We enhance the notion of a computation of the classical theory of computing with the notion of interaction. 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.

: From the physico-mathematical view point, the imitation game between man and machine, proposed by Turing in 1950, is a game between a discrete and a continuous system. Turing stresses several times the laplacian nature of his discrete-state machine, yet he tries to show the undetectability of a functional imitation, by his machine, of a system (the brain) that, in his words, is not a discrete...

Ohya and Volovich have proposed a new quantum computation model with chaotic amplification to solve the SAT problem, which went beyond usual quantum algorithm. In this paper, we generalize quantum Turing machine, and we show in this general quantum Turing machine (GQTM) that we can treat the Ohya-Volovich (OV) SAT algorithm.

This paper describes the simulation of an S(n) spacebounded deterministic Turing machine by a reversible Turing machine operating in space S(n). It thus answers a question posed by Bennett in 1989 and refutes the conjecture, made by Li and Vitanyi in 1996, that any reversible simulation of an irreversible computation must obey Bennett’s reversible pebble game rules.

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...