# String Assembling Systems

Martin Kutrib; Matthias Wendlandt

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2012)

- Volume: 46, Issue: 4, page 593-613
- ISSN: 0988-3754

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topKutrib, Martin, and Wendlandt, Matthias. "String Assembling Systems." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 46.4 (2012): 593-613. <http://eudml.org/doc/272991>.

@article{Kutrib2012,

abstract = {We introduce and investigate string assembling systems which form a computational model that generates strings from copies out of a finite set of assembly units. The underlying mechanism is based on piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. The generation is additionally controlled by the requirement that the first symbol of a unit has to be the same as the last symbol of the strand generated so far, as well as by the distinction of assembly units that may appear at the beginning, during, and at the end of the assembling process. We start to explore the generative capacity of string assembling systems. In particular, we prove that any such system can be simulated by some nondeterministic one-way two-head finite automaton, while the stateless version of the two-head finite automaton marks to some extent a lower bound for the generative capacity. Moreover, we obtain several incomparability and undecidability results as well as (non-)closure properties, and present questions for further investigations.},

author = {Kutrib, Martin, Wendlandt, Matthias},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {string assembling; double-stranded sequences; stateless; two-head finite automata; decidability; closure properties; string assembling systems; double-stranded sequence of symbols; piecewise assembly; nondeterministic one-way two-head finite automata},

language = {eng},

number = {4},

pages = {593-613},

publisher = {EDP-Sciences},

title = {String Assembling Systems},

url = {http://eudml.org/doc/272991},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Kutrib, Martin

AU - Wendlandt, Matthias

TI - String Assembling Systems

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2012

PB - EDP-Sciences

VL - 46

IS - 4

SP - 593

EP - 613

AB - We introduce and investigate string assembling systems which form a computational model that generates strings from copies out of a finite set of assembly units. The underlying mechanism is based on piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. The generation is additionally controlled by the requirement that the first symbol of a unit has to be the same as the last symbol of the strand generated so far, as well as by the distinction of assembly units that may appear at the beginning, during, and at the end of the assembling process. We start to explore the generative capacity of string assembling systems. In particular, we prove that any such system can be simulated by some nondeterministic one-way two-head finite automaton, while the stateless version of the two-head finite automaton marks to some extent a lower bound for the generative capacity. Moreover, we obtain several incomparability and undecidability results as well as (non-)closure properties, and present questions for further investigations.

LA - eng

KW - string assembling; double-stranded sequences; stateless; two-head finite automata; decidability; closure properties; string assembling systems; double-stranded sequence of symbols; piecewise assembly; nondeterministic one-way two-head finite automata

UR - http://eudml.org/doc/272991

ER -

## References

top- [1] R. Freund, G. Păun, G. Rozenberg and A. Salomaa, Bidirectional sticker systems, in Pacific Symposium on Biocomputing (PSB). World Scientific, Singapore (1998) 535–546.
- [2] J. Hartmanis, On non-determinancy in simple computing devices. Acta Inf.1 (1972) 336–344. Zbl0229.68014MR317582
- [3] M. Holzer, M. Kutrib and A. Malcher, Multi-head finite automata : origins and directions. Theoret. Comput. Sci.412 (2011) 83–96. Zbl1207.68188MR2779447
- [4] O.H. Ibarra, A note on semilinear sets and bounded-reversal multihead pushdown automata. Inf. Process. Lett.3 (1974) 25–28. Zbl0294.68019MR347142
- [5] O.H. Ibarra, J. Karhumäki and A. Okhotin, On stateless multihead automata : hierarchies and the emptiness problem. Theoret. Comput. Sci.411 (2009) 581–593. Zbl1184.68316MR2590137
- [6] L. Kari, G. Păun, G. Rozenberg, A. Salomaa and S. Yu, DNA computing, sticker systems, and universality. Acta Inf.35 (1998) 401–420. Zbl0904.68127MR1623221
- [7] R. McNaughton, Algebraic decision procedures for local testability. Math. Syst. Theory8 (1974) 60–76. Zbl0287.02022MR392544
- [8] W.F. Ogden, A helpful result for proving inherent ambiguity. Math. Syst. Theory2 (1968) 191–194. Zbl0175.27802MR233645
- [9] C.H. Papadimitriou, Computational Complexity. Addison-Wesley (1994) Zbl0833.68049MR1251285
- [10] G. Păun and G. Rozenberg, Sticker systems. Theoret. Comput. Sci.204 (1998) 183–203. Zbl0908.68058MR1637532
- [11] E.L. Post, A variant of a recursively unsolvable problem. Bull. AMS52 (1946) 264–268. Zbl0063.06329MR15343
- [12] A. Salomaa, Formal Languages. Academic Press, New York (1973) Zbl0686.68003MR438755
- [13] L. Yang, Z. Dang and O.H. Ibarra, On stateless automata and P systems, in Workshop on Automata for Cellular and Molecular Computing. MTA SZTAKI (2007) 144–157. Zbl1175.68180MR2454747
- [14] A.C. Yao and R.L. Rivest, k + 1 heads are better than k. J. ACM 25 (1978) 337–340. Zbl0372.68017MR483728
- [15] Y. Zalcstein, Locally testable languages. J. Comput. Syst. Sci.6 (1972) 151–167. Zbl0242.68038MR307538