Results 1  10
of
21
A DNA and restriction enzyme implementation of Turing Machines.
 DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
"... Bacteria employ restriction enzymes to cut or restrict DNA at or near specific words in a unique way. Many restriction enzymes cut the two strands of doublestranded DNA at different positions leaving overhangs of singlestranded DNA. Two pieces of DNA may be rejoined or ligated if their terminal ov ..."
Abstract

Cited by 80 (1 self)
 Add to MetaCart
Bacteria employ restriction enzymes to cut or restrict DNA at or near specific words in a unique way. Many restriction enzymes cut the two strands of doublestranded DNA at different positions leaving overhangs of singlestranded DNA. Two pieces of DNA may be rejoined or ligated if their terminal overhangs are complementary. Using these operations fragments of DNA, or oligonucleotides, may be inserted and deleted from a circular piece of plasmid DNA. We propose an encoding for the transition table of a Turing machine in DNA oligonucleotides and a corresponding series of restrictions and ligations of those oligonucleotides that, when performed on circular DNA encoding an instantaneous description of a Turing machine, simulate the operation of the Turing machine encoded in those oligonucleotides. DNA based Turing machines have been proposed by Charles Bennett but they invoke imaginary enzymes to perform the statesymbol transitions. Our approach differs in that every operation can be pe...
Pcompleteness of cellular automaton Rule 110
 In International Colloquium on Automata Languages and Programming (ICALP), volume 4051 of LNCS
, 2006
"... We show that the problem of predicting t steps of the 1D cellular automaton Rule 110 is Pcomplete. The result is found by showing that Rule 110 simulates deterministic Turing machines in polynomial time. As a corollary we find that the small universal Turing machines of Mathew Cook run in polyn ..."
Abstract

Cited by 20 (7 self)
 Add to MetaCart
(Show Context)
We show that the problem of predicting t steps of the 1D cellular automaton Rule 110 is Pcomplete. The result is found by showing that Rule 110 simulates deterministic Turing machines in polynomial time. As a corollary we find that the small universal Turing machines of Mathew Cook run in polynomial time, this is an exponential improvement on their previously known simulation time overhead.
On the time complexity of 2tag systems and small universal turing machines
 In FOCS; IEEE Computer Society, p 439448
, 2006
"... ..."
(Show Context)
A small fast universal Turing machine
 Theoretical Computer Science
, 2005
"... We present a small timeefficient universal Turing machine with 5 states and 6 symbols. This Turing machine simulates our new variant of tag system. It is the smallest known universal Turing machine that simulates Turing machine computations in polynomial time. ..."
Abstract

Cited by 15 (8 self)
 Add to MetaCart
(Show Context)
We present a small timeefficient universal Turing machine with 5 states and 6 symbols. This Turing machine simulates our new variant of tag system. It is the smallest known universal Turing machine that simulates Turing machine computations in polynomial time.
Four Small Universal Turing Machines
, 2009
"... We present universal Turing machines with statesymbol pairs of (5, 5), (6, 4), (9, 3) and (15, 2). These machines simulate our new variant of tag system, the bitag system and are the smallest known singletape universal Turing machines with 5, 4, 3 and 2symbols, respectively. Our 5symbol machin ..."
Abstract

Cited by 13 (4 self)
 Add to MetaCart
(Show Context)
We present universal Turing machines with statesymbol pairs of (5, 5), (6, 4), (9, 3) and (15, 2). These machines simulate our new variant of tag system, the bitag system and are the smallest known singletape universal Turing machines with 5, 4, 3 and 2symbols, respectively. Our 5symbol machine uses the same number of instructions (22) as the smallest known universal Turing machine by Rogozhin. Also, all of the universal machines we present here simulate Turing machines in polynomial time.
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 ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
(Show Context)
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
 Computability in Europe 2007, volume 4497 of LNCS
, 2007
"... Abstract. We present small polynomial time universal Turing machines with statesymbol pairs of (5, 5), (6, 4), (9, 3) and (18, 2). These machines simulate our new variant of tag system, the bitag system and are the smallest known universal Turing machines with 5, 4, 3 and 2symbols respectively. O ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We present small polynomial time universal Turing machines with statesymbol pairs of (5, 5), (6, 4), (9, 3) and (18, 2). These machines simulate our new variant of tag system, the bitag system and are the smallest known universal Turing machines with 5, 4, 3 and 2symbols respectively. Our 5symbol machine uses the same number of instructions (22) as the smallest known universal Turing machine by Rogozhin. 1
The complexity of small universal Turing machines: a survey
 In SOFSEM 2012: Theory and Practice of Computer Science
, 2012
"... ..."
(Show Context)
Cellular Automata, Decidability and Phasespace
 FUNDAMENTA INFORMATICAE
"... Cellular automata have rich computational properties and, at the same time, provide plausible models of physicslike computation. We study decidability issues in the phasespace of these automata, construed as automatic structures over infinite words. In dimension one, slightly more than the first or ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Cellular automata have rich computational properties and, at the same time, provide plausible models of physicslike computation. We study decidability issues in the phasespace of these automata, construed as automatic structures over infinite words. In dimension one, slightly more than the first order theory is decidable but the addition of an orbit predicate results in undecidability. We comment on connections between this “what you see is what you get” model and the lack of natural intermediate degrees.