perform one calculation at a time whereas a QTM can perform multiple calculations at a time. Normal computer works by manipulating bits in which there exists two states (0 or 1), but **Quantum** Computers are not limited to two states. They encode information as **Quantum** Bits (Qubit) which exist in superposition. Qubit represent atoms, ions, photons, electrons. The **quantum** **Turing** **machine** (QTM) has been introduced by Deutsch as the very first model of **quantum** computation. A **quantum** **Turing** **machine** can be seen as a generalisation of a probabilistic **Turing** **machine** where the probabilities which are associated with any transition are replaced by amplitudes i.e., complex numbers. The use of complex numbers leads to model fundamental phenomena of **quantum** mechanics like interferences and entanglement. A probabilistic **Turing** **machine** is submitted to well-formed ness conditions ensuring that for any configuration, the probabilities of all the possible evolutions sums to one a **quantum** **Turing** **machine** is submitted to similar well-formed ness conditions. These well-formed ness conditions ensures that the evolution of a **quantum** **Turing** **machine** (i) does not violate the law of **quantum** mechanics; (ii) is reversible. This later condition can be rephrased in more physical terms as an isolation of the **quantum** **Turing** **machine** from its environment during the computation. The reversibility assumption of **quantum** **Turing** machines is questionable for several reasons, including for instance the emergence of **quantum** computing models based on non reversible evolutions, like the one-way model or more generally the measurement-based **quantum** computations, which point out that a **quantum** computation is not necessary reversible. Moreover, the isolation assumption leads to technical issues like the impossibility to know whether a running computation is terminated or not i.e., whether the halting state is reached or not. Finally, due to the isolation assumption, **quantum** **Turing** machines are the natural **quantum** versions of reversible **Turing** machines. But the natural embedding of any reversible **Turing** **machine** into a **quantum** **Turing** **machine** cannot be extended to non- reversible and probabilistic **Turing** machines.

Show more
We can go on increasing the number of Registers and the number of Cohorts in each register (to compute and communicate various values). This will enable us to communicate and execute any complex operation. In this manner, we can also program K-Devices to interpret and execute smart contracts on a **Quantum** Blockchain (K-Chain). Such an idea can be extended to facilitate the construction of a **Quantum** **Turing** **Machine** (QTM), also known as a Universal **Quantum** Computer.

24 Read more

Before examining a **Quantum** **Turing** **Machine** for the Standard Model we will look at the features of “normal” **Turing** machines. A normal **Turing** **machine** consists of a finitely describable black box (its features are describable in a finite number of statements) and an infinite tape. The tape plays the role of computer memory. The tape is divided into squares. Each square contains a symbol or character. The character can be the “blank” character or a symbol. A tape contains blank characters followed by a finite string of input symbols followed by blank characters.

Show more
34 Read more

In the present work, we introduce E-infinity theory in which we can, in a manner of speech, “differentiate” and “integrate” the non-differentiable and non-integrible, namely geometrical structures made up entirely from transfinite point set of higher dimensional Cantor sets [12]-[16]. At a minimum, this is shockingly unconven- tional at least in the first few moments. However noting the use of non-standard analysis in the context of Not- tale’s theory of scale relativity as well as similar tools used in the work of the great French mathematical phy- sicist A. Connes, the inventor of noncommutative geometry [24] [28], the situation may start appearing slowly but surely in a different light. On this optimistic note, we will give in the present paper some more detail and explanation of the essential tools of the E-infinity Cantorian spacetime trade [20]-[34] before embarking upon applying our theory to the major problem of the discrepancy between the measured energy density of the cosmos as compared to the theoretical expectations. We are of course not divulging prematurely any secret when we say that one of our main tools in reaching our exact result is the fractal version of Witten’s eleven dimensional theory as it is clear from the title of the present work and it goes without saying that this fractal M-theory [18] [19] is as much the central piece of the work as it is the accurate determination of the ordinary and the dark energy density of this cosmos which turns out to be quite a surprise connected to what is probably the most famous equation in the history of theoretical physics, namely Einstein’s E = mc 2 where E is the energy, m is the mass and c is the speed of light [30]-[33]. The basic idea is that the fundamentally classical relativity theory E = mc 2 consists of two fundamentally non-classical **quantum** components that when added together, produce Eins tein’s beauty in the following manner: E ≅ mc 2 22 + mc 2 ( 21 22 ) = E O ( ) + E D ( ) = mc 2 where E(O) is the or- dinary energy and E(D) is the dark energy density of the cosmos [30]-[33].

