Difference between revisions of "Verification of aTAM systems"
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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 />. | 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 />. | ||
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 <ref name=Versus /> and co-NP-complete for temperature 2 in <ref name=AGKS05g /> by Cheng, et al. | 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 <ref name=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> | + | 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 /> |
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 />. | 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 />. | ||
Revision as of 19:26, 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 [2] and co-NP-complete for temperature 2 in [3] 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 [1] 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 [2].
References
- ↑ 1.0 1.1
Leonard M. Adleman, Qi Cheng, Ashish Goel, Ming-Deh A. Huang, David Kempe, Pablo Moisset de Espan\'es, Paul W. K. Rothemund - Combinatorial optimization problems in self-assembly
- Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing pp. 23--32,2002
- BibtexAuthor : Leonard M. Adleman, Qi Cheng, Ashish Goel, Ming-Deh A. Huang, David Kempe, Pablo Moisset de Espan\'es, Paul W. K. Rothemund
Title : Combinatorial optimization problems in self-assembly
In : Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing -
Address :
Date : 2002
- ↑ 2.0 2.1
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
BibtexAuthor : 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
- ↑
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
- BibtexAuthor : 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
<ref>tag; name "AGKS05g" defined multiple times with different content
Cite error: <ref> tag with name "AdChGoHu01" defined in <references> is not used in prior text.
