Verification of composed web service using Synthesized Nondeterministic Turing Model (SNTMM) with Multiple Tapes and Stacks

To verify the composed Web services, a general view of what traits of a service need to be identified is still lacking. The existing verification model did not address any mechanism for getting alternative services if we failed to reach the desired service and partially concentrated on the reachability problem for a deterministic and non-deterministic system in sequential. This paper proposes a Synthesised Non-deterministic Turing Machine Model (SNTMM) by combining the Multistacked Non-deterministic Turing Machine (MSNTM) model and Multitaped Non-deterministic Turing Machine (MTNTM) model to verify the composed Web services for both deterministic and non-deterministic systems in parallel. The deceased transition and departed service marking algorithm have been proposed to address each participated service’s reachability in composing service for all possible input in parallel. This article shows an example to demonstrate the meticulousness of the model. The experimental results show that the performance of the proposed model is measured efficiently

A Note on Non-deterministic Turing Machine and the "P vs. NP ( P versus NP problem )"

摘要：一个非确定型图灵机NDTM的计算过程，可以相当于其对应的确定型图灵机DTM的幂集。如果接受ZF公理系统的幂集公理，“P对NP”问题最可能的答案是：对于确定型图灵机，P≠NP。可以从另外3个角度对它进行一定的解释。ABSTRACT: The calculation process of a non-deterministic Turing machine (NDTM) can be equipotent to the power set of its corresponding deterministic Turing machine (DTM). If accepting the “Axiom of power set” of the ZF axiom system ( Zermelo–Fraenkel set theory ), the most likely answer to the "P vs. NP" ( P versus NP problem ) is: For a deterministic Turing machine, P≠NP ( P is not equal to NP ). This answer can be explained from three other perspectives.

A Short Essay towards if P not equal NP

We find a computational algorithmic task and prove that it is solvable in polynomial time by a non-deterministic Turing machine and cannot be solved in polynomial time by any deterministic Turing machine. The point is that our task does not look as very canonical one and if it may be classified as computational problem in standard terms

Axiomatizing Rectangular Grids with no Extra Non-unary Relations

We construct a first-order formula φ such that all finite models of φ are non-narrow rectangular grids without using any binary relations other than the grid neighborship relations. As a corollary, we prove that a set A ⊆ ℕ is a spectrum of a formula which has only planar models if numbers n ∈ A can be recognized by a non-deterministic Turing machine (or a one-dimensional cellular automaton) in time t(n) and space s(n), where t(n)s(n) ≤ n and t(n); s(n) = Ω(log(n)).

A restricted second-order logic for non-deterministic poly-logarithmic time

We introduce a restricted second-order logic $\textrm{SO}^{\textit{plog}}$ for finite structures where second-order quantification ranges over relations of size at most poly-logarithmic in the size of the structure. We demonstrate the relevance of this logic and complexity class by several problems in database theory. We then prove a Fagin’s style theorem showing that the Boolean queries which can be expressed in the existential fragment of $\textrm{SO}^{\textit{plog}}$ correspond exactly to the class of decision problems that can be computed by a non-deterministic Turing machine with random access to the input in time $O((\log n)^k)$ for some $k \ge 0$, i.e. to the class of problems computable in non-deterministic poly-logarithmic time. It should be noted that unlike Fagin’s theorem which proves that the existential fragment of second-order logic captures NP over arbitrary finite structures, our result only holds over ordered finite structures, since $\textrm{SO}^{\textit{plog}}$ is too weak as to define a total order of the domain. Nevertheless, $\textrm{SO}^{\textit{plog}}$ provides natural levels of expressibility within poly-logarithmic space in a way which is closely related to how second-order logic provides natural levels of expressibility within polynomial space. Indeed, we show an exact correspondence between the quantifier prefix classes of $\textrm{SO}^{\textit{plog}}$ and the levels of the non-deterministic poly-logarithmic time hierarchy, analogous to the correspondence between the quantifier prefix classes of second-order logic and the polynomial-time hierarchy. Our work closely relates to the constant depth quasipolynomial size AND/OR circuits and corresponding restricted second-order logic defined by David A. Mix Barrington in 1992. We explore this relationship in detail.

Application of Algorithmic Manifold to Exponential Time

In the previous paper, I defined algorithmic manifolds simulating polynomial-time algorithms, and I showed topological properties for P problem and NP problem and that NP problem can be transformed into deterministic Turing machine problem. In this paper, I define algorithmic manifolds simulating exponential-time algorithms and, I show topological properties for EXPTIME problem and NEXPTIME problem. I also discuss the relationship between NEXPTIME and deterministic Turing machines.

Can Ai Be Intelligent?

The aim of this paper is an attempt to give an answer to the question what does it mean that a computational system is intelligent. We base on some theses that though debatable are commonly accepted. Intelligence is conceived as the ability of tractable solving of some problems that in general are not solvable by deterministic Turing Machine.

Two-dimensional Kolmogorov complexity and an empirical validation of the Coding theorem method by compressibility

We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluatingn-dimensional complexity by using ann-dimensional deterministic Turing machine. The technique is interesting because it provides a natural algorithmic process for symmetry breaking generating complexn-dimensional structures from perfectly symmetric and fully deterministic computational rules producing a distribution of patterns as described by algorithmic probability. Algorithmic probability also elegantly connects the frequency of occurrence of a pattern with its algorithmic complexity, hence effectively providing estimations to the complexity of the generated patterns. Experiments to validate estimations of algorithmic complexity based on these concepts are presented, showing that the measure is stable in the face of some changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms when both methods overlap in their range of applicability. We then use the output frequency of the set of 2-dimensional Turing machines to classify the algorithmic complexity of the space-time evolutions of Elementary Cellular Automata.

Polynomially Bounded Sequences and Polynomial Sequences

In this article, we formalize polynomially bounded sequences that plays an important role in computational complexity theory. Class P is a fundamental computational complexity class that contains all polynomial-time decision problems [11], [12]. It takes polynomially bounded amount of computation time to solve polynomial-time decision problems by the deterministic Turing machine. Moreover we formalize polynomial sequences [5].

EFFICIENT TESTING OF FORECASTS

Each day a weather forecaster predicts a probability for each type of weather for the next day. After n days, all the predicted probabilities and the real weather data are sent to a test which decides whether to accept the forecaster as having prior knowledge about the distribution of nature. Consider tests that accept with high probability forecasters who know the distribution of nature. Sandroni shows that any such test can be passed with high probability by a forecaster who has no prior knowledge about the distribution of nature, provided that the duration n is revealed to the forecaster in advance [14]. However, Fortnow and Vohra show that Sandroni's result requires forecasters with high computational complexity [6]. Consider the family [Formula: see text] of forecasters who select a deterministic Turing-machine forecaster according to an arbitrary distribution and then use that machine for all future forecasts. We show that Sandroni's result requires forecasters even more powerful than those in [Formula: see text]. We also show that Sandroni's result does not apply when the duration n is not revealed to the forecaster in advance.