Show more
10 Read more

Differing-input obfuscation for **Turing** Machines: We define the notion of differing- input obfuscator for **Turing** machines and give a construction for **Turing** machines with bounded length inputs (without converting it to a circuit), assuming the existence of a differing-input obfuscator for circuits and SNARGs for P [BCCT13]. Additionally, assuming SNARKs for P [BCCT13], we can construct a differing-input obfuscator even for the setting where the length of the input is not bounded. (We stress that it is only for this extension that we need to assume SNARKs.) Moreover, our construction achieves input-specific running times (explained below). This means that evaluating the obfuscated **machine** on input x does not depend on the worst- case running time of the **machine** but just on the running time of the unobfuscated **machine** on input x.

Show more
34 Read more

In deterministic Turing machine delegation, the user needs to save the entire memory (thought of as the input to the computation), while in RAM delegation, the user only needs to save a [r]

36 Read more

Learning TOC – begins is a web application which is useful for Learning TOC (Theory of Computation). It covers hypothesis of the basic points with cases and it likewise has Exercise segment in which client can check different speculations for all intents and purposes. It likewise creates drawing of different cases. So the client can learn it adequately and additionally quick. Client can build FA of the string without anyone else and print or fare it for his task work. It has the office of Test to check his score and readiness work. So it is extremely valuable for client as exam arrangement. This Web Application is valuable for the educators and understudies and additionally different clients which are has a place with the Computer Science field. The fundamental reason for this web application is to pick up everything outwardly and graphically. It covers the listed topics given below- Regular Expression, Finite Automata, Context Free Grammar, Push Down Automata, **Turing** **Machine**, Exercise of the topics, Mock test.

Show more
In this section, first, we expressed intuitively how to create an interpreter **machine** that can receive and simulate all possible gFSA. The notion is put forward intuitively in the sense that a **Turing** **machine** is created without introducing gFSA encoding into an alphabet and then fed into a **Turing** **machine**. Our goal is to make it easier to introduce this **Turing** **machine**. Secondly, we wrote it in a formal form with the input encoding of the **Turing** **machine** so that it meets a formal definition. The construction of a **Turing** **machine** that can accept all of the gFSA is expressed intuitively as follows:

Show more
It has a one-way infinite read/write tape, a head that it uses for reading and writing on the cells of the tape and a register that holds the state of the **machine**. A single computation step is described by one application of the transition function: it reads a symbol in a specific state, and then writes down a symbol on that location, gets into some state and the head moves to the left, right or stays on that location.

54 Read more

The
Robotic
Turing
Test.
But
was
the
language‐only
Turing
Test,
T2,
really
the
one
Turing
intended
(or
should
have
intended)?
After
all,
if
the
essence
of
Turing’s
“cognition
is
as
cog[r]

11 Read more

We note that the measure of width complexity in the case of circuits is related to the measure of space complexity in the case of **Turing** machines. Indeed, we can transform a **Turing** **machine** M that requires space s on inputs of length n into a circuit of width O(n +s); similarly, a circuit of width w can be simulated by a **Turing** **machine** which takes space at most O(w). Moreover, there are actually major similarities between the security proofs of [HJO + 16] (for their width- dependent adaptive garbling scheme) and [BGL + 15] (for their space-dependent succinct garbling

Show more
53 Read more

Unfortunately the depth of this idea has been obscured by the interpretation of the test given by John Searle in his mental experiment of the Chinese Room. Searle’s challenge to artifi- cial intelligence was exactly a critique of the concept of “sym- bol manipulation”, considered literally as working with sym- bols detached from any real interaction with the environment. In Searle’s mental experiment an English speaker has some instructions in English to take Chinese symbols as input and is to give some other symbols as output; the rules in English per- mit the English speaker to produce as output reasonable an- swers to the questions in Chinese. A Chinese speaker therefore would understand the answers to her questions produced by this procedure, thinking that whoever is inside the room under- stands Chinese. It is apparently a rhetorical presentation of the **Turing** test with the aim of depriving the test of its significance. In fact, Searle asks whether we can say that the man in the room understands Chinese. Certainly not! He understands Eng- lish, and is able to use rules (formal or not) to give as output some patterns of Chinese symbols as answers to other patterns of Chinese symbols taken as input, without having any idea of what those symbols may mean. Symbol manipulation is not understanding language! What is missing is the understanding on the meaning of the Chinese symbols and the intentionality, that is the ability to understand what a symbol refers to. The English speaker inside the room has no idea what the Chinese symbols refer to; he only knows how to manipulate symbols, he is only using a syntactic ability without semantics.

