Abstract: Separating the origins of computer science and technology.

Abstract: Mathematical programming is Turing complete, and can be used as a general-purpose declarative language. We present a new constructive proof of this fact, and showcase its usefulness by discussing an application to finding the hardest input of any given program running on a Minsky Register Machine. We also discuss an application of mathematical programming to software verification obtained by relaxing one of the properties of Turing complete languages.

Abstract: We define the class of constrained cons-free rewriting systems and show that this class characterizes P, the set of languages decidable in polynomial time on a deterministic Turing machine. The main novelty of the characterization is that it allows very liberal properties of term rewriting, in particular non-deterministic evaluation: no reduction strategy is enforced, and systems are allowed to be non-confluent.

Abstract: The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to support arbitrary computation. However, these encodings are usually by simulating the entire Turing Machine within the language, or by encoding a language that does an encoding or simulation itself. This second category is typical for process calculi that show an encoding of lambda-calculus (often with restrictions) that in turn simulates a Turing Machine. Such approaches lead to indirect encodings of Turing Machines that are complex, unclear, and only weakly equivalent after computation. This paper presents an approach to encoding Turing Machines into intensional process calculi that is faithful, reduction preserving, and structurally equivalent. The encoding is demonstrated in a simple asymmetric concurrent pattern calculus before generalised to simplify infinite terms, and to show encodings into Concurrent Pattern Calculus and Psi Calculi.

Abstract: In this short paper, we show that the game description language (GDL) is Turing complete. In particular, we show how to simulate a Turing machine (TM) as a single-player game described in GDL. Positions in the game correspond to configurations of the machine, and the TM accepts its input exactly when the agent has a winning strategy from the initial position. As direct consequences of the Turing completeness of GDL, we show that well formedness as well as some other properties of a GDL description are undecidable. We propose to strengthen the recursion restriction of the original GDL specification into a general recursion restriction. The restricted language is not Turing complete, and the aforementioned properties become decidable. Checking whether a game description satisfies the suggested restriction is as easy as checking that the game is syntactically correct. Finally, we argue that practical expressivity is not affected as all syntactically correct games in a collection of more than 500 games having appeared in previous general game playing (GGP) competitions belong to the proposed GDL fragment.

Abstract: In the 1930s, mathematician Alan Turing proposed a mathematical model of computation now called a Turing Machine to describe how people follow repetitive procedures given to them in order to come up with final calculation result. This extraordinary computational model has been the foundation of all modern digital computers since the World War II. Turing also speculated that this model had some limits and that more powerful computing machines should exist. In 1993, Siegelmann and colleagues introduced a Super-Turing Computational Model that may be an answer to Turing’s call. Super-Turing computation models have no inherent problem to be realizable physically and biologically. This is unlike the general class of hyper-computer as introduced in 1999 to include the Super-Turing model and some others. This report is on research to design, develop and physically realize two prototypes of analog recurrent neural networks that are capable of solving problems in the Super-Turing complexity hierarchy, similar to the class BPP/log*. We present plans to test and characterize these prototypes on problems that demonstrate anticipated Super- Turing capabilities in modeling Chaotic Systems.

Abstract: We give new Turing machines that simulate the iteration of the Collatz 3x+1 function. First, a never halting Turing machine with 3 states and 4 symbols, improving the known 3x5 and 4x4 Turing machines. Second, Turing machines that halt on the final loop, in the classes 3x10, 4x6, 5x4, and 13x2.

Abstract: A nondeterministic Turning machine (NTM) performs computations using a spatial binary enumeration system, a three-dimensional relation system, a simulated-human logic system, and a bijective-set memory system. The NTM may be used to perform a variety of computational tasks, such as multiple sequence alignment, factorization, and other nondeterministic polynomial algorithms in polynomial time. The NTM may be constructed by a deterministic Turing machine (DTM) using the four systems listed above.

Abstract: We prove that every single-tape deterministic Turing machine working in \(t(n)\) time, for some function \(t:\mathbb {N}\rightarrow \mathbb {N}\), can be simulated by a uniform family of polarizationless P systems with active membranes. Moreover, this is done without significant slowdown in the working time. Furthermore, if \(\log t(n)\) is space constructible, then the members of the uniform family can be constructed by a family machine that uses \(O(\log t(n))\) space.

Abstract: A. N. Turing’s 1936 concept of computability, computing machines, and computable binary digital sequences, is subject to Turing’s Cardinality Paradox. The paradox conjoins two opposed but comparably powerful lines of argument, supporting the propositions that the cardinality of dedicated Turing machines outputting all and only the computable binary digital sequences can only be denumerable, and yet must also be nondenumerable. Turing’s objections to a similar kind of diagonalization are answered, and the implications of the paradox for the concept of a Turing machine, computability, computable sequences, and Turing’s effort to prove the unsolvability of the Entscheidungsproblem, are explained in light of the paradox. A solution to Turing’s Cardinality Paradox is proposed, positing a higher geometrical dimensionality of machine symbol-editing information processing and storage media than is available to canonical Turing machine tapes. The suggestion is to add volume to Turing’s discrete two-dimensional machine tape squares, considering them instead as similarly ideally connected massive three-dimensional machine information cells. Three-dimensional computing machine symbol-editing information processing cells, as opposed to Turing’s two-dimensional machine tape squares, can take advantage of a denumerably infinite potential for parallel digital sequence computing, by which to accommodate denumerably infinitely many computable diagonalizations. A three-dimensional model of machine information storage and processing cells is recommended on independent grounds as better representing the biological realities of digital information processing isomorphisms in the three-dimensional neural networks of living computers.

