Showing papers on "Non-deterministic Turing machine published in 2020"
1 Jun 2020
TL;DR: In this article, it was shown that polarizationless P-systems with charges are able to simulate a deterministic Turing machine working in polynomial time with a weaker uniformity condition and using only one level of membrane nesting.
Abstract: It is known that the polarizationless P systems of the kind involved in the definition of the P conjecture are able to solve problems in the complexity class $$\textsf {P}$$ by leveraging their uniformity condition. Here, we show that they are indeed able to simulate a deterministic Turing machine working in polynomial time with a weaker uniformity condition and using only one level of membrane nesting. This allows us to embed this construction into more complex membrane structures, possibly showing that constructions similar to the one performed for P systems with charges can be carried on.
13 citations
1 Jan 2020
TL;DR: This chapter presents several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques.
Abstract: Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. A solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI.
1 Sep 2020
TL;DR: This paper argues that humans' success as a species is due to Turing completeness, the ability to compute and solve problems through software, making it evolutionarily disruptive and explaining our unique cognitive characteristics and population growth.
Abstract: Why are we so many? Or, in other words, Why is our species so successful? The ultimate cause of our success as species is that we, Homo sapiens, are the first and the only Turing complete species. Turing completeness is the capacity of some hardware to compute by software whatever hardware can compute.
To reach the answer, I propose to see evolution and computing from the problem solving point of view. Then, solving more problems is evolutionarily better, computing is for solving problems, and software is much cheaper than hardware, resulting that Turing completeness is evolutionarily disruptive. This conclusion, together with the fact that we are the only Turing complete species, is the reason that explains why we are so many.
Most of our unique cognitive characteristics as humans can be derived from being Turing complete, as for example our complete language and our problem solving creativity.
To reach the answer, I propose to see evolution and computing from the problem solving point of view. Then, solving more problems is evolutionarily better, computing is for solving problems, and software is much cheaper than hardware, resulting that Turing completeness is evolutionarily disruptive. This conclusion, together with the fact that we are the only Turing complete species, is the reason that explains why we are so many.
Most of our unique cognitive characteristics as humans can be derived from being Turing complete, as for example our complete language and our problem solving creativity.
TL;DR: Turing's work on computation is presented as instituting a new stage in the long history of writing, characterized by the emergence of new forms and the constitution of computer science.
Abstract: Turing, from the Paradigm of Formal Writing to the Non-Written Emergence of Forms. The article is an introduction to the “Looking back at Turing : His Heritage Today” special issue # 72 of the review Intellectica and defends a new interpretation of Turing’s work : far from considering computation in an abstract way without taking into consideration its anthropological conditions of possibility, computation thereby appears as instituting a new stage in the long history of writing. Turing’s intellectual development which thus takes shape is not that of the discovery and application of computation in an undifferentiated way whatever the field of determination but an exploration in three phases going from the formalist notion of computation to the constitution of computer science and the further study of the emergence of biological forms. Hence the three parts of the issue that the introduction describes : computability ; cryptology and natural and social dynamics ; morphogenesis in theoretical biology. The internal coherence of Turing's development is hence grasped, based on the constantly reworked polarities of the computable and the uncomputable, the predictive and the non-predictive, the logico-arithmetic of the discrete and the geometry of the continuous, the written and the unwritten. It is in the light of these polarities that the influence of Turing is measured today.
TL;DR: The Cook-Levin Theorem is revisited but using a completely different approach to prove the theorem, which showed that Boolean satisfiability problem is NP-complete through the reduction of polynomial time algorithms for NP-completeness and circuit-SAT.
Abstract: Stephen Cook and Leonard Levin independently proved that there are problems called NonPolynomial-complete (NP-complete) problems. The theorem is today referred to as Cook-Levin theorem. The theorem states that Boolean satisfiability problem is NP-complete. That is to say, any problem in NP can be reduced in polynomial time by a deterministic Turing machine to the problem of determining whether a Boolean formula is satisfiable. Therefore, if there exists a deterministic polynomial time algorithm for solving a Boolean satisfiability, then there exists a deterministic polynomial time algorithm for solving all problems in NP. Thus Cook-Levin theorem provides a proof that the problem of SAT is NP-complete via reduction technique. In this paper, we revisit Cook-Levin Theorem but using a completely different approach to prove the theorem. The approach used combines the concepts of NP-completeness and circuit-SAT. Using this technique, we showed that Boolean satisfiability problem is NP-complete through the reduction of polynomial time algorithms for NP-completeness and circuit-SAT.