A P system is a natural computing model inspired by information processing in cells and cellular membranes. We show that confluent P systems with active membranes solve in polynomial time exactly the class of problems PSPACE. Consequently, these P systems prove to be equivalent (up to a polynomial time reduction) to the alternating Turing machine or the PRAM computer. Similar results were achieved also with other models of natural computation, such as DNA computing or genetic algorithms. Our result, together with the previous observations, suggests that the class PSPACE provides a tight upper bound on the computational potential of biological information processing models.
Abstract. Self-assembly, the process by which objects autonomously come together to form complex structures, is omnipresent in the physical world. Recent experiments in self-assembly demonstrate its potential for the parallel creation of a large number of nanostructures, including possibly computers. A systematic study of self-assembly as a mathematical process has been initiated by L. Adleman and E. Winfree. The individual components are modeled as square tiles on the infinite two-dimensional plane. Each side of a tile is covered by a specific "glue," and two adjacent tiles will stick iff they have matching glues on their abutting edges. Tiles that stick to each other may form various two-dimensional "structures" such as squares and rectangles, or may cover the entire plane. In this paper we focus on a special type of structure, called a ribbon: a non-self-crossing rectilinear sequence of tiles on the plane, in which successive tiles are adjacent along an edge and abutting edges of consecutive tiles have matching glues. We prove that it is undecidable whether an arbitrary finite set of tiles with glues (infinite supply of each tile type available) can be used to assemble an infinite ribbon. While the problem can be proved undecidable using existing techniques if the ribbon is required to start with a given "seed" tile, our result settles the "unseeded" case, an open problem formerly known as the "unlimited infinite snake problem." The proof is based on a construction, due to R. Robinson, of a special set of tiles that allow only aperiodic tilings of the plane. This construction is used to create a special set of directed tiles (tiles with arrows painted on the top) with the "strong plane-filling property"-a variation of the "plane-filling property" previously defined by J. Kari. A construction of "sandwich" tiles is then used in conjunction with this special tile set, to reduce the well-known undecidable tiling problem to the problem of the existence of an infinite directed zipper (a special kind of ribbon). A "motif" construction is then introduced that allows one tile system to simulate another by using geometry to represent glues. Using motifs, the infinite directed zipper problem is reduced to the infinite ribbon problem, proving the latter undecidable. An immediate consequence of our result is the undecidability of the existence of arbitrarily large structures self-assembled using tiles from a given tile set. 1. Introduction. Self-assembly, the process by which objects autonomously come together to form complex structures, is omnipresent in the physical world. Atoms bind to each other by chemical bonds to form molecules, molecules may form crystals or macromolecules, and cells interact to form biological organisms. Recently it has been suggested that complex self-assembly processes will ultimately be used in circuit fabrication, nanorobotics, DNA computation, and amorphous computing. Indeed, in electronics, engineering, medicine, material science, manufacturing, and other disciplines, there is a continuou...
The input data for DNA computing must be encoded into the form of single or double DNA strands. As complementary parts of single strands can bind together forming a double-stranded DNA sequence, one has to impose restrictions on these sets of DNA words (languages) to prevent them from interacting in undesirable ways. We recall a list of known properties of DNA languages which are free of certain types of undesirable bonds. Then we introduce a general framework in which we can characterize each of these properties by a solution of a uniform formal language inequation. This characterization allows us among others to construct (i) a uniform algorithm deciding in polynomial time whether a given DNA language possesses any of the studied properties, and (ii) in many cases also an algorithm deciding whether a given DNA language is maximal with respect to the desired property.
The spiking neural P systems are a class of computing devices recently introduced as a bridge between spiking neural nets and membrane computing. In this paper we prove a series of normal forms for spiking neural P systems, concerning the regular expressions used in the firing rules, the delay between firing and spiking, the forgetting rules used, and the outdegree of the graph of synapses. In all cases, surprising simplifications are found, without losing the computational universality -sometimes at the price of (slightly) increasing other parameters which describe the complexity of these systems. c c c c © d d d d
Word and language operations on trajectories provide a general framework for the study of properties of sequential insertion and deletion operations. A trajectory gives a syntactical constraint on the scattered insertion (deletion) of a word into(from) another one, with an intuitive geometrical interpretation. Moreover, deletion on trajectories is an inverse of the shuffle on trajectories. These operations are a natural generalization of many binary word operations like catenation, quotient, insertion, deletion, shuffle, etc. Besides they were shown to be useful, e.g. in concurrent processes modelling and recently in biocomputing area.We begin with the study of algebraic properties of the deletion on trajectories. Then we focus on three standard decision problems concerning linear language equations with one variable, involving the above mentioned operations. We generalize previous results and obtain a sequence of new ones. Particularly, we characterize the class of binary word operations for which the validity of such a language equation is (un)decidable, for regular and context-free operands.
Abstract. We formalize the notion of a DNA hairpin secondary structure, examining its mathematical properties. Two related secondary structures are also investigated, taking into the account imperfect bonds (bulges, mismatches) and multiple hairpins. We characterize maximal sets of hairpin-forming DNA sequences, as well as hairpin-free ones. We study their algebraic properties and their computational complexity. Related polynomial-time algorithms deciding hairpin-freedom of regular sets are presented. Finally, effective methods for design of long hairpinfree DNA words are given.
A membrane system (P system) is a distributed computing model inspired by information processes in living cells. P systems previously provided new characterizations of a variety of complexity classes and their borderlines. Specifically, in tissue-like membrane systems, cell separation rules have been considered joint with communication rules of the form symport/antiport. On the one hand, only tractable problems can be efficiently solved by using cell separation and communication rules with length at most 2. On the other hand, an efficient and uniform solution to the SAT problem by using cell separation and communication rules with length at most 8 has been recently given.In this paper we improve the previous result by showing that the SAT problem can be solved by a family of tissue P systems with cell separation in linear time, by using communication rules with length at most 3. Thus, in the framework of tissue P systems with cell separation, we provide an optimal tractability borderline: passing from length 2 to 3 amounts to passing from non-efficiency to efficiency, assuming that P = NP.
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