Related papers: The Busy Beaver Competition: a historical survey

It is common practice to compare the computational power of different models of computation. For example, the recursive functions are strictly more powerful than the primitive recursive functions, because the latter are a proper subset of…

One of the elegant achievements in the history of proof theory is the characterization of the provably total recursive functions of an arithmetical theory by its proof-theoretic ordinal as a way to measure the time complexity of the…

The field of computational complexity is concerned both with the intrinsic hardness of computational problems and with the efficiency of algorithms to solve them. Given such a problem, normally one designs an algorithm to solve it and sets…

Many programmers belive that Turing-based machines cannot think. We also believe in this, however it is interesting to note that the most sophisticated machines are not programmed by human beings. We have only discovered them. In this…

The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to…

We prove nonhalting of the Turing machine dubbed "Skelet #17", known to be one of the toughest 5-state, 2-symbol Turing machines to analyze. Combined with the efforts of The Busy Beaver Challenge, we are therefore able to show that BB(5),…

We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…

We revisit the problem of computing with noisy information considered in Feige et al. 1994, which includes computing the OR function from noisy queries, and computing the MAX, SEARCH and SORT functions from noisy pairwise comparisons. For…

What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical…

Previous approaches to systematic state-space exploration for testing multi-threaded programs have proposed context-bounding and depth-bounding to be effective ranking algorithms for testing multithreaded programs. This paper proposes two…

We report on the recent Loebner prize competition inspired by Turing's test of intelligent behavior. The presentation covers the structure of the competition and the outcome of its first instantiation in an actual event, and an analysis of…

In 1953, Lloyd Shapley defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that competitive stochastic games have a discounted value. In 1982, Jean-Fran\c{c}ois Mertens and…

We consider the approval-based model of elections, and undertake a computational study of voting rules which select committees whose size is not predetermined. While voting rules that output committees with a predetermined number of winning…

We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of…

Sophistication and logical depth are two measures that express how complicated the structure in a string is. Sophistication is defined as the minimal complexity of a computable function that defines a two-part description for the string…

The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be…

In this paper we develop a classification of real functions based on growth rates of repeated iteration. We show how functions are naturally distinguishable when considering inverses of repeated iterations. For example, $n+2\to 2n\to 2^n\to…

Anyone who has tried to memorize a one-hundred-digit number can attest that the human brain acquires abstract information slowly. However, following a three-decade increase of results at memory competitions, the best competitors manage to…

By closely rereading the original Turing's 1936 article, we can gain insight about that it is based on the claim to have defined a number which is not computable, arguing that there can be no machine computing the diagonal on the…

This work is a continuation of efforts to define and understand competitive analysis of algorithms in a distributed shared memory setting, which is surprisingly different from the classical online setting. In fact, in a distributed shared…