Algorithmic applications of XPCR

Franco, Giuditta; Manca, Vincenzo

doi:10.1007/s11047-010-9199-8

Cited by 17 publications

(13 citation statements)

References 32 publications

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“…Note that a previous paper [3] uses the name "outfix-guided insertion" for the same operation. The current name is better consistent with terminology used in applications to site-directed mutagenesis [13,25]. The site-directed insertion operation is extended in the usual way for languages by setting…”

Section: Site-directed Insertionmentioning

confidence: 99%

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Site-directed insertion: Language equations and decision problems

Cho

Han

Salomaa

et al. 2019

Theoretical Computer Science

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Site-directed insertion is an overlapping insertion operation that can be viewed as analogous to the overlap assembly or chop operations that concatenate strings by overlapping a suffix and a prefix of the argument strings. We consider decision problems and language equations involving site-directed insertion. By relying on the tools provided by semantic shuffle on trajectories (M. Domaratzki, Developments in Language Theory 2004) we show that one variable equations involving site-directed insertion and regular constants can be solved algorithmically. We consider also maximal and minimal variants of the site-directed insertion operation and the nondeterministic state complexity of site-directed insertion.

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Section: Site-directed Insertionmentioning

confidence: 99%

“…The algorithmic applications of mutagenesis have been considered e.g. by Franco and Manca [13]. Contextual insertion/deletion systems in the study of molecular computing have been used, e.g.…”

Section: Introductionmentioning

confidence: 99%

Site-directed insertion: Language equations and decision problems

Cho

Han

Salomaa

et al. 2019

Theoretical Computer Science

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show abstract

“…The algorithmic applications of mutagenesis have been considered e.g. by Franco and Manca [10]. Contextual insertion/deletion systems in the study of molecular computing have been used, e.g.…”

Section: Introductionmentioning

confidence: 99%

Site-Directed Insertion: Decision Problems, Maximality and Minimality

Cho

Han

Salomaa

et al. 2018

Descriptional Complexity of Formal Systems

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Site-directed insertion is an overlapping insertion operation that can be viewed as analogous to the overlap assembly or chop operations that concatenate strings by overlapping a suffix and a prefix of the argument strings. We consider decision problems and language equations involving site-directed insertion. By relying on the tools provided by semantic shuffle on trajectories we show that one variable equations involving site-directed insertion and regular constants can be solved. We consider also maximal and minimal variants of the site-directed insertion operation.

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“…In the context of experimental DNA computing, overlap assembly was used in, e.g., [7,12,24,32] for the formation of combinatorial DNA or RNA libraries. Overlap assembly can also be viewed as modeling a special case of an experimental lab procedure called cross-pairing PCR, introduced in [15] and studied in, e.g., [13,14,16,27].…”

Section: Introductionmentioning

confidence: 99%

State Complexity of Overlap Assembly

Brzozowski

Kari

Bai

et al. 2018

Implementation and Application of Automata

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The state complexity of a regular language Lm is the number m of states in a minimal deterministic finite automaton (DFA) accepting Lm. The state complexity of a regularity-preserving binary operation on regular languages is defined as the maximal state complexity of the result of the operation where the two operands range over all languages of state complexities ≤ m and ≤ n, respectively. We find a tight upper bound on the state complexity of the binary operation overlap assembly on regular languages. This operation was introduced by Csuhaj-Varjú, Petre, and Vaszil to model the process of self-assembly of two linear DNA strands into a longer DNA strand, provided that their ends "overlap". We prove that the state complexity of the overlap assembly of languages Lm and Ln, where m ≥ 2 and n ≥ 1, is at most 2(m − 1)3 n−1 + 2 n . Moreover, for m ≥ 2 and n ≥ 3 there exist languages Lm and Ln over an alphabet of size n whose overlap assembly meets the upper bound and this bound cannot be met with smaller alphabets. Finally, we prove that m + n is a tight upper bound on the overlap assembly of unary languages, and that there are binary languages whose overlap assembly has exponential state complexity at least m(2 n−1 − 2) + 2. /15/B/ST6/00615.3 Informally, during a shuffle between two words with a trajectory over {0, 1, σ} + , the symbols of the trajectory are interpreted as follows: 0 (respectively 1) signifies that the corresponding letter from the first (respectively second) word is retained, and σ signifies that a letter from the first word is retained, provided it coincides with the corresponding letter in the second word.

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Algorithmic applications of XPCR

Cited by 17 publications

References 32 publications

Site-directed insertion: Language equations and decision problems

Site-directed insertion: Language equations and decision problems

Site-Directed Insertion: Decision Problems, Maximality and Minimality

State Complexity of Overlap Assembly

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