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Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
Encouraged by significant advances in algorithms and tools for verification and analysis, high level modeling and programming techniques, natural language programming, etc., we feel it is time for a major change in the way complex software…
Physical processes are computations only when we use them to externalize thought. Computation is the performance of one or more fixed processes within a contingent environment. We reformulate the Church-Turing thesis so that it applies to…
There are inherent limits in classical computation for it to serve as an adequate model of human cognition. In particular, non-commutativity, while ubiquitous in physics and psychology, cannot be sufficiently handled. We propose that we…
The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of…
We believe that economic design and computational complexity---while already important to each other---should become even more important to each other with each passing year. But for that to happen, experts in on the one hand such areas as…
A century ago, discoveries of a serious kind of logical error made separately by several leading mathematicians led to acceptance of a sharply enhanced standard for rigor within what ultimately became the foundation for Computer Science. By…
Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative.…
Since the Turing test was first proposed by Alan Turing in 1950, the primary goal of artificial intelligence has been predicated on the ability for computers to imitate human behavior. However, the majority of uses for the computer can be…
Computation has changed the world more than any previous expressions of knowledge. In its particular algorithmic embodiment, it offers a perspective, within which the digital computer (one of many possible) exercises a role reminiscent of…
The "easy" problem of cognitive science is explaining how and why we can do what we can do. The "hard" problem is explaining how and why we feel. Turing's methodology for cognitive science (the Turing Test) is based on doing: Design a model…
The primordial model of quantum computation was introduced over thirty years ago and the first quantum algorithms have appeared for over twenty years. Yet the exact architectures for quantum computer seem foreign to an undergraduate student…
Quantum physics is surprising in many ways. One surprise is the threat to locality implied by Bell's Theorem. Another surprise is the capacity of quantum computation, which poses a threat to the complexity-theoretic Church-Turing thesis. In…
Hypercomputational formal theories will, clearly, be both structurally and foundationally different from the formal theories underpinning computational theories. However, many of the maps that might guide us into this strange realm have…
Human societies continuously transform scattered information into collective judgments and coordinated action, whether through markets discovering prices, governments allocating resources, communities enforcing norms, or science converging…
In a recent article, Luciano Floridi explains his view of Turing's legacy in connection to the philosophy of information. I will very briefly survey one of Turing's other contributions to the philosophy of information and computation,…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. This paper studies consciousness from the perspective of theoretical computer science. It…
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…
We recall from previous work a model-independent framework of computational complexity theory. Notably for the present paper, the framework allows formalization of the issues of precision that present themselves when one considers physical,…