A Theoretical Computer Science Perspective on Free Will

We consider the paradoxical concept of free will from the perspective of Theoretical Computer Science (TCS), a branch of mathematics concerned with understanding the underlying principles of computation and complexity, including the implications and surprising consequences of resource limitations.Comment: arXiv admin note: text overlap with arXiv:2107.1370

A Theory of Consciousness from a Theoretical Computer Science Perspective: Insights from the Conscious Turing Machine

The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. We examine consciousness from the perspective of theoretical computer science (TCS), a branch of mathematics concerned with understanding the underlying principles of computation and complexity, including the implications and surprising consequences of resource limitations. In the spirit of Alan Turing's simple yet powerful definition of a computer, the Turing Machine (TM), and perspective of computational complexity theory, we formalize a modified version of the Global Workspace Theory (GWT) of consciousness originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, Jean-Pierre Changeaux and others. We are not looking for a complex model of the brain nor of cognition, but for a simple computational model of (the admittedly complex concept of) consciousness. We do this by defining the Conscious Turing Machine (CTM), also called a conscious AI, and then we define consciousness and related notions in the CTM. While these are only mathematical (TCS) definitions, we suggest why the CTM has the feeling of consciousness. The TCS perspective provides a simple formal framework to employ tools from computational complexity theory and machine learning to help us understand consciousness and related concepts. Previously we explored high level explanations for the feelings of pain and pleasure in the CTM. Here we consider three examples related to vision (blindsight, inattentional blindness, and change blindness), followed by discussions of dreams, free will, and altered states of consciousness.Comment: arXiv admin note: text overlap with arXiv:2011.0985

Computation with Advice

Computation with advice is suggested as generalization of both computation with discrete advice and Type-2 Nondeterminism. Several embodiments of the generic concept are discussed, and the close connection to Weihrauch reducibility is pointed out. As a novel concept, computability with random advice is studied; which corresponds to correct solutions being guessable with positive probability. In the framework of computation with advice, it is possible to define computational complexity for certain concepts of hypercomputation. Finally, some examples are given which illuminate the interplay of uniform and non-uniform techniques in order to investigate both computability with advice and the Weihrauch lattice

Computing over the Reals: Where Turing meets Newton

The classical (Turing) theory of computation has been extraordinarily successful in providing the foundations and framework for theoretical computer science. Yet its dependence on 0s and 1s is fundamentally inadequate for providing such a foundation for modern scientific computation, in which most algorithms—with origins in Newton, Euler, Gauss, et al.—are real number algorithms. In 1989, Mike Shub, Steve Smale, and I introduced a theory of computation and complexity over an arbitrary ring or field R [BSS89]. If R is Z2 = ({0, 1},+,·), the classical computer science theory is recovered. If R is the field of real numbers R, Newton’s algorithm, the paradigm algorithm of numerical analysis, fits naturally into our model of computation. Complexity classes P, NP and the fundamental question “Does P=NP? ” can be formulated naturally over an arbitrary ring R. The answer to the fundamental question depends in general on the complexity of deciding feasibility of polynomial systems over R. When R is Z2, this becomes the classical satisfiability problem of Cook–Levin [Cook71, Levin73]. When R is the field of complex numbers C, the answer depends on the complexity of Hilbert’s Nullstellensatz. The notion of reduction between problems (e.g., between traveling salesman and satisfiability) ha

As the Culture of Computing Evolves, Similarity can be the Difference

this article. Brief Background In 1995, just 7% (7 out of 96) of the entering freshmen CS majors were women. Since 1999, about a third of the entering CS class (on average, 45 out of 132) each year has Research supported by a grant from the Alfred P. Sloan Foundatio

Complexity and real computation

xvi, 453 p. : ill. ; 21x30 cm

CS4HS: An Outreach Program for High School CS Teachers

In this paper, we describe a pilot summer workshop (CS4HS) held at Carnegie Mellon University in July 2006 for high school CS teachers to provide compelling material that the teachers can use in their classes to emphasize computational thinking and the many possibilities of computer science. Diversity and broadening participation was explicitly addressed throughout the workshop. We focused on broadening the image of what CS is – and who computer scientists are – since the reasons for underrepresentation in the field are very much the same as the reasons for the huge decline in interest. We describe the design of the workshop along with results from initial surveys and evaluations. Short-term evaluations show that this workshop was successful in changing the perception of CS for these teachers and giving them the impetus to include broader topics in their programming courses for the upcoming school year. Future surveys will track the long-term effect of this workshop