Catálogo de publicaciones - libros

We study the computational efficiency of recognizer P systems with active membranes without polarizations and without dissolution. The main result of the paper is the following: the polynomial computational complexity class associated with the class of recognizer P systems is equal to the standard complexity class .

This paper deals with a kind of hybrid system that is obtained by making cellular automata infinitely small. Each point on a continuous space is defined as a state transition system with a finite number of discrete states that changes its state according to its previous state and the states of its neighbors. Time is also defined as continuous, so that state transitions may propagate through the space continuously over time. Discrete state transitions can be made instantaneously, as in the case of ordinary hybrid systems. It turned out that even defining the global behaviors that satisfy local transition rules is not trivial. The framework that we propose here can be regarded as a framework for amorphous computing.

Discrete quantum cellular automata are cellular automata with reversible transition. This paper deals with 1d cellular automata with finite cell array and triplet local transition rules. We present the necessary condition of local transition rules for cellular automata to be reversible, and prove the reversibility of some cellular automata.

We present a theoretical model for self-assembling tiles with flexible branches motivated by DNA branched junction molecules. We encode an instance of a “problem” as a pot of such tiles, and a “solution” as an assembled complete complex without any free sticky ends (called ports), whose number of tiles is within predefined bounds. We develop an algebraic representation of this self-assembly process and use it to prove that this model of self-assembly precisely captures NP-computability when the number of tiles in the minimal complete complexes is bounded by a polynomial.

We propose a novel formulation of the firing squad synchronization problem. In this formulation we may use more than one general state and the general state to be used is determined by the boundary condition of the general. We show that the usual formulation and the new formulation yield different minimum firing times for some variations of the problem. Our results suggest that the new formulation is more suited for the general theory of the firing squad synchronization problem.

The computation in low-dimensional system is related to many long standing open problems. In this paper we show the universality of a one-dimensional iterative map defined by elementary functions. The computation in iterative maps have a number of connections with other unconventional models of computations. In particular, one-dimensional iterative maps can be simulated by a planar pseudo-billiard system. As a consequence of our main result we show that a planar pseudo-billiard system is not only can demonstrate a chaotic behaviour, but also has ability of universal computation.

The role played by parallelism in the theory of computation depends on the particular paradigm or computational environment considered, but its importance has been confirmed with the emergence of each novel computing technology. In this paper we study the implications of parallelism in quantum information theory and show that a parallel approach can make the difference between success and failure when trying to distinguish among (entangled) quantum states. A (perhaps surprising) consequence of this fact is the impossibility of constructing a Universal Computer, as defined herein.

We study computational complexity of the in certain classes of graph automata viewed as discrete dynamical systems. We prove that both exact and approximate counting of FPs in and (SDSs and SyDSs, respectively) are computationally intractable, even when each node is required to update according to a symmetric Boolean function. We also show that the problems of counting exactly the as well as all are in general intractable, as well. Moreover, exactly enumerating FPs or GEs remains hard even in some severely restricted cases, such as when the nodes of an SDS or SyDS use only two different symmetric Boolean update rules, and every node has a neighborhood size bounded by a small constant.

We describe a quantum complexity class which is contained in AWPP. This class has a compact and simple mathematical definition, involving only polynomial-time computable functions and a unitarity condition. It contains both Deutsch-Jozsa’s and Shor’s algorithm, while it’s relation to BQP is unknown. This shows that in the complexity class hierarchy, BQP is not an extraordinary isolated island, but has ”siblings” which as well can solve prime-factorization.

The firing squad synchronization problem has been studied extensively for more than 40 years [1-18]. The present authors are involved in research on firing squad synchronization algorithms on two-dimensional (2-D) rectangular cellular arrays. Several synchronization algorithms on 2-D arrays have been proposed, including Beyer [2], Grasselli [3], Kobayashi [4], Shinahr [10], Szwerinski [12] and Umeo et al. [13, 15]. To date, the smallest number of cell states for which an optimum-time synchronization algorithm has been developed is 14 for rectangular array, achieved by Umeo et al. [15]. In the present paper, we propose a new optimum-time synchronization algorithm that can synchronize any 2-D × rectangular arrays in + + (, ) –3 steps. We progressively reduce the number of internal states of each cellular automaton on rectangular arrays, achieving twelve states. This is the smallest number of states reported to date for synchronizing rectangular arrays in optimum-step.