Results 1  10
of
33
The complexity of theoremproving procedures
 In STOC
, 1971
"... It is shown that any recognition problem solved by a polynomial timebounded nondeterministic Turing machine can be “reduced ” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved determinist ..."
Abstract

Cited by 775 (4 self)
 Add to MetaCart
It is shown that any recognition problem solved by a polynomial timebounded nondeterministic Turing machine can be “reduced ” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved deterministically in polynomial time provided an oracle is available for solving the second. From this notion of reducible, polynomial degrees of difficulty are defined, and it is shown that the problem of determining tautologyhood has the same polynomial degree as the problem of determining whether the first of two given graphs is isomorphic to a subgraph of the second. Other examples are discussed. A method of measuring the complexity of proof procedures for the predicate calculus is introduced and discussed. Throughout this paper, a set of strings 1 means a set of strings on some fixed, large, finite alphabet Σ. This alphabet is large enough to include symbols for all sets described here. All Turing machines are deterministic recognition devices, unless the contrary is explicitly stated. 1 Tautologies and Polynomial ReReducibility. Let us fix a formalism for the propositional calculus in which formulas are written as strings on Σ. Since we will require infinitely many proposition symbols (atoms), each such symbol will consist of a member of Σ followed by a number in binary notation to distinguish that symbol. Thus a formula of length n can
Algorithmic SelfAssembly of DNA
, 1998
"... How can molecules compute? In his early studies of reversible computation, Bennett imagined an enzymatic Turing Machine which modified a heteropolymer (such as DNA) to perform computation with asymptotically low energy expenditures. Adleman's recent experimental demonstration of a DNA computation, ..."
Abstract

Cited by 104 (6 self)
 Add to MetaCart
How can molecules compute? In his early studies of reversible computation, Bennett imagined an enzymatic Turing Machine which modified a heteropolymer (such as DNA) to perform computation with asymptotically low energy expenditures. Adleman's recent experimental demonstration of a DNA computation, using an entirely different approach, has led to a wealth of ideas for how to build DNAbased computers in the laboratory, whose energy efficiency, information density, and parallelism may have potential to surpass conventional electronic computers for some purposes. In this thesis, I examine one mechanism used in all designs for DNAbased computer  the selfassembly of DNA by hybridization and formation of the double helix  and show that this mechanism alone in theory can perform universal computation. To do so, I borrow an important result in the mathematical theory of tiling: Wang showed how jigsawshaped tiles can be designed to simulate the operation of any Turing Machine. I propose...
Simulations of Computing by SelfAssembly
, 1998
"... Winfree (1996) proposed a Turinguniversal model of DNA selfassembly. In this abstract model, DNA doublecrossover molecules selfassemble to form an algorithmicallypatterned twodimensional lattice. Here, we develop a more realistic model based on the thermodynamics and kinetics of oligonucleo ..."
Abstract

Cited by 69 (15 self)
 Add to MetaCart
Winfree (1996) proposed a Turinguniversal model of DNA selfassembly. In this abstract model, DNA doublecrossover molecules selfassemble to form an algorithmicallypatterned twodimensional lattice. Here, we develop a more realistic model based on the thermodynamics and kinetics of oligonucleotide hydridization. Using a computer simulation, we investigate what physical factors influence the error rates, i.e., when the more realistic model deviates from the ideal of the abstract model. We find, in agreement with rules of thumb for crystal growth, that the lowest error rates occur at the melting temperature when crystal growth is slowest, and that error rates can be made arbitrarily low by decreasing concentration and increasing binding strengths. 1 Introduction Early work in DNA computing (Adleman 1994; Lipton 1995; Boneh et al. 1996; Ouyang et al. 1997) showed how computations can be accomplished by first creating a combinatorial library of DNA and then, through successiv...
The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2000
"... We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C², the two variable fragment of predicate logic with counting quantifiers, which yi ..."
Abstract

Cited by 56 (0 self)
 Add to MetaCart
We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C², the two variable fragment of predicate logic with counting quantifiers, which yields decidability in NExpTime. We show that this approach leads to an optimal solution for ALCQI, as ALCQI with cardinality restrictions has the same complexity as C² (NExpTimecomplete). In contrast, we show that for ALCQ, the problem can be solved in ExpTime. This result is obtained by a reduction of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals . Using the same reduction, we show that, for the extension of ALCQI with nominals, reasoning with general axioms is a NExpTimecomplete problem. Finally, we sharpen this result and show that pure concept satisfiability for A...
Proofreading tile sets: Error correction for algorithmic selfassembly
 In DNA Based Computers 9, volume 2943 of LNCS
, 2004
"... Abstract. For robust molecular implementation of tilebased algorithmic selfassembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (ε) can be reduced to an arbitrarily low ..."
Abstract