Abstract: Turing machines are the most powerful computational machines and are the theoretical basis for modern computers. Universal Turing machine works for all classes of languages including regular languages (Res), Context-free languages (CFLs), as well as recursively enumerable languages (RELs). In this paper, we discuss the concept of Universal Turing machine as a computing device that can be used for solving any problem that a computer or a human can solve. We show how the machine works in solving computational problems and design some algorithms showing to show the operational procedure of input symbols such as moving left, right, or stationary depending on the input symbol. Finally, we argue that the Universal Turing machine is a generalpurpose machine that can be used to compute any computable problem.

Abstract: In this paper we sketch an ACL2-checked proof that a simple but unbounded Von Neumann machine model is Turing Complete, i.e., can do anything a Turing machine can do. The project formally revisits the roots of computer science. It requires re-familiarizing oneself with the definitive model of computation from the 1930s, dealing with a simple “modern” machine model, thinking carefully about the formal statement of an important theorem and the specification of both total and partial programs, writing a verifying compiler, including implementing an X86-like call/return protocol and implementing computed jumps, codifying a code proof strategy, and a little “creative” reasoning about the non-termination of two machines.

Abstract: The success of machine’s intelligence which is nothing but a machine with brain is possible now a day. The intelligence could be addressed into machines as in humans. Artificial intelligence came into existence because of humankind; they have named themselves as Homo sapiens. Today’s era is artificial intelligence era anything could be possible, machines have capabilities to think, intimate and sense like humans. Learning Artificial intelligence is nothing but learning about ourselves. Systems such as machines or software could able to monitor their emotions like happy, love, angry and hunger. In this paper we would analyze clear picture of capabilities of machine with intelligence. Turing test, which is still used as a key gauge of how close machines have come to human intelligence with the Imitation Game example. The Turing test has given the inspiration for the instigation and exponentially development of artificial intelligence. Turing test is done by Turing machine which is hypothetical device that modifies symbols on a tape according to protocols. In later section we will be explaining a scenario which proves the machines intelligence. Keywords— Artificial intelligence, Turing Machine

Abstract: DNA computing is a novel parallel computation paradigm. Existing models were mostly based on molecular biological technology and different from the traditional computers,they were less universal than traditional ones,so the algorithm or a DNA computer just for one kind of problem could not be transplanted to solve other problems without any modification. This paper put forward a new generalized molecular computational model(designated by GMCM) based on Turing machine,which did not rely on biotechnology and included an ordinary single tape Turing machine,a finite write-only tape,and a special working tape. Through the topological mapping between the write-only tape and the wokring tape,it could realize read or write in parallel. Validation test proves that GMCM can solve the satisfiability problem in a polynomial time and has obvious advantages compared with exsiting DNA computer on computation accuracy and universal property.

Abstract: In this paper, we propose the Ω-machine model for social machines By introducing a cluster of "oracles" to a traditional Turing machine, the Ω-machine is capable of describing the interaction between human participants and mechanical machines We also give two examples of social machines, collective intelligence and rumor spreading, and demonstrate how the general Ω-machine model could be used to simulate their computations

Abstract: The article deals with some ideas by Turing concern ing the background and the birth of the well-known Turing Test, showing the e volution of the main question proposed by Turing on thinking machine. The notions he used, especially that one of imitation, are not so much exactly defined a nd shaped, but for this very reason they have had a deep impact in artificial in telligence and cognitive science research from an epistemological point of v iew. Then, it is suggested that the fundamental concept involved in Turing’s imitat ion game, conceived as a test for detecting the presence of intelligence in an ar tificial entity, is the concept of interaction, that Turing adopts in a wider, more in tuitive and more fruitful sense than the one that is proper to the current research in interactive computing.

Abstract: The paper briefly considers the conceptual and actual developments in art as a result of advances in computation and communications. It postulates various advances and developments that might take place in the future and expresses the view that, in the long term, computation itself, as introduced by Alan Turing will prove to have changed art practice in the most profound way.

Abstract: We adopt corecursion and coinduction to formalize Turing Machines and their operational semantics in the proof assistant Coq. By combining the formal analysis of converging and diverging evaluations, our approach allows us to certify the implementation of the functions computed by concrete Turing Machines. Our effort may be seen as a first step towards the formal development of basic computability theory.

