Two very different insights motivate characterizing the brain as a computer. One depends on mathematical theory that defines computability in a highly abstract sense. Here the foundational idea is that of a Turing machine. Not an actual machine, the Turing machine is really a conceptual way of making the point that any well-defined function could be executed, step by step, according to simple “...

Let UTM(m,n) be the class of universal Turing machine with m states and n symbols. Universal Turing machines are proved to exist in the following classes: UTM(24,2), UTM( 10,3), UTM(7,4), UTM(5,5), UTM(4,6), UTM(3,lO) and UTM(2,18).

During the centennial year of his birth Alan Turing (1912-1954) has been widely celebrated as having laid the foundations for Computer Science, Automated Decryption, Systems Biology and the Turing Test. In this paper we investigate Turing’s motivations and expectations for the development of Machine Intelligence, as expressed in his 1950 article in Mind. We show that many of the trends and deve...

Within the framework of info-computationalism, morphological computation is described as fundamental principle for all natural computation (information processing). Foundations of a New Science of Computation Present computational machinery evolved from mechanical calculators to electronic machines with vacuum tubes and then transistors, and to integrated circuits and eventually microprocessors...

We prove that the complexity of computing the table of primes between 1 and n on a multitape Turing machine is O(n log n).

We wish to present a mirrored language structure (MLS) and four logic rules determined by this structure for the model of a computable Oracle Turing machine. MLS has novel features that are of considerable biological and computational significance. It suggests an algorithm of relation learning and recognition (RLR) that enables the deterministic computers to simulate the mechanism of the Oracle...

The computational power of self-stabilizing distributed systems is examined. Assuming availability of any number of processors, each with (small) constant size memory we show that any computable problem can be realized in a self-stabilizing fashion. The result is derived by presenting a distributed system which tolerates transient faults and simulates the execution of a Turing machine. The tota...

‘Leaf-size’ (or ‘branching’) is the minimum number of leaves of some accepting computation trees of alternating devices. For example, one leaf corresponds to nondeterministic computation. In this paper, we investigate the effect of constant leaves of three-dimensional alternating Turing machines, and show the following facts : (1) For cubic input tapes, k leafand L(m) space-bounded three-dimens...

Modeling efficient algorithms as polynomial size circuits rather than as polynomial time Turing machines has been the rule with few exceptions in cryptographic constructions which provide “secure versions” of general efficient algorithms. A consequence of this modeling is that the resulting “secure version” of an efficient algorithm A incurs the worst-case runtime of A over all inputs of a cert...

The early 1930s were bad years for the worldwide economy, but great years for what would eventually be called Computer Science. In 1932, Alonzo Church at Princeton described his λ-calculus as a formal system for mathematical logic,and in 1935 argued that any function on the natural numbers that can be effectively computed, can be computed with his calculus [4]. Independently in 1935, as a maste...