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Small semiweakly universal Turing machines
 Machines, Computations and Universality (MCU), volume 4664 of LNCS
, 2007
"... Abstract. We present three small universal Turing machines that have 3 states and 7 symbols, 4 states and 5 symbols, and 2 states and 13 symbols, respectively. These machines are semiweakly universal which means that on one side of the input they have an infinitely repeated word, and on the other s ..."
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Abstract. We present three small universal Turing machines that have 3 states and 7 symbols, 4 states and 5 symbols, and 2 states and 13 symbols, respectively. These machines are semiweakly universal which means that on one side of the input they have an infinitely repeated word, and on the other side there is the usual infinitely repeated blank symbol. This work can be regarded as a continuation of early work by Watanabe on semiweak machines. One of our machines has only 17 transition rules, making it the smallest known semiweakly universal Turing machine. Interestingly, two of our machines are symmetric with Watanabe’s 7state and 3symbol, and 5state and 4symbol machines, even though we use a different simulation technique. 1.
Small weakly universal Turing machines
"... Abstract. We give small universal Turing machines with statesymbol pairs of (6, 2), (3,3) and (2,4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest ..."
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Cited by 7 (4 self)
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Abstract. We give small universal Turing machines with statesymbol pairs of (6, 2), (3,3) and (2,4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest known weakly universal Turing machines. Despite their small size these machines are efficient polynomial time simulators of Turing machines. 1
The complexity of small universal Turing machines: a survey
 In SOFSEM 2012: Theory and Practice of Computer Science
, 2012
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Simplicity via Provability for Universal Prefixfree Turing Machines
, 2008
"... Universality is one of the most important ideas in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more complex than it may appear at a first glance. In this note w ..."
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Universality is one of the most important ideas in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more complex than it may appear at a first glance. In this note we review recent results in Algorithmic Information Theory and propose three new criteria of simplicity for universal prefixfree Turing machines. These criteria refer to the possibility of proving various natural properties of such a machine (its universality, for example) in a formal theory, PA or ZFC. In all cases some, but not all, machines are simple.
NatureLike Computation and a Measure of Programmability
, 2012
"... I will propose an alternative behavioural definition of computation (naturelike) based on whether a system is capable of reacting to the environment—the input—as reflected in a measure of programmability. This will be done by using a phase transition coefficient previously defined in an attempt to ..."
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I will propose an alternative behavioural definition of computation (naturelike) based on whether a system is capable of reacting to the environment—the input—as reflected in a measure of programmability. This will be done by using a phase transition coefficient previously defined in an attempt to characterise the dynamical behaviour of cellular automata and other rulebased systems. The transition coefficient measures the sensitivity of a system to external stimuli and will be used to define the susceptibility of a system to being (efficiently) programmed.