Braid is a 2008 puzzle game centered around the ability to reverse time. We show that Braid can simulate an arbitrary computation. Our construction makes no use of Braid’s unique time mechanics, and therefore may apply to many other video games. We also show that a plausible “bounded” variant of Braid lies within 2-EXPSPACE. Our proof relies on a technical lemma about Turing machines which may ...

The recent advances in computer animation, motion image processing, robotics and so on prompted us to analyze computational complexity of four-dimensional pattern processing. Thus, the research of four-dimensional automata as a computational model of four-dimensional pattern processing has also been meaningful. From this viewpoint, we introduced a four-dimensional alternating Turing machine (4-...

In classical computation, any computable function can be computed by a universal Turing machine, and the program is independent of the value of the variable. Trying to generalize this universality to quantum computation, one anticipates that there is a universal quantum Turing machine which can perform any desired unitary transformation on an arbitrary number of qubits, by including a program a...

While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more than a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set X may be coded as a probability pX such that if a Turing machine is given a coin which lands heads with probability pX it can compute any function recursive in X with arbitrarily hig...

The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of enormous benefit in the classical theory of computation. We propose that quantum computation, like its classical counterpart, may benefit from a version of the lam...

The halting problem for Turing machines is decidable on a set of asymptotic probability one. The proof is sensitive to the particular computational model. The halting problem for Turing machines is perhaps the canonical undecidable set. Nevertheless, we prove that there is an algorithm deciding almost all instances of it. The halting problem is therefore among the growing collection of those ex...

ii Preface Prelude The year is 1900. The world's most renowned mathematician, David Hilbert, proposes 10 challenging mathematical problems for the nascent century at the second international congress in Paris. One of these problems, the Entscheidungsproblem, asks if there exists an algorithm that decides whether a first-order statement is derivable from the axioms of first-order predicate calcu...

This paper shows that a constraint on universal Turing machines is necessary for Legg's and Hutter's formal measure of intelligence to be unbiased. Their measure, defined in terms of Turing machines, is adapted to finite state machines. A No Free Lunch result is proved for the finite version of the measure, and this motivates a less

Intelligent nanomechanical devices that operate in an autonomous fashion are of great theoretical and practical interest. Recent successes in building large scale DNA nano-structures, in constructing DNA mechanical devices, and in DNA computing provide a solid foundation for the next step forward: designing autonomous DNA mechanical devices capable of arbitrarily complex behavior. One prototype...

Finite-state transducers are simple theoretical machines that are useful in expressing easilycomputable functions and relations. This investigation considers the relations formed when transducers are iterated arbitrarily many times, a construction which is useful in model checking. In particular, we consider a number of decision problems over various classes of transducers, and attempt to deter...