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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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Cited by 9 (4 self)
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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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On the computational complexity of spiking neural P systems
 In 7th International Conference on Unconventional Computation (UC 2008), volume 5204 of LNCS
, 2008
"... Abstract. It is shown here that there is no standard spiking neural P system that simulates Turing machines with less than exponential time and space overheads. The spiking neural P systems considered here have a constant number of neurons that is independent of the input length. Following this, we ..."
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Cited by 3 (3 self)
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Abstract. It is shown here that there is no standard spiking neural P system that simulates Turing machines with less than exponential time and space overheads. The spiking neural P systems considered here have a constant number of neurons that is independent of the input length. Following this, we construct a universal spiking neural P system with exhaustive use of rules that simulates Turing machines in linear time and has only 10 neurons. 1
TILING SIMPLY CONNECTED REGIONS WITH RECTANGLES
"... Abstract. In 1995, Beauquier, Nivat, Rémila, and Robson showed that tiling of general regions with two rectangles is NPcomplete, except for a few trivial special cases. In a different direction, in 2005, Rémila showed that for simply connected regions by two rectangles, the tileability can be solve ..."
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Cited by 3 (3 self)
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Abstract. In 1995, Beauquier, Nivat, Rémila, and Robson showed that tiling of general regions with two rectangles is NPcomplete, except for a few trivial special cases. In a different direction, in 2005, Rémila showed that for simply connected regions by two rectangles, the tileability can be solved in quadratic time (in the area). We prove that there is a finite set of at most 10 6 rectangles for which the tileability problem of simply connected regions is NPcomplete, closing the gap between positive and negative results in the field. We also prove that counting such rectangular tilings is #Pcomplete, a first result of this kind. 1.
A Concrete View of Rule 110 Computation
, 906
"... Rule 110 is a cellular automaton that performs repeated simultaneous updates of an infinite row of binary values. The values are updated in the following way: 0s are changed to 1s at all positions where the value to the right is a 1, while 1s are changed to 0s at all positions where the values to th ..."
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Rule 110 is a cellular automaton that performs repeated simultaneous updates of an infinite row of binary values. The values are updated in the following way: 0s are changed to 1s at all positions where the value to the right is a 1, while 1s are changed to 0s at all positions where the values to the left and right are both 1. Though trivial to define, the behavior exhibited by Rule 110 is surprisingly intricate, and in [1] we showed that it is capable of emulating the activity of a Turing machine by encoding the Turing machine and its tape into a repeating left pattern, a central pattern, and a repeating right pattern, which Rule 110 then acts on. In this paper we provide an explicit compiler for converting a Turing machine into a Rule 110 initial state, and we present a general approach for proving that such constructions will work as intended. The simulation was originally assumed to require exponential time, but surprising results of Neary and Woods [2] have shown that in fact, only polynomial time is required. We use the methods of Neary and Woods to exhibit a direct simulation of a Turing machine by a tag system in polynomial time. 1 Compiling a Turing machine into a Rule 110 State In this section we give a concrete algorithm for compiling a Turing machine and its tape into an initial state for Rule 110, following the construction given in [1]. We will create an initial state that will eventually
Some Considerations on Universality
, 906
"... The paper puts into discussion the concept of universality, in particular for structures not of the power of Turing computability. The question arises if for such structures a universal structure of the same kind exists or not. For that the construction of universal Turing machines and those with so ..."
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The paper puts into discussion the concept of universality, in particular for structures not of the power of Turing computability. The question arises if for such structures a universal structure of the same kind exists or not. For that the construction of universal Turing machines and those with some constraints are presented in some detail. 1
Zeno Squeezing of Cellular Automata
 INT. JOURN. OF UNCONVENTIONAL COMPUTING, VOL. 6, PP. 399–416
, 2010
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"... Abstract. In search of a single number like Shannon’s statesymbol product to compare the complicacy of Turing Machines including those with multiple tapes and tape heads, a number called TM index is proposed, using a generic definition for single and multi tape machines. Several examples are shown ..."
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Abstract. In search of a single number like Shannon’s statesymbol product to compare the complicacy of Turing Machines including those with multiple tapes and tape heads, a number called TM index is proposed, using a generic definition for single and multi tape machines. Several examples are shown together with their TM indices, including the recently rediscovered physical
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.