Show more
Indistinguishability Obfuscation. Constructing iO for TMs given miFE for TM is straightforward, and adapts the miFE to iO circuit compiler by [GGG + 14] to the TM setting. As in the circuit case, an miFE for TM that supports two ciphertext queries and single key query suffices for this transformation. Please see Section 5 for details. Since our security proof for miFE for TM is tight, this compiler yields iO for TM from sub-exponentially secure FE for circuits rather than sub-exponentially secure iO for circuits. Organization of the paper. The paper is organized as follows. In Section 2 we provide the definitions and preliminaries used by our constructions. In Section 3, we provide our construction for single input FE for **Turing** machines. In Section 4, we provide our construction for multi-input FE for **Turing** machines for any fixed arity k and in Section 5 we describe the construction of iO for **Turing** machines for bounded inputs. Our constructions use constrained PRFs which are instantiated in Appendix D and decomposable FE which is constructed in Appendix F.

Show more
70 Read more

A Turing Machine needs a 'list representation' for both its paper tape and its sequence of instructions.. This first example shows how to represent the sequence of binary numbers on the [r]

28 Read more

The **Turing** test extends this polite convention to machines: don’t ask the question "can M think?" If a **machine** acts as intelligently as a human being, then it is intelligent and it should lay aside the mystery about consciousness for the moment. **Turing** declared in [1] that "I do not wish to give the impression that I think there is no mystery about consciousness.""But I do not think these mysteries necessarily need to be solved before we can answer the question (Can machines think?) with which we are concerned in this paper." **Turing** test's idea is the correct basic concepts of AI and is consistent with the approximate separability hypothesis of the whole and the definition of AI. On today's vibrant internet, chatbots, which serve customers, have exceeded Turing's expectations in their ability to talk to people.

Show more
10 Read more

I would like to warmly thank Joel Hamkins for suggesting to me the idea of doing Kleene’s O in the infinite time **Turing** **machine** setting; for providing guidance and ideas – many of the results reported below were anticipated by him; for reading and commenting extensively on several earlier drafts of this thesis; finally, but not least, his great interest in my work all along the way, and his vitality and passion for mathematics, was an indispensable source of inspiration. Further, I would like to thank Benedikt L¨ owe for letting me change thesis topic at a late stage; for providing guidance in my individual study projects during my time at the ILLC; for spawning my interest in infinite time **Turing** machines, and for convincing me to come to Amsterdam. I would also like to thank Dick de Jongh for wanting to sit on my thesis committee, and for providing support as my academic mentor. Finally, I want to thank Peter Koepke and the Hausdorff Center for Mathematics in Bonn for inviting me to Bonn International Workshop for Ordinal Computability.

Show more
61 Read more

The Robotic **Turing** Test. But was the language-‐only **Turing** Test, T2, really the one **Turing** intended (or should have intended)? After all, if the essence of Turing’s “cognition is as cognition does” criterion is **Turing**-‐indistinguishability from what a human cognizer can do, then a human cognizer can certainly do a lot more than just produce and understand language. A human cognizer can do countless other kinds of things in the real world of objects, actions, events, states and traits, and if the T2 candidate could not do all those kinds of things too, then that incapacity would be immediately detectable, and the candidate would fail the test. To be able to do all those things successfully, the T2 candidate would have to be a lot more than just a computer: It would have to be a sensorimotor robot, capable of sensing and acting upon all those objects, etc. -‐-‐ again **Turing**-‐indistinguishably from the way real human cognizers do.

Show more
10 Read more

BotPrize Turing test in board games chess Turing test in video games UT2004 Player modelling and mimic player types The goal of game AI When the goals merge, a reversed Turing test in Sp[r]

22 Read more

In 1936, **Turing** developed his theoretical computational model [18]. The deterministic and nondeterministic **Turing** machines have become in two of the most important definitions related to this theoretical model for computation [18]. A deterministic **Turing** **machine** has only one next action for each step defined in its program or transition function [18]. A nondeterministic **Turing** **machine** could contain more than one action defined for each step of its program, where this one is no longer a function, but a relation [18].

Another interesting application of the algorithmic the- ory of randomness is the following explanation why the bulk of work in **machine** learning under the gen- eral iid assumption (such as statistical learning theory and PAC theory) has been done in the batch setting. (The on-line setting has also been very popular, eg, in the theory of prediction with expert advice, but it uses dierent assumptions.) The algorithmic theory of ran- domness implies that on-line prediction under the iid

10 Read more