We enhance the notion of a computation of the classical theory of computing with the notion of interaction from concurrency theory. In this way, we enhance a Turing machine as a model of computation to a Reactive Turing Machine that is an abstract model of a computer as it is used nowadays, always interacting with the user and the world.

In this note we prove that any Turing machine which uses only a finite computational space for every input cannot solve an uncomputable problem even in case it runs in accelerated mode. We also propose two ways to define the language accepted by an accelerated Turing machine. Accordingly, the classes of languages accepted by accelerated Turing machines are the closure under Boolean operations o...

This paper introduces a new, finer space complexity measure of computations on Turing machines. The complexity of a computation on a Turing machine now takes into account also the capacity of the finite control. It is proved that a slight enlarging (by an additive constant) of the complexity bound increases the computing power. The proofs are based on a new principle of diagonalization. The res...

We consider graph Turing machines, a model of parallel computation on a graph, in which each vertex is only capable of performing one of a finite number of operations. This model of computation is a natural generalization of several well-studied notions of computation, including ordinary Turing machines, cellular automata, and parallel graph dynamical systems. We analyze the power of computatio...

A universal deterministic inhibitor Petri net with 14 places, 29 transitions and 138 arcs was constructed via simulation of Neary and Woods’ weakly universal Turing machine with 2 states and 4 symbols; the total time complexity is exponential in the running time of their weak machine. To simulate the blank words of the weakly universal Turing machine, a couple of dedicated transitions insert th...

Many years ago I was invited to give a lecture on what is today called " computer science " at a large eastern university. I titled my lecture " Turing machines " , because the most famous abstract model of a computer is the model presented by Alan Turing. Today biographies of Turing are reviewed in the New York Times, but in those early days of the computer Turing was virtually unheard of. Thu...

Many years ago I was invited to give a lecture on what is today called " computer science " at a large eastern university. I titled my lecture " Turing machines " , because the most famous abstract model of a computer is the model presented by Alan Turing. Today biographies of Turing are reviewed in the New York Times, but in those early days of the computer Turing was virtually unheard of. Thu...

i? recent years the need for a rigorous formaliza!ion’hbf the mathematical properties of computer programs has become increasingly evident. Problems in program proving, for exampie, require that a precise meanir!.: be given to otherwise intuitive notions. One such formalization has been suggested by Milner [6] and has been successfully used in areas such as program and machine verification (see...

We obtain the first deterministic randomness extractors for n-bit sources with minentropy ≥ n1−α generated (or sampled) by single-tape Turing machines running in time n2−16α, for all sufficiently small α > 0. We also show that such machines cannot sample a uniform n-bit input to the Inner Product function together with the output. The proofs combine a variant of the crossing-sequence technique ...

Recently, Neural Turing Machine and Memory Networks have shown that adding an external memory can greatly ameliorate a traditional recurrent neural network’s tendency to forget after a long period of time. Here we present a new design of an external memory, wherein memories are stored in an Euclidean key space R. An LSTM controller performs read and write via specialized structures called read ...