Cited by 48 (10 self)
 Add to MetaCart
Abstract. For robust molecular implementation of tilebased algorithmic selfassembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (ε) can be reduced to an arbitrarily low rate – but at the cost of reduced speed (r) for the selfassembly process. For tile sets directly implementing blocked cellular automata, it was shown that r ≈ βε 2 was optimal. Here, we show that an improved construction, which we refer to as proofreading tile sets, can in principle exploit the cooperativity of tile assembly reactions to dramatically improve the scaling behavior to r ≈ βε and better. This suggests that existing DNAbased molecular tile approaches may be improved to produce macroscopic algorithmic crystals with few errors. Generalizations and limitations of the proofreading tile set construction are discussed. 1
Experimental Progress in Computation by SelfAssembly of DNA Tilings
, 1999
"... Approaches to DNAbased computing by selfassembly require the use of DNA nanostructures, called tiles, that have efficient chemistries, expressive computational power, and convenient input and output (I/O) mechanisms. We have designed two new classes of DNA tiles, TAO and TAE, both of which contain ..."
Abstract

Cited by 27 (14 self)
 Add to MetaCart
Approaches to DNAbased computing by selfassembly require the use of DNA nanostructures, called tiles, that have efficient chemistries, expressive computational power, and convenient input and output (I/O) mechanisms. We have designed two new classes of DNA tiles, TAO and TAE, both of which contain three doublehelices linked by strand exchange. Structural analysis of a TAO molecule has shown that the molecule assembles efficiently from its four component strands. Here we demonstrate a novel method for I/O whereby multiple tiles assemble around a singlestranded (input) scaffold strand. Computation by tiling theoretically results in the formation of structures that contain singlestranded (output) reported strands, which can then be isolated for subsequent steps of computation if necessary. We illustrate the advantages of TAO and TAE designs by detailing two examples of massively parallel arithmetic: construction of complete XOR and addition tables by linear assemblies of DNA t...
The Decision Problem for Standard Classes
 Journal of Symbolic Logic
, 1976
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
Abstract

Cited by 16 (1 self)
 Add to MetaCart
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Toward Reliable Algorithmic SelfAssembly of DNA Tiles: A FixedWidth Cellular Automaton Pattern NANO LETTERS
, 2007
"... Bottomup fabrication of nanoscale structures relies on chemical processes to direct selfassembly. The complexity, precision, and yield achievable by a onepot reaction are limited by our ability to encode assembly instructions into the molecules themselves. Nucleic acids provide a platform for inv ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
Bottomup fabrication of nanoscale structures relies on chemical processes to direct selfassembly. The complexity, precision, and yield achievable by a onepot reaction are limited by our ability to encode assembly instructions into the molecules themselves. Nucleic acids provide a platform for investigating these issues, as molecular structure and intramolecular interactions can encode growth rules. Here, we use DNA tiles and DNA origami to grow crystals containing a cellular automaton pattern. In a onepot annealing reaction, 250 DNA strands first assemble into a set of 10 free tile types and a seed structure, then the free tiles grow algorithmically from the seed according to the automaton rules. In our experiments, crystals grew to ∼300 nm long, containing ∼300 tiles with an initial assembly error rate of ∼1.4 % per tile. This work provides evidence that programmable molecular selfassembly may be sufficient to create a wide range of complex objects in onepot reactions. The WatsonsCrick complementarity of DNA molecules allows one to design not only simple doublestranded helices but also complicated woven structures consisting of many DNA strands. 1 Welldesigned structures will selfassemble during annealing from a high initial temperature at which point all molecules are singlestranded to a lower final
Resets vs. Aborts in Linear Temporal Logic
, 2003
"... There has been a major emphasis recently in the semiconductor industry on designing industrialstrength property specification languages. Two major languages are ForSpec and Sugar 2.0, which are both extensions of Pnueli's LTL. Both ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
There has been a major emphasis recently in the semiconductor industry on designing industrialstrength property specification languages. Two major languages are ForSpec and Sugar 2.0, which are both extensions of Pnueli's LTL. Both
Description Logics with Symbolic Number Restrictions
 PROCEEDINGS OF THE TWELFTH EUROPEAN CONFERENCE ON ARTIFICIAL INTELLIGENCE (ECAI96
, 1996
"... ..."