A simple reversible Turing machine with four states, three symbols and no halting configuration is constructed that has no periodic orbit, simplifying a construction by Blondel, Cassaigne and Nichitiu and positively answering a conjecture by Kari and Ollinger. The constructed machine has other interesting properties: it is symmetric both for space and time and has a topologically minimal associ...

Turing wrote that the "guiding principle" of his investigation into the possibility of intelligent machinery was "The analogy [of machinery that might be made to show intelligent behavior] with the human brain." (Turing 1948) In his discussion of the investigations that Turing said were guided by this analogy, however, he employs a more farreaching analogy: he eventually expands the analogy fro...

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Turing machines are playing an increasingly significant role in Computer Science domains such as bioinformatics. Instead of directly formulating a solution to a problem, a Turing machine which produces a solution algorithm is generated. The original problem is reduced to that of inducing an acceptor for a recursively enumerable language or a Turing machine transducer. This paper reports on a ge...

In the 1960’s Gisbert Hasenjaeger built Turing Machines from electromechanical relays and uniselectors. Recently, Glaschick reverse engineered the program of one of these machines and found that it is a universal Turing machine. In fact, its program uses only four states and two symbols, making it a very small universal Turing machine. (The machine has three tapes and a number of other features...

We present a variant with no control states of the Turing machine model of computation in which, at each computation step, the operation to be performed next is determined by the symbol currently scanned and by a bounded-length suffix of the sequence of the operations already executed on the tape. We show that our variant is Turing complete, i.e., it can simulate any (standard) Turing machine. ...

We show that, for all reasonable functions T (n) = o(n log n), we can algorithmically verify whether a given one-tape Turing machine runs in time at most T (n). This is a tight bound on the order of growth for the function T because we prove that, for T (n) ≥ (n+1) and T (n) = Ω(n log n), there exists no algorithm that would verify whether a given one-tape Turing machine runs in time at most T ...

Synchronized alternating machine is an alternating machine with a special subset of internal states called synchronizing states. This paper introduces a four-dimensional synchronized alternating Turing machine (4-SATM ), and investigates fundamental properties of 4-SATM ’s. The main topics of this paper are: (1) a relationship between the accepting powers of 4-SATM ’s and four-dimensional alter...

Synchronized alternating machine is an alternating machine with a special subset of internal states called synchronizing states. This paper introduces a four-dimensional synchronized alternating Turing machine (4-SATM ), and investigates fundamental properties of 4-SATM ’s. The main topics of this paper are: (1) a relationship between the accepting powers of 4-SATM ’s and four-dimensional alter...

This paper proposes Neural Network architecture for implementing associative memory. A new model has been developed that has good learning structure and high storage capacity. Hybrid Network Learning comprises interactive counter propagation network and associative memory. Interactive counter propagation network is used for pattern completion. The associative memory is applied for pattern assoc...