Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T08:59:46.975Z Has data issue: false hasContentIssue false
  • English
  • Français

Bidirectional string assembling systems

Published online by Cambridge University Press:  20 January 2014

Martin Kutrib  and
Matthias Wendlandt
Martin Kutrib
Affiliation:
Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany.. [email protected], [email protected]
Matthias Wendlandt
Affiliation:
Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany.. [email protected], [email protected]
Get access

Abstract

We introduce and investigate several variants of a bidirectional string assemblingsystem, which is a computational model that generates strings from copies of assemblyunits. The underlying mechanism is based on two-sided piecewise assembly of adouble-stranded sequence of symbols, where the upper and lower strand have to match. Thegenerative capacities and the relative power of the variants are our main interest. Inparticular, we prove that bidirectional string assembling system generate languages notrepresented as any finite concatenation of one-sided string assembling systems. The latterbuild an infinite, strict and tight concatenation hierarchy. Moreover, it is shown thateven the strongest system in question can only generate NL languages, while there areunary regular languages that cannot be derived. Furthermore, a finite strict hierarchywith respect to the different variants considered is shown and closure properties of thelanguages generated are presented.

Keywords

String assemblingdouble-stranded sequencesconcatenation hierarchystatelessmulti-head finite automataclosure properties
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 1: Non-Classical Models of Automata and Applications (NCMA 2012) , January 2014 , pp. 39 - 59
Copyright
© EDP Sciences 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

R. Freund, G. Păun, G. Rozenberg and A. Salomaa, Bidirectional sticker systems, in Pacific Symposium on Biocomputing (PSB 1998). World Scientific, Singapore (1998) 535–546.
Hartmanis, J., On non-determinancy in simple computing devices. Acta Inform. 1 (1972) 336–344. Google Scholar
Kari, L., Păun, G. and Rozenberg, G., Salomaa, A. and Yu, S., DNA computing, sticker systems, and universality. Acta Inform. 35 (1998) 401–420. Google Scholar
M. Kutrib and M. Wendlandt, Bidirectional string assembling systems, in vol. 290 of Non-Classical Models of Automata and Applications (NCMA 2011). [email protected]. Austrian Computer Society, Vienna (2012) 107–121.
Kutrib, M. and Wendlandt, M., String assembling systems. RAIRO: ITA 46 (2012) 593–613. Google Scholar
McNaughton, R., Algebraic decision procedures for local testability. Math. Systems Theory 8 (1974) 60–76. Google Scholar
Păun, G. and Rozenberg, G., Sticker systems. Theoret. Comput. Sci. 204 (1998) 183–203. Google Scholar
Post, E.L., A variant of a recursively unsolvable problem. Bull. AMS 52 (1946) 264–268. Google Scholar
Yao, A.C. and Rivest, R.L., k + 1 heads are better than k. J. ACM 25 (1978) 337–340. Google Scholar
Zalcstein, Y., Locally testable languages. J. Comput. System Sci. 6 (1972) 151–167. Google Scholar