universal Turing Machine during the execution of p, until the halt) tends to zero as the inverse law ∝ 1/t. This means that the greater is the time an n-bit program is running on an Universal Turing Machine (provided that t > 2n+1 − 2), the lesser is the probability that it will ever halt. Some mathematical consequences are also discussed. 1 Introductory remarks As it has been proved by Alan M. Turing in 1936 [1], if we have a program p running on an Universal Turing Machine (UTM), then we have no finite, deterministic algorithm which allows us to know whether and when it will halt (this is the well known halting problem). This is to say that the halting behaviour of a program, with the trivial exception of the simplest ones, is generally uncomputable and unpredictable. In this paper we show that, for what concerns the probability of its halt, every program running on an UTM is characterized by a peculiar asymptotic behaviour in time. Such trend provides us with some information which allows to theoretically solve the halting problem with an arbitrary degree of confidence.

Abstract: Knowledge, cognition and intelligence are three tightly connected concepts. The Turing test is widely accepted as a test stone for machine intelligence. This paper analyzes experiences obtained in a research project on a Turing test for children and discusses its meaning with respect to some knowledge and cognition issues.

Abstract: We prove that there is no algorithm to tell whether an arbitrarily constructed Quantum Turing Machine has same time steps for different branches of computation. We, hence, cannot avoid the notion of halting to be probabilistic in Quantum Turing Machine.

Abstract: Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing machine with an arbitrary input can be encoded into the topology of a 4-manifold, such that the 4-manifold is homeomorphic to a certain other 4-manifold if and only if the corresponding Turing machine halts on the associated input. Physical implications are briefly discussed.

Abstract: A structure is said to be computable if its domain can be represented by a set which is accepted by a Turing machine and if its relations can then be checked using Turing machines. Restricting the Turing machines in this definition to finite automata gives us a class of structures with a particularly simple computational structure; these structures are said to have automatic presentations. Given their nice algorithmic properties, these have been of interest in a wide variety of areas. An area of particular interest has been the classification of automatic structures. One of the prime examples under consideration has been the class of groups. We give a complete characterization in the case of finitely generated groups and show that such a group has an automatic presentation if and only if it is virtually abelian.