Shinnosuke Seki

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We investigate the role of nondeterminism in Winfree's abstract tile assembly model, which was conceived to model artificial molecular self-assembling systems constructed from DNA. By nondeterminism we do not mean a magical ability such as that possessed by a nondeterministic algorithm to search an exponential-size space in polynomial time. Rather, we study(More)
We investigate the power of (1-reversal) counter machines (finite automata with multiple counters, where each counter can ‘‘reverse’’ only once, i.e., once a counter decrements, it can no longer increment) and one-way multihead finite automata (finite automata with multiple one-way input heads) as a language acceptor. They can be non-deterministic as well(More)
When representing DNA molecules as words, it is necessary to take into account the fact that a word u encodes basically the same information as its Watson–Crick complement θ(u), where θ denotes the Watson–Crick complementarity function. Thus, an expression which involves only a word u and its complement can be still considered as a repeating sequence. In(More)
Pattern self-assembly tile set synthesis (Pats) is a combinatorial optimization problem which aim at minimizing a rectilinear tile assembly system (RTAS) that uniquely self-assembles a given rectangular pattern, and is known to be NP-hard. Pats gets practically meaningful when it is parameterized by a constant c such that any given pattern is guaranteed to(More)
We discuss theoretical aspects of the self-assembly of triangular tiles, in particular, right triangular tiles and equilateral triangular tiles, and the self-assembly of hexagonal tiles. We show that triangular tile assembly systems and square tile assembly systems cannot be simulated by each other in a non-trivial way. More precisely, there exists a(More)
Winfree’s abstract Tile Assembly Model is a model of molecular self-assembly of DNA complexes known as tiles, which float freely in solution and attach one at a time to a growing “seed” assembly based on specific binding sites on their four sides. We show that there is a polynomial-time algorithm that, given an $$n \times n$$ n × n square, finds the minimal(More)
In this paper, we introduce the notion of k-comma codes a proper generalization of the notion of comma-free codes. For a given positive integer k, a k-comma code is a set L over an alphabet Σ with the property that LΣL ∩ ΣLΣ = ∅. Informally, in a k-comma code, no codeword can be a subword of the catenation of two other codewords separated by a “comma” of(More)
We propose a novel theoretical biomolecular design to implement any Boolean circuit using the mechanism of DNA strand displacement. The design is scalable: all species of DNA strands can in principle be mixed and prepared in a single test tube, rather than requiring separate purification of each species, which is a barrier to large-scale synthesis. The(More)
a r t i c l e i n f o a b s t r a c t We study a generalization of the classical notions of bordered and unbordered words, motivated by biomolecular computing. DNA strands can be viewed as finite strings over the alphabet {A, G, C, T}, and are used in biomolecular computing to encode information. Due to the fact that A is Watson–Crick complementary to T and(More)