Abstract: Purpose. The purpose of this paper is to study a class of the natural languages called the lattice-valued phrase structure languages, which can be generated by the lattice-valued type 0 grammars and recognized by the lattice-valued Turing machines. Design/Methodology/Approach. From the characteristic of natural language, this paper puts forward a new concept of the l-valued Turing machine. It can be used to characterize recognition, natural language processing, and dynamic characteristics. Findings. The mechanisms of both the generation of grammars for the lattice-valued type 0 grammar and the dynamic transformation of the lattice-valued Turing machines were given. Originality/Value. This paper gives a new approach to study a class of natural languages by using lattice-valued logic theory.

Abstract: Turing thesis states that any algorithm procedure that can be carried by human beings/computer can be carried out by a Turing Machine. Turing Machines are also used for determining the undesirability of certain languages and measuring the space and time complexity of problems. ‘Snapshots’ of a Turing machine in action can be used to describe a Turing machine. The machine must remember the past symbol scanned. The Turing machine can remember this by going to the next unique state. In a multiple track TM, a single tape is assumed to be divided into several tracks. We know subroutines are used in computer languages, when some task has to be done repeatedly. This facility can implement for Turing Machines. Turing machines are useful in several ways. As an automaton, the Turing machine is the most general model. The Turing machine can be thought of as finite control connected to a R/W (read/write) head. A Turing machine computes a function f : ∑* → ∑* if, for any input word w, it always stops in configuration where f(w) is on the tape. The functions that are computable by an effective procedure are those that are computable by a Turing Machine.

Abstract: This paper posits fundamental artificial intelligence is founded on Turing’s two implementations for his imitation game: a simultaneous comparison 3-participant test, and a 2-participant viva voce test. In the former the human interrogator questions two hidden interlocutors in parallel deciding which is the human and which is the machine. In the latter test the judge interrogates one hidden entity and decides whether it is a human or a machine. The results from an original experiment implementing both tests side-by-side show the simultaneous comparison is a stronger test for artificial intelligence

Abstract: An efficient algorithm computing the rank of a group (that is, the size of a minimum generating subset) benefits mathematicians, who use numerical algebra systems for research, cryptographers, who rely on algebraic systems for proofs of security, and theoretical computer scientists, who seek to understand which problems can be solved in a particular model of computation. Before now, the best algorithm for computing the rank of a group required a polylogarithmic amount of space, which induces a superpolynomial (hence, inefficient) algorithm. We reduced the best upper bound on the complexity of the group rank problem and provide a theoretically efficient algorithm for it. This paper proves that with very short certificates of correctness, the group rank problem can be verified by highly restricted models of computation. We prove that the problem of deciding whether the rank of a finite group, given as a multiplication table, is smaller than a specified number is decidable not only by a circuit of depth $O(\log \log n)$ augmented with $O(\log^2 n)$ nondeterministic bits, but also by a Turing machine using $O(\log n)$ space and $O(\log^2 n)$ bits of nondeterminism. These models of computation are extremely limited in computational power, and hence can be simulated by a deterministic Turing machine in polynomial time. Using limited nondeterminism and restrictive models of computation as verifiers may be useful in examining other algebraic problems.

Abstract: This paper divide some complexity class by using fixpoint and fixpointless area of Decidable Universal Turing Machine (UTM). Decidable Deterministic Turing Machine (DTM) have fixpointless combinator that add no extra resources (like Negation), but UTM makes some fixpoint in the combinator. This means that we can jump out of the fixpointless combinator system by making more complex problem from diagonalisation argument of UTM. As a concrete example, we proof L is not P . We can make Polynomial time UTM that emulate all Logarithm space DTM (LDTM). LDTM set close under Negation, therefore UTM does not close under LDTM set. (We can proof this theorem like halting problem and time/space hierarchy theorem, and also we can extend this proof to divide time/space limited DTM set.) In the same way, we proof P is not NP. These are new hierarchy that use UTM and Negation.

Abstract: We assume there are one-way functions and obtain a contradiction following a solid argumentation, and therefore, one-way functions do not exist applying the reductio ad absurdum method. Indeed, for every language $L$ that is in $EXP$ and not in $P$, we show that any configuration, which belongs to the accepting computation of $x \in L$ and is at most polynomially longer or shorter than $x$, has always a non-polynomial time algorithm that find it from the initial or the acceptance configuration on a deterministic Turing Machine which decides $L$ and has always a string in the acceptance computation that is at most polynomially longer or shorter than the input $x \in L$. Next, we prove the existence of one-way functions contradicts this fact, and thus, they should not exist. Hence, function problems such as the integer factorization of two large primes can be solved efficiently. In this way, this work proves that is not safe many of the encryption and authentication methods such as the public-key cryptography. It could be the case of $P = NP$ or $P eq NP$, even though there are no one-way functions. However, we prove that $P = UP$.

Abstract: This paper explores and clarifies several issues surrounding Zeno machines and the issue of running a Turing machine for infinite time. Without a minimum hypothetical bound on physical conditions, any magical machine can be created, and therefore, a thesis on the bound is formulated. This paper then proves that the halting problem algorithm for every Turing-recognizable program and every input cannot be devised whatever method is used to exploit infinite running-time of Turing machine.