Difference between revisions of "Verification of aTAM systems"

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Several "verification problems" (answering the question of whether or not a given system has a specific property) have been studied in relation to the aTAM, and characterized by their complexity.  Among them are:
 
Several "verification problems" (answering the question of whether or not a given system has a specific property) have been studied in relation to the aTAM, and characterized by their complexity.  Among them are:
  
−
\begin{enumerate}
+
     1) Does aTAM system $\mathcal{T}$ uniquely produce a given assembly?  This was shown to require time polynomial in the size of the assembly and tile set by Adleman, et al. in <ref name=ACGHKMR02 />.
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     \item Does aTAM system $\mathcal{T}$ uniquely produce a given assembly?  This was shown to require time polynomial in the size of the assembly and tile set by Adleman, et al. in <ref name=ACGHKMR02 />.
+
     2) Does aTAM system $\calT$ uniquely produce a given shape?  This was shown to be in co-NP-complete for temperature 1 by Cannon, et al. in \cite{Versus} and co-NP-complete for temperature 2 in <ref name=AGKS05g /> by Cheng, et al.
−
     \item Does aTAM system $\calT$ uniquely produce a given shape?  This was shown to be in co-NP-complete for temperature 1 by Cannon, et al. in \cite{Versus} and co-NP-complete for temperature 2 in <ref name=AGKS05g /> by Cheng, et al.
+
     3) Is a given assembly terminal in aTAM system $\mathcal{T}$?  This was shown to require time linear in the size of the assembly and tile set in <ref name=ACGHKMR02>
−
     \item Is a given assembly terminal in aTAM system $\mathcal{T}$?  This was shown to require time linear in the size of the assembly and tile set in <ref name=ACGHKMR02>
+
     4) Given an aTAM system $\calT$, does it produce a finite terminal assembly?  An infinite terminal assembly?  These were both shown to be uncomputable in <ref name=Versus />.
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     \item Given an aTAM system $\calT$, does it produce a finite terminal assembly?  An infinite terminal assembly?  These were both shown to be uncomputable in <ref name=Versus />.
 
 
\end{enumerate}
 
\end{enumerate}
  

Revision as of 20:24, 10 July 2013

Several "verification problems" (answering the question of whether or not a given system has a specific property) have been studied in relation to the aTAM, and characterized by their complexity. Among them are: 

   1) Does aTAM system \(\mathcal{T}\) uniquely produce a given assembly?  This was shown to require time polynomial in the size of the assembly and tile set by Adleman, et al. in [1].
   2) Does aTAM system \(\calT\) uniquely produce a given shape?  This was shown to be in co-NP-complete for temperature 1 by Cannon, et al. in \cite{Versus} and co-NP-complete for temperature 2 in [2] by Cheng, et al.
   3) Is a given assembly terminal in aTAM system \(\mathcal{T}\)?  This was shown to require time linear in the size of the assembly and tile set in Cite error: Closing </ref> missing for <ref> tag

[2]

[3]

[2]

[4]

</references>

  1. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named ACGHKMR02
  2. ↑ 2.0 2.1 2.2 Qi Cheng, Gagan Aggarwal, Michael H. Goldwasser, Ming-Yang Kao, Robert T. Schweller, Pablo Moisset de Espan\'es - Complexities for Generalized Models of Self-Assembly
    SIAM Journal on Computing 34:1493--1515,2005
    Bibtex
    Author : Qi Cheng, Gagan Aggarwal, Michael H. Goldwasser, Ming-Yang Kao, Robert T. Schweller, Pablo Moisset de Espan\'es
    Title : Complexities for Generalized Models of Self-Assembly
    In : SIAM Journal on Computing -
    Address :
    Date : 2005
    Cite error: Invalid <ref> tag; name "AGKS05g" defined multiple times with different content
  3. ↑ Leonard Adleman, Qi Cheng, Ashish Goel,, Ming-Deh Huang - Running time and program size for self-assembled squares
    pp. 740--748,2001
    Bibtex
    Author : Leonard Adleman, Qi Cheng, Ashish Goel,, Ming-Deh Huang
    Title : Running time and program size for self-assembled squares
    In : -
    Address :
    Date : 2001
  4. ↑ Sarah Cannon, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Matthew J. Patitz, Robert Schweller, Scott M. Summers, Andrew Winslow - Two Hands Are Better Than One (up to constant factors)
    Technical Report, Computing Research Repository (1201.1650),2012
    http://arxiv.org/abs/1201.1650
    Bibtex
    Author : Sarah Cannon, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Matthew J. Patitz, Robert Schweller, Scott M. Summers, Andrew Winslow
    Title : Two Hands Are Better Than One (up to constant factors)
    In : Technical Report, Computing Research Repository -
    Address :
    Date : 2012
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